research article global chassis control system using
TRANSCRIPT
Research ArticleGlobal Chassis Control System Using SuspensionSteering and Braking Subsystems
Carlos A Vivas-Lopez1 Juan C Tudon-Martinez2
Diana Hernandez-Alcantara1 and Ruben Morales-Menendez1
1Tecnologico de Monterrey School of Engineering and Sciences Avenida E Garza Sada No 2501 64849 Monterrey NL Mexico2Universidad de Monterrey Avenida Ignacio Morones Prieto No 4500 66238 San Pedro Garza Garcıa NL Mexico
Correspondence should be addressed to Carlos A Vivas-Lopez a00794204itesmmx
Received 4 August 2015 Accepted 21 October 2015
Academic Editor Xinggang Yan
Copyright copy 2015 Carlos A Vivas-Lopez et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
AnovelGlobal Chassis Control (GCC) systembased on amultilayer architecturewith three levels top decision layermiddle controllayer and bottom system layer is presented The main contribution of this work is the development of a data-based classificationand coordination algorithm into a single control problem Based on a clustering technique the decision layer classifies thecurrent driving condition Afterwards heuristic rules are used to coordinate the performance of the considered vehicle subsystems(suspension steering and braking) using local controllers hosted in the control layer The control allocation system uses fuzzylogic controllers The performance of the proposed GCC system was evaluated under different standard tests Simulation resultsillustrate the effectiveness of the proposed system compared to an uncontrolled vehicle and a vehicle with a noncoordinated controlThe proposed system decreases by 14 the braking distance in the hard braking test with respect to the uncontrolled vehicle theroll and yaw movements are reduced by 10 and 12 respectively in the Double Line Change test and the oscillations caused byload transfer are reduced by 7 in a cornering situation
1 Introduction
A road vehicle has a conjunction of interconnected subsys-tems such as brakes steering suspension engine and tireswhich is difficult to be controlled [1]These subsystems inter-act among them modifying their individual behavior andconsequently the overall performance of the vehicle theseinteractions could cause negative effects For example theway the suspension system is tuned can dramatically affectthe performance of the steering system a soft suspensionaffects the tire grip decreasing the ability of the vehicle tosteer if the suspension is too stiff tires will hop causing loss ofcontrol Additionally all vehicle subsystems have a nonlinearbehavior making their coordination a complex task
Normally each vehicle subsystem has an independentcontrol system to accomplish a specific objective For exam-ple the brake system has the Antilock Braking System (ABS)to prevent tires from locking during hard braking avoidingskidding and loss of control [2] Also it has the Electronic
Stability Control (ESC) which creates a turning momentusing the brakes to prevent loss of control Both controlsystems have conflicting principles the ABS releases thebrake pressure whereas the ESC generates an additional oneTable 1 summarizes the used acronyms in this document
Studies in global trends aim towards achieving intelligentvehicles in upcoming years [3]These vehicles are required tomeet present and future state regulations related to efficiencyautonomy ecology safety and comfort [4] Particularly theglobal automotive industry is paying special attention tosafety systems that guarantee the integrity of occupantspedestrians andor other drivers when an accident occursEven the newest safety features (Collision Mitigation or LineKeeping Systems) are oriented to prevent possible dangeroussituations themain topic of research refers to the systems thatreact against a dangerous situation [5]
These opportunities demand more of the actual VehicleControl Systems (VCS) The standard solutions was to inde-pendently treat any new objective by adding a new VCS
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 263424 18 pageshttpdxdoiorg1011552015263424
2 Mathematical Problems in Engineering
Table 1 Acronyms definition
Acronyms DescriptionABS Antilock Braking SystemAS Active SteeringAFS Active Front SteeringCDC Continuous Damping ControllerDC Decentralized ControllersDL Decision LogicDLC Double Line ChangeDoF Degree of FreedomDBC Data-Based ControllerEMB Electromechanical BrakingESC Electronic Stability ControlECU Electronic Control UnitFH Fish HookFCS Force control systemFL Fuzzy logicFIS Fuzzy Inference SystemGCC Global Chassis ControlIVDC Integrated Vehicle Dynamics Control119896-NN 119896-Nearest NeighborLPV Linear parameter varyingMBC Model-Based ControllerMF Membership FunctionPC Principal ComponentPCA Principal Component AnalysisRMS Root Mean SquareROC Receiver operating characteristicSA SemiactiveSAS Semiactive suspensionSAP Suspension Adjustment PlaneSCS Steering control systemSISO Single-Input Single-OutputSMC Sliding Mode ControlTRC Traction ControlUC UncontrolledVCS Vehicle Control SystemVDC Vehicle Dynamics Control4WIB Four-Wheel Independent Braking4WS Four-Wheel Steering
This parallel architecture can lead to some drawbacks forexample a VCS is normally designed to seek a specific goalbut when it interacts with other VCS the result could degradethe global performance overruling the original objectives ofthe individual controllers due to inherent coupling effectsSince those controllers have to work simultaneously theyhave their own information system and Electronic ControlUnit (ECU) demanding more costs and space that is vehicleinfrastructure and complexity increase [6]
The concept of GCC also called Integrated VehicleDynamics Control (IVDC) proposes the coordinated integra-tion of those different VCS to pursuit a common goal [7]
This integration offers (1) the ability to simultaneously controlvarious subsystems (2) the ability to coordinate the actionsof individual subsystems regarding a general goal [8] and (3)the ability to share information from sensors and actuators(also functions) [9]
This concept has been investigated in the literatureThe approaches can be differentiated regarding the numberof Degrees of Freedom (DoF) in which they act (verticallongitudinal or lateral dynamics) Some cases have beenstudied as functional integrations (specific objective or singleDoF) In [10] an integration of the braking and Semiactive(SA) suspension system is proposed to decrease brakingdistance in an emergency maneuver but in this case thereis no coordination An integration of active suspension andbraking is proposed in [11] to prevent a rollover situationusing a Linear Parameter-Varying (LPV) controller driven bya scheduling parameter related to load transfer the controlleris highly model dependent
Most of the research of this topic lays in the case ofmultipurpose integration (ie multiple DoF) An integrationof steering and braking to enhance horizontal dynamicsusing robust control is proposed in [12] however the coor-dination algorithm and controller synthesis are not clearIn [13] the authors proposed a controller based on inverse-model dynamics to generate the desired control commandsfor braking and steering subsystems the method is highlydependent in an accurate model of the system and sensitiveto modeled dynamics In [14] an integration of steering andbraking systems is proposed The goal is to maintain anoptimum tire forces using Sliding Mode Control (SMC) Ituses an optimization procedure to compute the optimumforce distribution among the tires In [15] a control strategyto improve the horizontal dynamics involving the brakingand steering subsystems is proposed it uses an optimizationprocedure to allocate the desired yaw moment but the costfunctions have to be modified depending on the situationIn [16] a loss prevention control system is introduced usingthe braking and steering subsystems this strategy relies onphysical infrastructure in the road to calculate the referencesignals which nowadays is not available in most roads
Only few works have been published on full dynamicsintegration (able to act in the vertical longitudinal and lateraldynamics) In [17] an integration of an active suspension a4-Wheel Steering (4WS) and a drivingbraking force controlusing Traction Control (TRC) and ABS is proposed but thecoordination algorithm is not clear and the use of activesuspension and 4WS is expensive In [1] a strategy usingthe differential braking for horizontal dynamics and theactive suspension for vertical is proposed this method hasto calculate the control command of each sampling time byoptimization this demands a lot of computational resourcesThe authors in [18] divide the problem they treated verticaland horizontal dynamics separately For vertical dynamics itdetermines the desired force for each damper based on theLPV framework but its performance is fixed by design Forhorizontal dynamics it uses a gain scheduling parameter todecide when to apply braking control or a combination ofsteering with braking control It defines some driving con-ditions (ie stable or unstable) but they are limitedThe work
Mathematical Problems in Engineering 3
of [19] proposed a control architecture capable of identifyingthe actual driving situation based on the estimated situationthe control mode of each subsystem is changed Even whenthis method is capable of reacting against different situationsit does not consider the switching implications in the controlsystem which could lead to unexpected behaviors In [20] acontrol systembased on LPV is proposed in this case all threedirections are simultaneously controlled using two varyingparameters one for suspension-steering and another forbraking however the controller operates under predefinedconditions without depending on the driving situation
Although there are interesting results they do not includethe full dynamics integration others are strongly model-dependent or they are robust to some uncertainty whichcould generate conservatism issues Furthermore some ofthem are not easy to implement in on-board Vehicle Dynam-ics Controllers
The main contribution of this proposal lays in a newGCC system based on a discrimination of the operationconditions of the vehicle The strategy architecture is asupervisory decentralized control to improve flexibility andmodularity [21] The goal is to identify the current drivingsituation based on vehicle measurements using clusteringmethods [22] then the control modes of each subsystem arecoordinated to ensure the best global performanceThe coor-dination includes three subsystems SAS AFS and 4-WheelIndependent Braking (4WIB) a full dynamics integrationTheeffectiveness of the new strategy was validated in CarSim
The paper is organized as follows Section 2 describesthe problem Section 3 presents the GCC architecture andmodules in detail Section 4 discusses the results based ona case study Section 5 concludes the research and proposesfuture work Tables 2 and 3 summarize all the used variablesin this work
2 Problem Description
Passenger vehicles are equipped with a wide diversity of on-board VCS and those focused on the management of thedynamical behavior of the vehicle are calledVehicle DynamicsControllers (VDC) for example Continuous Damping Con-troller (CDC) and Electronic Stability Control (ESC) Usuallyeach VDC operates in a set of DoF defined by the vehiclereference system Figure 1 the most important variables foreach vehicle motion are as follows
(i) Vertical dynamics refers to the movements that affectmainly the comfort of the passengers (vibrationreductions) the important variables are pitch (turnaround 119910-axis 120601) roll (turn around 119909-axis 120579) andvertical acceleration () in the Chassis and wheels
(ii) Lateral dynamics refers mainly to the stability andhandling (safety) of the vehicle the important vari-ables are lateral displacement (119910) side slip angle (120573)and yaw (turn around 119911-axis 120595)
(iii) Longitudinal dynamics refers to vehicle stability(safety) and its performance (power train) the impor-tant variables are longitudinal velocity (119881
119909) wheel
rotational velocity (120596) and tire slip ratio (120582)
Table 2 Modeling variables description
Variable Description Units
1198861 1198862
Hysteresis coefficients related todisplacement and velocity sm 1m
119888119901 Viscous damping coefficient Nsm
119891brake 119891steerCut-off frequency of the actuatordynamics Hz
119891119888
Force coefficient due tomanipulation NV
119865119863 Damper force N
119865SA Semiactive damper force N119896119901 Stiffness coefficient Nm
119897 Vehicle wheel base m119898119904119898us Sprungunsprung mass kg
119879+
119887 120575+ Actuator output MPa deg
119879lowast
119887 120575lowast Actuator controller output MPa deg
119881119909 V119909119894119895
Vehicletire longitudinal vel ms
119909 119910 119911 Longitudinallateralverticaldisplacement m
Longitudinallateralverticalvelocity ms
Longitudinallateralverticalacceleration ms2
119911def def Damper deflection and velocity m ms
119911119903 119911119904 119911us
Roadsprung massunsprungmass vertical position m
120573 Vehicle side slip angle deg120575 Steering wheel angle deg120575driver Driverrsquos steering command deg120582 Tire slip ratio mdash120592 Damper manipulation V120601 120579 120595 Pitchrollyaw angle deg Pitchrollyaw rate degs119889
Desired yaw rate degs120596 Rotational speed of the tires rads
A VDC can have one ormore of these three control goalsstability handling or vibration mitigation
(1) Stability when a vehicle has crossed its handlinglimits and tires lost their grip it is said that the vehiclehas become unstable and cannot be controlled by theaction of the driver only here the main objective isto recover the driverrsquos control to guarantee passengerssafety
(2) Handling it refers to how well a vehicle can achievecornering at high speeds this condition is related tothe safety characteristic of the vehicle
(3) Vibration mitigation it refers to the comfort that thepassengers will experience during riding this consistsin the limitation of the unpleasant vibrations andmovements caused by road irregularities also road-holding is considered that is vibration reduction inthe unsprung mass at high vehicle velocities
4 Mathematical Problems in Engineering
Table 3 Algorithms variables description
Variable Description119886119898
Actuation vector
119886119906
Gain of the allocationcoordination
119886119906susp
119886119906braking
119886119906steer
Suspensionbrakingsteeringcoordination gain
119888min 119888maxSoftesthardest dampingcoefficient
119862119894
Driving class
Con119894119896
Contribution index of the 119894thvariable in a 119896 driving situation
CS119896
Minimal set of importantvariables for a driving situation
119889(119909 119910119895) Euclidian distance
119863119862
Driving situation119890(120573) 119890() Slip angleyaw rate error119866ABS ABS braking gainIS Initial set of vehicle variables119896119894
Number of nearest neighbors119897119896
First 119897 principal components119898 Number of measurements
MS Minimal set of importantvariables for all driving situations
119872119911
Corrective yaw moment
119899 119899lowast Originalreduced number ofvariables
119903 Number of driving conditions
119904119904
Driving situation criticalcondition
119904119894
Driving situation importance119905crit Situation changing waiting time119905con Variable contribution threshold119879driver Driver braking torque
119879ESC119903 119879ESC119897Rightleft corrective brakingpressure
119879119866
Pressure gain119905119899119910
Noise variance threshold
119906119888 119906lowast119888
Allocatedcoordinated controlleroutput
119880|rh 119880|conf
Full suspensionroad-holdingcomfortsuspension command
119906susp119894119895 119880lowast
suspSingle cornerfull suspensioncontrol command
119909 Data point
119883119894passive
119883119894controlled
Passivecontrolled 119894thperformance variable
119894119896
Residual data point of the 119894thmeasure in a 119896 driving situation
120573119889 119889
Desired vehicle slip angleyawrate
120575AFS Corrective steering angle
120575lowast
steering wheel 120575lowast
wheelsSteering wheelwheelsdirectional angle
Table 3 Continued
Variable Description120582crit Critical tire slip ratio
120590119909119894119896
Variance of the 119894th variable in a 119896
driving situationR119896 Covariance matrix
X119896 Data matrix of 119899 variables
P119896 P119896
Principalresiduals componentsmatrix
T119896 T119896 Principalresidual scores matrix
X119896 X119896
Principalresidual transformedvariables
119894 Variable number119896 Driving situation119895 Number of neighborhoods
ω λθ
ψ
X
Y
Z
υβ
120601
Figure 1 Vehicle reference system and important dynamical vari-ables
To develop a full dynamics integration in the vehicle itis necessary to controlcoordinate the different subsystemssimultaneously [17] Usually the selected subsystems are (1)Active Front Steering (2) Independent Braking and (3)SAS Another requirement is the use of different controllersacting in those subsystems depending on the current drivingsituation [23] but this feature leads to switching thosecontrollers which could cause unstability [24]
In road vehicles the inherent coupling effects amongtheir subsystems impact the overall performance of thevehicle The coupled effects plus the issues that come withthe interactions of different independent control systemsincrease the complexity of controlling the vehicle dynamics
The above conditions can be handled with integratedcontrol strategies where subsystems and control actions areefficiently coordinated Such strategies avoid contradictionsin the control goals of the subsystems to obtain a better globalperformance from them at each situation [25] Model-basedcontrol approaches represent a complex and unpracticalsolution considering the vehicle as a highly nonlinear systemOn the other hand Data-Based Controllers could representa reliable option in practice assuming that the vehicle
Mathematical Problems in Engineering 5
DBC
MBCPassive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
DBCMBC
Passive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 2 Comparison of MBC and DBC approaches
dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867
infincontroller designed
to minimize the vertical acceleration (119904) and the pitch
(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms
From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller
Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic
3 Global Chassis Control
Thearchitecture of theGCC system is divided into threemainlayers Figure 3
(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode
(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers
(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors
This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces
Dec
ision
laye
rC
ontro
lla
yer
Phys
ical
laye
r
Info
rmat
ion
bus
FCS ABS SCS
Local controllers
Control allocation
Classification algorithm
Decision logic
Subsystems
Sens
ors
Control command(outer loop)
Control objective
Driving situation
Control command(inner loop)
Figure 3 GCC architecture hierarchical approach
a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem
31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation
311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
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2 Mathematical Problems in Engineering
Table 1 Acronyms definition
Acronyms DescriptionABS Antilock Braking SystemAS Active SteeringAFS Active Front SteeringCDC Continuous Damping ControllerDC Decentralized ControllersDL Decision LogicDLC Double Line ChangeDoF Degree of FreedomDBC Data-Based ControllerEMB Electromechanical BrakingESC Electronic Stability ControlECU Electronic Control UnitFH Fish HookFCS Force control systemFL Fuzzy logicFIS Fuzzy Inference SystemGCC Global Chassis ControlIVDC Integrated Vehicle Dynamics Control119896-NN 119896-Nearest NeighborLPV Linear parameter varyingMBC Model-Based ControllerMF Membership FunctionPC Principal ComponentPCA Principal Component AnalysisRMS Root Mean SquareROC Receiver operating characteristicSA SemiactiveSAS Semiactive suspensionSAP Suspension Adjustment PlaneSCS Steering control systemSISO Single-Input Single-OutputSMC Sliding Mode ControlTRC Traction ControlUC UncontrolledVCS Vehicle Control SystemVDC Vehicle Dynamics Control4WIB Four-Wheel Independent Braking4WS Four-Wheel Steering
This parallel architecture can lead to some drawbacks forexample a VCS is normally designed to seek a specific goalbut when it interacts with other VCS the result could degradethe global performance overruling the original objectives ofthe individual controllers due to inherent coupling effectsSince those controllers have to work simultaneously theyhave their own information system and Electronic ControlUnit (ECU) demanding more costs and space that is vehicleinfrastructure and complexity increase [6]
The concept of GCC also called Integrated VehicleDynamics Control (IVDC) proposes the coordinated integra-tion of those different VCS to pursuit a common goal [7]
This integration offers (1) the ability to simultaneously controlvarious subsystems (2) the ability to coordinate the actionsof individual subsystems regarding a general goal [8] and (3)the ability to share information from sensors and actuators(also functions) [9]
This concept has been investigated in the literatureThe approaches can be differentiated regarding the numberof Degrees of Freedom (DoF) in which they act (verticallongitudinal or lateral dynamics) Some cases have beenstudied as functional integrations (specific objective or singleDoF) In [10] an integration of the braking and Semiactive(SA) suspension system is proposed to decrease brakingdistance in an emergency maneuver but in this case thereis no coordination An integration of active suspension andbraking is proposed in [11] to prevent a rollover situationusing a Linear Parameter-Varying (LPV) controller driven bya scheduling parameter related to load transfer the controlleris highly model dependent
Most of the research of this topic lays in the case ofmultipurpose integration (ie multiple DoF) An integrationof steering and braking to enhance horizontal dynamicsusing robust control is proposed in [12] however the coor-dination algorithm and controller synthesis are not clearIn [13] the authors proposed a controller based on inverse-model dynamics to generate the desired control commandsfor braking and steering subsystems the method is highlydependent in an accurate model of the system and sensitiveto modeled dynamics In [14] an integration of steering andbraking systems is proposed The goal is to maintain anoptimum tire forces using Sliding Mode Control (SMC) Ituses an optimization procedure to compute the optimumforce distribution among the tires In [15] a control strategyto improve the horizontal dynamics involving the brakingand steering subsystems is proposed it uses an optimizationprocedure to allocate the desired yaw moment but the costfunctions have to be modified depending on the situationIn [16] a loss prevention control system is introduced usingthe braking and steering subsystems this strategy relies onphysical infrastructure in the road to calculate the referencesignals which nowadays is not available in most roads
Only few works have been published on full dynamicsintegration (able to act in the vertical longitudinal and lateraldynamics) In [17] an integration of an active suspension a4-Wheel Steering (4WS) and a drivingbraking force controlusing Traction Control (TRC) and ABS is proposed but thecoordination algorithm is not clear and the use of activesuspension and 4WS is expensive In [1] a strategy usingthe differential braking for horizontal dynamics and theactive suspension for vertical is proposed this method hasto calculate the control command of each sampling time byoptimization this demands a lot of computational resourcesThe authors in [18] divide the problem they treated verticaland horizontal dynamics separately For vertical dynamics itdetermines the desired force for each damper based on theLPV framework but its performance is fixed by design Forhorizontal dynamics it uses a gain scheduling parameter todecide when to apply braking control or a combination ofsteering with braking control It defines some driving con-ditions (ie stable or unstable) but they are limitedThe work
Mathematical Problems in Engineering 3
of [19] proposed a control architecture capable of identifyingthe actual driving situation based on the estimated situationthe control mode of each subsystem is changed Even whenthis method is capable of reacting against different situationsit does not consider the switching implications in the controlsystem which could lead to unexpected behaviors In [20] acontrol systembased on LPV is proposed in this case all threedirections are simultaneously controlled using two varyingparameters one for suspension-steering and another forbraking however the controller operates under predefinedconditions without depending on the driving situation
Although there are interesting results they do not includethe full dynamics integration others are strongly model-dependent or they are robust to some uncertainty whichcould generate conservatism issues Furthermore some ofthem are not easy to implement in on-board Vehicle Dynam-ics Controllers
The main contribution of this proposal lays in a newGCC system based on a discrimination of the operationconditions of the vehicle The strategy architecture is asupervisory decentralized control to improve flexibility andmodularity [21] The goal is to identify the current drivingsituation based on vehicle measurements using clusteringmethods [22] then the control modes of each subsystem arecoordinated to ensure the best global performanceThe coor-dination includes three subsystems SAS AFS and 4-WheelIndependent Braking (4WIB) a full dynamics integrationTheeffectiveness of the new strategy was validated in CarSim
The paper is organized as follows Section 2 describesthe problem Section 3 presents the GCC architecture andmodules in detail Section 4 discusses the results based ona case study Section 5 concludes the research and proposesfuture work Tables 2 and 3 summarize all the used variablesin this work
2 Problem Description
Passenger vehicles are equipped with a wide diversity of on-board VCS and those focused on the management of thedynamical behavior of the vehicle are calledVehicle DynamicsControllers (VDC) for example Continuous Damping Con-troller (CDC) and Electronic Stability Control (ESC) Usuallyeach VDC operates in a set of DoF defined by the vehiclereference system Figure 1 the most important variables foreach vehicle motion are as follows
(i) Vertical dynamics refers to the movements that affectmainly the comfort of the passengers (vibrationreductions) the important variables are pitch (turnaround 119910-axis 120601) roll (turn around 119909-axis 120579) andvertical acceleration () in the Chassis and wheels
(ii) Lateral dynamics refers mainly to the stability andhandling (safety) of the vehicle the important vari-ables are lateral displacement (119910) side slip angle (120573)and yaw (turn around 119911-axis 120595)
(iii) Longitudinal dynamics refers to vehicle stability(safety) and its performance (power train) the impor-tant variables are longitudinal velocity (119881
119909) wheel
rotational velocity (120596) and tire slip ratio (120582)
Table 2 Modeling variables description
Variable Description Units
1198861 1198862
Hysteresis coefficients related todisplacement and velocity sm 1m
119888119901 Viscous damping coefficient Nsm
119891brake 119891steerCut-off frequency of the actuatordynamics Hz
119891119888
Force coefficient due tomanipulation NV
119865119863 Damper force N
119865SA Semiactive damper force N119896119901 Stiffness coefficient Nm
119897 Vehicle wheel base m119898119904119898us Sprungunsprung mass kg
119879+
119887 120575+ Actuator output MPa deg
119879lowast
119887 120575lowast Actuator controller output MPa deg
119881119909 V119909119894119895
Vehicletire longitudinal vel ms
119909 119910 119911 Longitudinallateralverticaldisplacement m
Longitudinallateralverticalvelocity ms
Longitudinallateralverticalacceleration ms2
119911def def Damper deflection and velocity m ms
119911119903 119911119904 119911us
Roadsprung massunsprungmass vertical position m
120573 Vehicle side slip angle deg120575 Steering wheel angle deg120575driver Driverrsquos steering command deg120582 Tire slip ratio mdash120592 Damper manipulation V120601 120579 120595 Pitchrollyaw angle deg Pitchrollyaw rate degs119889
Desired yaw rate degs120596 Rotational speed of the tires rads
A VDC can have one ormore of these three control goalsstability handling or vibration mitigation
(1) Stability when a vehicle has crossed its handlinglimits and tires lost their grip it is said that the vehiclehas become unstable and cannot be controlled by theaction of the driver only here the main objective isto recover the driverrsquos control to guarantee passengerssafety
(2) Handling it refers to how well a vehicle can achievecornering at high speeds this condition is related tothe safety characteristic of the vehicle
(3) Vibration mitigation it refers to the comfort that thepassengers will experience during riding this consistsin the limitation of the unpleasant vibrations andmovements caused by road irregularities also road-holding is considered that is vibration reduction inthe unsprung mass at high vehicle velocities
4 Mathematical Problems in Engineering
Table 3 Algorithms variables description
Variable Description119886119898
Actuation vector
119886119906
Gain of the allocationcoordination
119886119906susp
119886119906braking
119886119906steer
Suspensionbrakingsteeringcoordination gain
119888min 119888maxSoftesthardest dampingcoefficient
119862119894
Driving class
Con119894119896
Contribution index of the 119894thvariable in a 119896 driving situation
CS119896
Minimal set of importantvariables for a driving situation
119889(119909 119910119895) Euclidian distance
119863119862
Driving situation119890(120573) 119890() Slip angleyaw rate error119866ABS ABS braking gainIS Initial set of vehicle variables119896119894
Number of nearest neighbors119897119896
First 119897 principal components119898 Number of measurements
MS Minimal set of importantvariables for all driving situations
119872119911
Corrective yaw moment
119899 119899lowast Originalreduced number ofvariables
119903 Number of driving conditions
119904119904
Driving situation criticalcondition
119904119894
Driving situation importance119905crit Situation changing waiting time119905con Variable contribution threshold119879driver Driver braking torque
119879ESC119903 119879ESC119897Rightleft corrective brakingpressure
119879119866
Pressure gain119905119899119910
Noise variance threshold
119906119888 119906lowast119888
Allocatedcoordinated controlleroutput
119880|rh 119880|conf
Full suspensionroad-holdingcomfortsuspension command
119906susp119894119895 119880lowast
suspSingle cornerfull suspensioncontrol command
119909 Data point
119883119894passive
119883119894controlled
Passivecontrolled 119894thperformance variable
119894119896
Residual data point of the 119894thmeasure in a 119896 driving situation
120573119889 119889
Desired vehicle slip angleyawrate
120575AFS Corrective steering angle
120575lowast
steering wheel 120575lowast
wheelsSteering wheelwheelsdirectional angle
Table 3 Continued
Variable Description120582crit Critical tire slip ratio
120590119909119894119896
Variance of the 119894th variable in a 119896
driving situationR119896 Covariance matrix
X119896 Data matrix of 119899 variables
P119896 P119896
Principalresiduals componentsmatrix
T119896 T119896 Principalresidual scores matrix
X119896 X119896
Principalresidual transformedvariables
119894 Variable number119896 Driving situation119895 Number of neighborhoods
ω λθ
ψ
X
Y
Z
υβ
120601
Figure 1 Vehicle reference system and important dynamical vari-ables
To develop a full dynamics integration in the vehicle itis necessary to controlcoordinate the different subsystemssimultaneously [17] Usually the selected subsystems are (1)Active Front Steering (2) Independent Braking and (3)SAS Another requirement is the use of different controllersacting in those subsystems depending on the current drivingsituation [23] but this feature leads to switching thosecontrollers which could cause unstability [24]
In road vehicles the inherent coupling effects amongtheir subsystems impact the overall performance of thevehicle The coupled effects plus the issues that come withthe interactions of different independent control systemsincrease the complexity of controlling the vehicle dynamics
The above conditions can be handled with integratedcontrol strategies where subsystems and control actions areefficiently coordinated Such strategies avoid contradictionsin the control goals of the subsystems to obtain a better globalperformance from them at each situation [25] Model-basedcontrol approaches represent a complex and unpracticalsolution considering the vehicle as a highly nonlinear systemOn the other hand Data-Based Controllers could representa reliable option in practice assuming that the vehicle
Mathematical Problems in Engineering 5
DBC
MBCPassive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
DBCMBC
Passive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 2 Comparison of MBC and DBC approaches
dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867
infincontroller designed
to minimize the vertical acceleration (119904) and the pitch
(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms
From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller
Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic
3 Global Chassis Control
Thearchitecture of theGCC system is divided into threemainlayers Figure 3
(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode
(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers
(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors
This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces
Dec
ision
laye
rC
ontro
lla
yer
Phys
ical
laye
r
Info
rmat
ion
bus
FCS ABS SCS
Local controllers
Control allocation
Classification algorithm
Decision logic
Subsystems
Sens
ors
Control command(outer loop)
Control objective
Driving situation
Control command(inner loop)
Figure 3 GCC architecture hierarchical approach
a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem
31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation
311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Function Spaces
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
of [19] proposed a control architecture capable of identifyingthe actual driving situation based on the estimated situationthe control mode of each subsystem is changed Even whenthis method is capable of reacting against different situationsit does not consider the switching implications in the controlsystem which could lead to unexpected behaviors In [20] acontrol systembased on LPV is proposed in this case all threedirections are simultaneously controlled using two varyingparameters one for suspension-steering and another forbraking however the controller operates under predefinedconditions without depending on the driving situation
Although there are interesting results they do not includethe full dynamics integration others are strongly model-dependent or they are robust to some uncertainty whichcould generate conservatism issues Furthermore some ofthem are not easy to implement in on-board Vehicle Dynam-ics Controllers
The main contribution of this proposal lays in a newGCC system based on a discrimination of the operationconditions of the vehicle The strategy architecture is asupervisory decentralized control to improve flexibility andmodularity [21] The goal is to identify the current drivingsituation based on vehicle measurements using clusteringmethods [22] then the control modes of each subsystem arecoordinated to ensure the best global performanceThe coor-dination includes three subsystems SAS AFS and 4-WheelIndependent Braking (4WIB) a full dynamics integrationTheeffectiveness of the new strategy was validated in CarSim
The paper is organized as follows Section 2 describesthe problem Section 3 presents the GCC architecture andmodules in detail Section 4 discusses the results based ona case study Section 5 concludes the research and proposesfuture work Tables 2 and 3 summarize all the used variablesin this work
2 Problem Description
Passenger vehicles are equipped with a wide diversity of on-board VCS and those focused on the management of thedynamical behavior of the vehicle are calledVehicle DynamicsControllers (VDC) for example Continuous Damping Con-troller (CDC) and Electronic Stability Control (ESC) Usuallyeach VDC operates in a set of DoF defined by the vehiclereference system Figure 1 the most important variables foreach vehicle motion are as follows
(i) Vertical dynamics refers to the movements that affectmainly the comfort of the passengers (vibrationreductions) the important variables are pitch (turnaround 119910-axis 120601) roll (turn around 119909-axis 120579) andvertical acceleration () in the Chassis and wheels
(ii) Lateral dynamics refers mainly to the stability andhandling (safety) of the vehicle the important vari-ables are lateral displacement (119910) side slip angle (120573)and yaw (turn around 119911-axis 120595)
(iii) Longitudinal dynamics refers to vehicle stability(safety) and its performance (power train) the impor-tant variables are longitudinal velocity (119881
119909) wheel
rotational velocity (120596) and tire slip ratio (120582)
Table 2 Modeling variables description
Variable Description Units
1198861 1198862
Hysteresis coefficients related todisplacement and velocity sm 1m
119888119901 Viscous damping coefficient Nsm
119891brake 119891steerCut-off frequency of the actuatordynamics Hz
119891119888
Force coefficient due tomanipulation NV
119865119863 Damper force N
119865SA Semiactive damper force N119896119901 Stiffness coefficient Nm
119897 Vehicle wheel base m119898119904119898us Sprungunsprung mass kg
119879+
119887 120575+ Actuator output MPa deg
119879lowast
119887 120575lowast Actuator controller output MPa deg
119881119909 V119909119894119895
Vehicletire longitudinal vel ms
119909 119910 119911 Longitudinallateralverticaldisplacement m
Longitudinallateralverticalvelocity ms
Longitudinallateralverticalacceleration ms2
119911def def Damper deflection and velocity m ms
119911119903 119911119904 119911us
Roadsprung massunsprungmass vertical position m
120573 Vehicle side slip angle deg120575 Steering wheel angle deg120575driver Driverrsquos steering command deg120582 Tire slip ratio mdash120592 Damper manipulation V120601 120579 120595 Pitchrollyaw angle deg Pitchrollyaw rate degs119889
Desired yaw rate degs120596 Rotational speed of the tires rads
A VDC can have one ormore of these three control goalsstability handling or vibration mitigation
(1) Stability when a vehicle has crossed its handlinglimits and tires lost their grip it is said that the vehiclehas become unstable and cannot be controlled by theaction of the driver only here the main objective isto recover the driverrsquos control to guarantee passengerssafety
(2) Handling it refers to how well a vehicle can achievecornering at high speeds this condition is related tothe safety characteristic of the vehicle
(3) Vibration mitigation it refers to the comfort that thepassengers will experience during riding this consistsin the limitation of the unpleasant vibrations andmovements caused by road irregularities also road-holding is considered that is vibration reduction inthe unsprung mass at high vehicle velocities
4 Mathematical Problems in Engineering
Table 3 Algorithms variables description
Variable Description119886119898
Actuation vector
119886119906
Gain of the allocationcoordination
119886119906susp
119886119906braking
119886119906steer
Suspensionbrakingsteeringcoordination gain
119888min 119888maxSoftesthardest dampingcoefficient
119862119894
Driving class
Con119894119896
Contribution index of the 119894thvariable in a 119896 driving situation
CS119896
Minimal set of importantvariables for a driving situation
119889(119909 119910119895) Euclidian distance
119863119862
Driving situation119890(120573) 119890() Slip angleyaw rate error119866ABS ABS braking gainIS Initial set of vehicle variables119896119894
Number of nearest neighbors119897119896
First 119897 principal components119898 Number of measurements
MS Minimal set of importantvariables for all driving situations
119872119911
Corrective yaw moment
119899 119899lowast Originalreduced number ofvariables
119903 Number of driving conditions
119904119904
Driving situation criticalcondition
119904119894
Driving situation importance119905crit Situation changing waiting time119905con Variable contribution threshold119879driver Driver braking torque
119879ESC119903 119879ESC119897Rightleft corrective brakingpressure
119879119866
Pressure gain119905119899119910
Noise variance threshold
119906119888 119906lowast119888
Allocatedcoordinated controlleroutput
119880|rh 119880|conf
Full suspensionroad-holdingcomfortsuspension command
119906susp119894119895 119880lowast
suspSingle cornerfull suspensioncontrol command
119909 Data point
119883119894passive
119883119894controlled
Passivecontrolled 119894thperformance variable
119894119896
Residual data point of the 119894thmeasure in a 119896 driving situation
120573119889 119889
Desired vehicle slip angleyawrate
120575AFS Corrective steering angle
120575lowast
steering wheel 120575lowast
wheelsSteering wheelwheelsdirectional angle
Table 3 Continued
Variable Description120582crit Critical tire slip ratio
120590119909119894119896
Variance of the 119894th variable in a 119896
driving situationR119896 Covariance matrix
X119896 Data matrix of 119899 variables
P119896 P119896
Principalresiduals componentsmatrix
T119896 T119896 Principalresidual scores matrix
X119896 X119896
Principalresidual transformedvariables
119894 Variable number119896 Driving situation119895 Number of neighborhoods
ω λθ
ψ
X
Y
Z
υβ
120601
Figure 1 Vehicle reference system and important dynamical vari-ables
To develop a full dynamics integration in the vehicle itis necessary to controlcoordinate the different subsystemssimultaneously [17] Usually the selected subsystems are (1)Active Front Steering (2) Independent Braking and (3)SAS Another requirement is the use of different controllersacting in those subsystems depending on the current drivingsituation [23] but this feature leads to switching thosecontrollers which could cause unstability [24]
In road vehicles the inherent coupling effects amongtheir subsystems impact the overall performance of thevehicle The coupled effects plus the issues that come withthe interactions of different independent control systemsincrease the complexity of controlling the vehicle dynamics
The above conditions can be handled with integratedcontrol strategies where subsystems and control actions areefficiently coordinated Such strategies avoid contradictionsin the control goals of the subsystems to obtain a better globalperformance from them at each situation [25] Model-basedcontrol approaches represent a complex and unpracticalsolution considering the vehicle as a highly nonlinear systemOn the other hand Data-Based Controllers could representa reliable option in practice assuming that the vehicle
Mathematical Problems in Engineering 5
DBC
MBCPassive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
DBCMBC
Passive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 2 Comparison of MBC and DBC approaches
dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867
infincontroller designed
to minimize the vertical acceleration (119904) and the pitch
(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms
From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller
Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic
3 Global Chassis Control
Thearchitecture of theGCC system is divided into threemainlayers Figure 3
(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode
(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers
(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors
This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces
Dec
ision
laye
rC
ontro
lla
yer
Phys
ical
laye
r
Info
rmat
ion
bus
FCS ABS SCS
Local controllers
Control allocation
Classification algorithm
Decision logic
Subsystems
Sens
ors
Control command(outer loop)
Control objective
Driving situation
Control command(inner loop)
Figure 3 GCC architecture hierarchical approach
a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem
31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation
311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
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Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
Table 3 Algorithms variables description
Variable Description119886119898
Actuation vector
119886119906
Gain of the allocationcoordination
119886119906susp
119886119906braking
119886119906steer
Suspensionbrakingsteeringcoordination gain
119888min 119888maxSoftesthardest dampingcoefficient
119862119894
Driving class
Con119894119896
Contribution index of the 119894thvariable in a 119896 driving situation
CS119896
Minimal set of importantvariables for a driving situation
119889(119909 119910119895) Euclidian distance
119863119862
Driving situation119890(120573) 119890() Slip angleyaw rate error119866ABS ABS braking gainIS Initial set of vehicle variables119896119894
Number of nearest neighbors119897119896
First 119897 principal components119898 Number of measurements
MS Minimal set of importantvariables for all driving situations
119872119911
Corrective yaw moment
119899 119899lowast Originalreduced number ofvariables
119903 Number of driving conditions
119904119904
Driving situation criticalcondition
119904119894
Driving situation importance119905crit Situation changing waiting time119905con Variable contribution threshold119879driver Driver braking torque
119879ESC119903 119879ESC119897Rightleft corrective brakingpressure
119879119866
Pressure gain119905119899119910
Noise variance threshold
119906119888 119906lowast119888
Allocatedcoordinated controlleroutput
119880|rh 119880|conf
Full suspensionroad-holdingcomfortsuspension command
119906susp119894119895 119880lowast
suspSingle cornerfull suspensioncontrol command
119909 Data point
119883119894passive
119883119894controlled
Passivecontrolled 119894thperformance variable
119894119896
Residual data point of the 119894thmeasure in a 119896 driving situation
120573119889 119889
Desired vehicle slip angleyawrate
120575AFS Corrective steering angle
120575lowast
steering wheel 120575lowast
wheelsSteering wheelwheelsdirectional angle
Table 3 Continued
Variable Description120582crit Critical tire slip ratio
120590119909119894119896
Variance of the 119894th variable in a 119896
driving situationR119896 Covariance matrix
X119896 Data matrix of 119899 variables
P119896 P119896
Principalresiduals componentsmatrix
T119896 T119896 Principalresidual scores matrix
X119896 X119896
Principalresidual transformedvariables
119894 Variable number119896 Driving situation119895 Number of neighborhoods
ω λθ
ψ
X
Y
Z
υβ
120601
Figure 1 Vehicle reference system and important dynamical vari-ables
To develop a full dynamics integration in the vehicle itis necessary to controlcoordinate the different subsystemssimultaneously [17] Usually the selected subsystems are (1)Active Front Steering (2) Independent Braking and (3)SAS Another requirement is the use of different controllersacting in those subsystems depending on the current drivingsituation [23] but this feature leads to switching thosecontrollers which could cause unstability [24]
In road vehicles the inherent coupling effects amongtheir subsystems impact the overall performance of thevehicle The coupled effects plus the issues that come withthe interactions of different independent control systemsincrease the complexity of controlling the vehicle dynamics
The above conditions can be handled with integratedcontrol strategies where subsystems and control actions areefficiently coordinated Such strategies avoid contradictionsin the control goals of the subsystems to obtain a better globalperformance from them at each situation [25] Model-basedcontrol approaches represent a complex and unpracticalsolution considering the vehicle as a highly nonlinear systemOn the other hand Data-Based Controllers could representa reliable option in practice assuming that the vehicle
Mathematical Problems in Engineering 5
DBC
MBCPassive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
DBCMBC
Passive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 2 Comparison of MBC and DBC approaches
dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867
infincontroller designed
to minimize the vertical acceleration (119904) and the pitch
(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms
From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller
Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic
3 Global Chassis Control
Thearchitecture of theGCC system is divided into threemainlayers Figure 3
(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode
(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers
(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors
This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces
Dec
ision
laye
rC
ontro
lla
yer
Phys
ical
laye
r
Info
rmat
ion
bus
FCS ABS SCS
Local controllers
Control allocation
Classification algorithm
Decision logic
Subsystems
Sens
ors
Control command(outer loop)
Control objective
Driving situation
Control command(inner loop)
Figure 3 GCC architecture hierarchical approach
a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem
31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation
311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Algebra
Discrete Dynamics in Nature and Society
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Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
DBC
MBCPassive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
DBCMBC
Passive
02 04 06 08 1 12 14 160Time (s)
minus08
minus04
0
04
08
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 2 Comparison of MBC and DBC approaches
dynamics is monitored by some sensors Figure 2 comparesthe two approaches under the road profile with bump testThistest is used to evaluate the road isolation characteristics ofthe control systems Here 3 cases are compared (1) Passivea vehicle with nominal shock absorbers (2) a Model-BasedController (MBC) a full suspension 119867
infincontroller designed
to minimize the vertical acceleration (119904) and the pitch
(120601) movements of the sprung mass and (3) a Data-BasedController (DBC) a controller that considers the classical Sky-Hook and Ground-Hook algorithms
From Figure 2 it can be seen that the two approacheshave a very similar performance Quantitatively the MBCimproved the vertical acceleration in 145 and the pitchmovements in 974with respect to the Passive case whereasthe DBC achieved an improvement of 91 and 178respectively Both approaches result in similar performancesbut the DBC is simpler and faster to implement comparedto the MBC which has large dimension matrices inside thecontroller
Based on the results of the literature review VDC systemsthat achieve full dynamics integration are still a researchtopic
3 Global Chassis Control
Thearchitecture of theGCC system is divided into threemainlayers Figure 3
(1) Decision layer it identifies the current driving situa-tion and its stability it decides how to coordinate thesubsystems actions and their operating mode
(2) Control layer it receives the control goal from thedecision layer and determines the proper orientationfor each of the local controllers
(3) Physical layer it comprehends the actuators andsensors from the vehicle it receives the control outputfrom the control layer and sends the process variablesfrom the sensors
This multilayer and hierarchical architecture has someadvantages (1) it divides the computational load into severalECUs (2) it allows information sharing (3) it improvessystem flexibility (reconfigurability) and (4) it introduces
Dec
ision
laye
rC
ontro
lla
yer
Phys
ical
laye
r
Info
rmat
ion
bus
FCS ABS SCS
Local controllers
Control allocation
Classification algorithm
Decision logic
Subsystems
Sens
ors
Control command(outer loop)
Control objective
Driving situation
Control command(inner loop)
Figure 3 GCC architecture hierarchical approach
a modular scheme capability [26] The information bus con-tains sensors measurements and actuators functions Sincethe methods to observe or estimate the considered variablesare not within the scope of this work they are assumed to beavailable Figure 4 shows a full scheme of the proposed GCCsystem
31 Decision Layer This layer has two main tasks (1) classifythe current driving situation and (2) coordinate the controlstrategy for the classified situation
311 Classification Algorithm The first step of the algorithmis to decide from an Initial Set (IS) of variables which is theMinimal Set (MS) to classify the current driving situationThe elements of IS must be variables that describe the global
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
Decision
logic
SAP
Sensorsactuators signals
Local controllersk-means
algorithm
SA suspension
Active frontsteering
Braking system
Physical layer
Sens
ors
Brake control
Angle control
Voltage control
ESC
AFS
Control layer
Decision layer
Suspcontrol
Control allocation
Actuators
aususp
austeer
aubraking
Tdriver
120575lowaststeering wheel =2874
118120575lowasttires
Tlowastb = GABS middot max(Tdriver T
lowastESC)
120575driver
cmin
cmax120592 =
10
90
rceilrfloorrceilrfloorrceilrfloor rceilrfloor997888rarr
Figure 4 Control scheme of the GCC system
behavior of the vehicle as well as variables that are commonlyused in VCS
MS sube IS |MS| le |IS| (1)
Some vehicle variables are correlated for example pitchis correlated to deflections of the suspension Besides not allvariables have the same importance in all driving situationsfor example in a riding situation the vertical acceleration willgain more importance but during cornering yaw momentcould be the most important To determine the most rep-resentative vehicle variables during a driving situation aPrincipal Component Analysis (PCA) is carried out
Measurements of the variables in the IS set under differentdriving situations are used in this step where 119903 is thenumber of driving situations to be considered X
119896 with 119896 =
1 2 119903 is the data matrix of 119899 variables and |IS| = 119899and119898measurements with zero mean and unit variance aftera scaling process To neglect the noise effect in the scalingprocess variables with small variance are not considered120590119909119894119896
lt 119905119899119910 where 119905
119899119910gt 0 is a defined threshold
Based on [27] P119896
isin R119899times119897119896 is obtained it contains thefirst 119897119896eigenvectors from the covariance matrix R
119896and P
119896isin
R119899times(119899minus119897119896) which contains the last 119897119896minus 119899 eigenvectors The first
119897119896eigenvectors associated with the PC have to explain at least
90 of the total variance of the original data for each driving
situation Then the scores matrices T119896
isin R119898times119897119896 and T119896
isin
R119898times(119899minus119897119896) are obtained
T119896= X119896P119896
T119896= X119896P119896
(2)
By decomposing X119896= X119896+ X119896with
X119896= T119896P119879119896
X119896= T119896P119879k
(3)
the modeled data is obtained with principal and residualcomponents respectively
According to [28] using the residual components X119896
the contribution of each variable 119894 can be obtained in each119896 driving situation as
Con119894119896
=sum119898
119895=12
119894119896(119895)
sum119899
119894=1sum119898
119895=12
119894119896(119895)
forall119894 = 1 2 119899 (4)
Once the contributions are obtained if Con119894119896
gt 119905conthen Con
119894119896997891rarr CS
119896 where CS
119896is the set of the variables
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
and
lfloorlceil
rfloorrceilDC119894
[si] lt DC119895[si]
DC119894[ss] = DC119895
[ss] = 0
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t gt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1
rceil
rfloor
[
lfloor
lceil[[[[[
[[[[and
and
t lt tcrit
DC119894[si] lt DC119895
[si]
DC119894[ss] le DC119895
[ss] = 1or
DC119894DCj
DC119894[si] lt DC119895
[si]
middot middot middot middot middot middot
Figure 5 Graph for the DL module
that contributes in each 119896 driving situation and 119905con gt 0 isa defined threshold Finally the MS set is formed by
MS =
119903
⋃
119896=1
CS119896
forall119896 = 1 2 119903 (5)
with the resultant number variables equal to |MS| = 119899lowast
After defining theMS set that contains themost represen-tative variables for all studied driving situations a clusteringtechnique is exploited as classifier Because of its easy com-putation fast clustering response and good performance the119896-Nearest Neighbor (119896-NN) algorithm was used
The 119896-NN approach is one of the simplest machinelearning algorithms which it is based on the minimumdistance criterion A data set of reference patterns in amultidimensional feature space is required to establish thelearning of this classifier where the Euclidian distance isthe most common metric In this case MS set contains thereference patterns of the studied driving situations
Given a new data vector 1199091 1199092 119909
119899of 119899 variables the
119896-NN algorithm assigns each new observation into a class ofdriving situation 119862
119894according to
119909 isin 119862119894when min
119862
1
119896119894
119896119894
sum
119895=1
119889 (119909 119910119895) (6)
where 119896119894is the number of nearest neighbors used in the
classification associated with the driving situation 119894 and119889(119909 119910
119895) is the Euclidian distance between a new observation
119909 and the nearest neighbors of reference defined by 119910 A largevalue of 119896 reduces the effect of noise in the classificationcross-validation can be used to define this parameter For thevehicle the sensor measurements contained in theMS set areused to construct the features space The online result givenby this clustering technique is sent to theDecision Logic (DL)module to classify the situation
312 Decision LogicModule Based on a set of heuristic rulesthe DL module is in charge to decide (1) whether a drivingsituation is critical or normal (2) if the control actions shouldchange and (3) when to change from one situation to anotherbased on the importance of the previous situation
First the structure for a driving situation 119863119862 must be
defined For this purpose the DL module depends on thenumber of subsystems to use and the amount of drivingsituations 119903 to consider The definition of a119863
119862is as follows
(i) Each driving situation is defined with a vector in R3
in the form119863119862= [119904119904 119904119894 119886119898]
(ii) 119904119904isin 0 1 refers to normal (119904
119904= 0) or critical (119904
119904= 1)
situation(iii) 119904119894isin 1 119902 indicates the critical level of the driving
situation 119904119894rarr 1 is a stable situation with negligible
danger while 119904119894
rarr 119902 corresponds to the mostdangerous condition
(iv) 119886119898
isin R119906 is the actuation vector for the 119906 subsystemsthat must be accomplished according to the detecteddriving situation that is 119886
119898= 1198861 119886
119906 Consid-
ering an on-off control law for each subsystem thecontrol output is dichotomic 119886
119894isin [0 1]
Then a set of rules that manage the transition betweendriving situations is defined Figure 5 shows the graph dia-gram with the transition rules the DL rules are carried asfollows
(1) A 119863119862with bigger 119904
119894overrules a 119863
119862with a smaller 119904
119894
index and 119886119898is updated
(2) At any safe driving situation independently of the 119904119894
index the current119863119862updates the actuation vector 119886
119898
(3) In an unsafe driving situation the current 119863119862keeps
the actuation vector in safe mode until the 119904119894index
decreases through the time (119905 gt 119905crit) to ensurecompletely the vehicle safety and avoid any falsealarms
Finally the DL layer sends the mode of operation of thesubsystems controllers in the control layer
32 Control Layer This layer comprehends the controlactions (allocation manipulation) to be taken through thephysical layer The desired control allocation is determinedbased on the information received from the previous layerand then the desired control manipulations are computed
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Mathematical Problems in Engineering
321 Control Allocation Based on the driving situation thedesired control action for each subsystem is defined in thissublayer The control mode acts as a gain in the form of
119906lowast
119888= 119886119906sdot 119906119888 (7)
where 119906lowast
119888is the controller output which depends directly on
the gain of the coordinated allocation 119886119906 that is 119886
119906= 1means
that the GCC demands the actuation on the subsystemand vice versa (ie when 119886
119906= 0) Thus 119906
119888is the local
controller output of the subsystem obtained from any controllaw but before the full dynamics integration The allocationcontrollers for each subsystems are defined as follows
(i) SAS The SA dampers must always receive a manipulationthe decision is whether to select a manipulation oriented tocomfort (119880|comf ) or to road-holding (119880|rh) for each corner ofthe vehicle
119880lowast
susp = (1 minus 119886119906susp
) sdot 119880|comf + 119886119906susp
sdot 119880|rh (8)
where 119880lowast
susp = 119906susp119865119871
119906susp119865119877
119906susp119877119871
119906susp119877119877
Note thataccording to the driving situation the GCC can orient thesuspension to comfort or to road-holding using theweightingparameter 119886
119906susp At each corner the SAS controller output can
be oriented to comfort (119906119894119895|comf ) or to road-holding (119906
119894119895|rh)
inspired in the classical Sky-Hook and Ground-Hook controlstrategies
119906119894119895
10038161003816100381610038161003816rh =
119888min if minus 119906119904
sdot def le 0
119888max if minus 119906119904
sdot def gt 0
119906119894119895
10038161003816100381610038161003816comf =
119888min if 119904sdot def le 0
119888max if 119904sdot def gt 0
(9)
where 119888min = 0 and 119888max = 1 represent the softest and hardestdamping coefficient respectively
(ii) Braking System The braking action is computed by thefuzzy logic (FL) controller [29] It uses two inputs (1) side slipangle error (119890(120573) = 120573 minus 120573
119889isin [minus10 10]) and (2) yaw rate error
(119890() = minus 119889
isin [minus10 10]) and one output (1) correctiveyaw moment (119872
119911isin [minus1 1]) The control goal is to reduce
the errors to zero for this purpose the reference signals aredefined as 120573
119889= 0 since the goal is to have 120573 as close to zero
as possible and
119889=
119881119909
119897120575driver (10)
where 119881119909is the longitudinal velocity of the vehicle 119897 is the
wheel base and 120575driver is the drivers steering angle commandFor the two input variables five fuzzy sets with triangular
Membership Functions (MFs) were used for each variable119890(120573) 119890() = NBNSZPSPB whereas for the outputvariable seven fuzzy sets also with triangular MFs were used119872119911 = NBNMNSZPSPMPB Table 4 describes the
meanings of the used linguistic terms and Table 5 shows
Table 4 Linguistic terms
NB Negative bigNMH Negative medium highNM Negative mediumNMS Negative medium smallNS Negative smallZ ZeroPS Positive smallPMS Positive medium smallPM Positive mediumPMH Positive medium highPB Positive big
Table 5 FL inference rules for the braking system
119890(120573)119890()
NB NS Z PS PBNB PB PB NS NB NBNS PB PM NS NM NBZ PM PS Z NS NMPS PB PM PS NM NBPB PB PS PS NS NB
the rules for the proposed FL controller This FL controlleruses aMamdani Fuzzy Inference System (FIS)
To allocate the desired output for the braking localcontrollers119872
119911is transformed in terms of ESCs as
119872119911gt 0 997888rarr Brake rear left wheel
119879ESC119903 = 0 119879ESC119897 = 119879119866sdot 119872119911
119872119911= 0 997888rarr No added braking
119879ESC119903 = 0 119879ESC119897 = 0
119872119911lt 0 997888rarr Brake rear right wheel
119879ESC119903 = minus119879119866sdot 119872119911 119879ESC119897 = 0
(11)
where 119879119866
is a parameter that relates the corrective yawmoment (119872
119911) and the brake pressure to be applied by the
braking systemAdditionally the coordinated allocation affects the action
of the braking FL controller including or ignoring it usingthe value of 119886
119906brakingas a gain
119879lowast
ESC = 119886119906braking
sdot 119879ESC (12)
(iii) AFS System For this subsystem the allocation decides tointroduce or not the AFS control action as
120575lowast
= 120575driver + 119886119906steer
sdot 120575AFS (13)
where 120575lowast is the desired steering wheel angle 120575driver is
the driverrsquos command and 120575AFS is the compensation anglecalculated by the AFS system From (13) it can be seen
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
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Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 9
Table 6 FL inference rules for the steering system
120573 120575driver119890()
NB NS Z PS PB
Low
NB NS NS Z PB PBNS NMS NMS Z PMH PMHZ NM NM Z PM PMPS NMH NMH Z PMS PMSPB NH NH Z PS PS
High
NB NH NH Z PS PSNS NMH NMH Z PMS PMSZ NM NM NS PMS PMSPS NMS NMS NS NS NSPB NS NS NS NS NS
that the driverrsquos command is always considered but thecompensation angle is considered if 119886
119906steer= 1 or not if 119886
119906steer=
0As for the braking system the steering action is computed
using a FL controller [30]Three input variableswere selected(1) side slip angle (120573 isin [minus10 10]) (2) yaw rate error(119890() = minus
119889isin [minus10 10]) and (3) steering angle input
(120575driver isin [minus10 10]) and one output (1) steering correctionangle (120575AFS isin [minus5 5]) The FL controller is oriented to createa steering wheel angle correction that minimizes the yaw rateerror the desired yaw rate is calculated using (10)
For input 120573 two fuzzy sets with sigmoid MFs were used120573 = LowHigh For the other two input variables fivefuzzy sets with triangular MFs were used 119890() 120575driver =
NBNSZPSPB whereas for the output variable elevenfuzzy sets also with triangular standard MFs were used120575AFS = NBNMHNMNMSNSZPSPMSPMPMHPB Table 6 shows the rules for the proposed FL controllerwhose linguistic definitions are given in Table 4
322 Local Controllers This sublayer contains the localcontrollers for each subsystem These controllers are Single-Input Single-Output (SISO) and only interact with theirparticular subsystem These controllers receive the desiredset-point 119906
lowast
119888from the control allocation sublayer and are
in charge of executing it Also these controllers have to beselected regarding the subsystem to control The subsystemcontrollers for this strategy are the following
(i) SAS because the control command coming from theallocation step is binary the force control system isdefined as follows
[119888min
119888max] = [
0
1] 997891997888rarr 120592 = [
1090
] (14)
where 120592 is the manipulation delivered to the SAdamper (ie electric current voltage and duty cycle)
(ii) Steering the command in terms of tire angles totransform it to a single gain controller is
120575lowast
steering wheel =2874
118120575lowast
tires (15)
(iii) Braking the local controller is an ABS it modifies thedesired command as
119879lowast
119887= 119866ABS sdotmax (119879driver 119879
lowast
ESC) (16)
where 119879driver is the driver braking command 119879ESCis the braking command from the allocation systemand 119866ABS is the gain of the ABS that releases thetire when it is locked This control law selects themaximum between the command coming from theallocation system and the command from the driverThe 119866ABS gain is obtained by the function
119866ABS119894119895 =
0 if 120582119894119895
ge 120582crit
1 if 120582119894119895
lt 120582crit(17)
with
120582119894119895
=
119881119909minus V119909119894119895
119881119909
(18)
where 120582119894119895
is the slip ratio for each wheel Theoperation of this ABS controller is guided by 120582 if 120582grows beyond the admissible range (120582crit = 01) thebraking system releases the tire until it recovers gripand the slip ratio decreases to the admissible rangewhere the braking torque is again applied to the tire
33 Physical Layer The physical layer is integrated by thesensors and actuators of the SAS AFS system and 4WIBsystem
331 Suspension System Thesuspension system is composedof a linear spring and a SA shock absorberThe key element isthe set of SA shock absorber one at each corner which needsto be modeled as a function of a manipulation signal (120592) Thedamper force (119865
119863) is modeled as a function of the damper
deflection (119911def ) deflection velocity (def ) and manipulationsignal [31]
119865119863
= 119888119901(def) + 119896
119901(119911def) + 119865SA (19)
where 119865SA = 120592 sdot 119891119888sdot tanh(119886
1sdot def + 119886
2sdot 119911def ) is the SA force
due to 120592 119888119901is a viscous damping coefficient 119896
119901is a stiffness
coefficient and 1198861and 119886
2are hysteresis coefficients due to
velocity and displacement respectively The SA dampingforce at each damper is continuous from [minus10000 6000]N
332 Steering System A steer-by-wire Active Steering (AS)system is used to provide an additional steering angle forcorrective purposes the actuator model is given by [32]
+
= 2120587119891steer (120575lowast
minus 120575+
) (20)
where 119891steer = 10Hz is the cut-off frequency of the actuatordynamics 120575
lowast is the steering controller output and 120575+ is
the actuator output the bounded limits of actuation are[minus5∘ +5∘]
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
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OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Mathematical Problems in Engineering
50 100 150 2000Station (m)
minus10
0
10
z r(m
m)
(a) Road profile with bump (b) Brake distance test (hard braking)
(c) DLC test (rapid steering) (d) FH test (cornering)
(e) Split 120583-surface braking (loss of vehicle control)
Figure 6 Implemented tests in CarSim
333 Braking System The corrective front and rear brakingtorques are provided by brake-by-wire ElectromechanicalBraking (EMB) actuators the model of these EMB actuatorsis given by [32]
+
119887= 2120587119891brake (119879
lowast
119887minus 119879+
119887) (21)
where 119891brake = 10Hz is the cut-off frequency of the actuatordynamics 119879lowast
119887is the braking controller output and 119879
+
119887is the
actuator output The bounded limits of actuation for eachbraking actuator are [0 15]MPa
4 GCC System Evaluation
The results of this proposal are presented based on a casestudy
41 Case Study CarSim was used to generate an accuratevehicle model whose VDC were hosted in MatlabSimulinkA 119863-class sedan was the selected vehicle Seven drivingsituations were considered (119903 = 7) Figure 6 illustrates some
of the implemented tests to represent the driving situationsthese tests are as follows
(a) Road profile with bump test this test is intendedto evaluate the road isolation characteristics of thecontrol strategy it consists in a rough road with asharp bump of 35mm height and 400mm length
(b) Brake distance test it consists in a hard braking actionby the driver to measure the distance that takes thevehicle when it goes from 100 kmh to a full stop
(c) Double Line Change (DLC) maneuver it consists ina change of driving line to simulate an obstacleavoidance maneuver or an overtaking action at highspeed (120 kmh) a rapid steering maneuver is takenby the driver to change from the original line andthen another rapid steering action to turn back to theoriginal line
(d) Fish Hook (FH) maneuver this maneuver consists ina wide but constant steering action first a movementof 270∘ of the steering wheel is taken to one sideat a constant turning rate then a turn of 540∘ to
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 11
Table 7 IS set
ID Variable Description1ndash4 119911def119894119895 Damper deflection5ndash8 def119894119895 Damper deflection rate9 120601 Pitch10 Pitch rate11 120579 Roll12 Roll rate13 120595 Yaw14 Yaw rate15 Longitudinal acceleration16 Lateral acceleration17 Vertical acceleration18 120573 Vehicle slip angle19 Vehicle slip angle rate20 120575 Steering wheel angle21 Steering wheel angle rate
the opposite side is executed transferring the vehicleload from one side to another then the steering angleis held to create a cornering situationwhichmaintainsthe load transfer at a dangerous limit
(e) Split 120583-surface braking test the intention of this testis to evaluate how well a vehicle can keep its lineduring a braking action while riding with differentfriction coefficients in each side of the vehicle thistest is intended to cause loss of vehicle control fromthe driver
42 Decision Layer For space limitations the results of theDL are presented just for the rapid steering driving situation
421 Classification Algorithm The IS set has a cardinality of|IS| = 21 elements (variables) Table 7 describes the consid-ered variable set These variables were selected because theydescribe completely the behavior of the vehicle
Figure 7 shows the correlation level among the elementsin the IS set for the DLC test Each square represents thelevel of correlation between two variables for example inthe grid the principal diagonal shows a correlation of 1 (darkred) because it is the correlation of the variable with itselfA correlation of minus1 (dark blue) indicates that the variablehas an inverse correlation with the variable in question forexample variable 1 (119911def119865119871) has a correlation of 1with variable2 (119911def119877119871) and a correlation of minus1 with variable 3 (119911def119865119877)The above example can be interpreted as follows during aroll situation caused by the steering maneuver the dampersof the same side (left) have the same compression whereasthe dampers of the other side have the same movementbut in the opposite direction It is notable that there is aninherent correlation among some variables some of them canbe neglected
To find the MS set for this situation the PCA algorithmwas performed Figure 8 These results point out that only4 PC could explain more than 90 of the total variance of
5
10
15
20
Varia
bles
Variables correlations matrix
5 10 15 2000
Variables
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
Figure 7 Correlationmatrix of the IS set for a rapid steering drivingsituation
90 of thevariance
4 components
0
50
100
Cum
ulat
ive v
aria
nce (
)
5 10 15 211Number of components
0
2
4
6
8Ei
genv
alue
Figure 8 PCA result for the rapid steering situation
120595
0
5
10
15
20
25
Con
trib
utio
n to
dat
a var
ianc
e (
)
5 10 15 200Variables
120575
x
120601
Figure 9 Contribution plot of the variables in the IS set
the test Figure 8 demonstrates thatwhen the cumulative vari-ance marker (green line) surpasses the 90mark (horizontalred dotted line) the number of components is 4
It is important to relate the result with the IS set suchthat the contribution of each variable to explain the totaldata variance can be studied in the residual space Figure 9shows the contribution of all variables for theDLC testThosevariables that overshoot the threshold 119905con = 10 (red dotted
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Mathematical Problems in Engineering
Table 8 PCA results
ID Test of PC of explained variance Variables in MS set1 Ride 7 927 8 12 14 17 212 Road irregularity 4 902 9 10 173 Accelerationbraking 4 978 5 6 7 8 104 Hard braking 5 975 5 6 7 8 105 Cornering 7 931 10 13 18 206 Rapid steering 4 937 10 13 15 217 Loss of control 7 926 13 14 18 19
04 06 08 102Pitch (deg)
minus15
minus10
minus5
0
5
10
15
Roll
rate
(deg
s)
CorneringLoss of controlRapid steeringRiding
CorneringRapid steeringRidingCentroids
Figure 10 Clustering distribution for 2 dimensions
line) are considered the most representative variables in thisdriving situation they integrate the MS set
Table 8 presents the PCA results for the seven drivingsituations It can be concluded that the minimum set ofvariables for identifying any driving situation in MS =
5ndash10 12ndash15 17ndash21 Once MS set is defined the clusteringstep runs
A 119896-NN classifier with 119896 = 7 was trained to classify 4major driving situations (riding cornering rapid steeringand loss of control) where the first four tests in Table 8are tagged as riding situation Figure 10 shows the clustersdistribution in 2D (pitch angle versus roll rate) note thatclusters are differentiated by color More than one clusterdetermine one of the four driving conditions a corneringsituation uses two clusters (red and cyan cluster)
To evaluate the classifier performance a test with a seriesof different driving situations was designed The test beginswith the vehicle being driven in a rough road (119863
119862= 1)
afterwards it has a rapid steering maneuver (119863119862
= 6)once the DLC maneuver passes and the vehicle is stabilizedagain the test finishes with a cornering action (119863
119862= 5
FH maneuver) Figure 11 shows the target as well as theclassification result for this testThis test was selected because
Target
Output
DC = 6
DC = 5
DC = 1
5 10 15 20 250Time (s)
Figure 11 Validation test for the 119896-NN classifier
the two conditions (119863119862
= 5 and 119863119862
= 6) are reallysimilar in essence both include steering action but thedifference lays in the velocity of the steering movementFrom Figure 11 it is clear that rapid steering action is welldetected by the classifier but cornering has some drawbacksDuring the rapid steering situation some variables relatedto the vertical and lateral dynamics are highly sensitive butduring cornering the steady behavior of some movements ismisjudged as riding conditions
Figure 12 presents the ROC of the classifier results for thetest in Figure 11 The riding situation is well classified with afalse alarm rate of 20 For the other two situations the falsealarm is zero but the detection error is 10 because of therapid steering situation while the cornering condition has theworst identification performance (error of 50)
From the previous analysis it can be concluded thatthe situations that involve roll and yaw movements can bewell classified but other driving situations (road irregularityaccelerationbraking and hard braking) which are mostlypitch related can not be classified since all other drivingsituations also involve pitch movement
To assist the 119896-NN classifier a Suspension AdjustmentPlane (SAP)was designed SAP studies the vertical load trans-fer caused by vehicle movements to adjust the SAS systemIts objective is to select the suspension settings depending onwhich area of the plane the vehicle is in For example if thevehicle is in a frontal pitch situation (braking) the system setsthe two front dampers in road-holding mode since most ofthe load is transferred to those tires The same happens witha roll movement where the tires of the same side receive mostof the load The center area (between the red dotted lines) ofthe SAP is concernedwith a normal riding situationThis area
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 13
DC = 6
DC = 5
DC = 1
02 04 06 08 10False positive rate
0
02
04
06
08
1
True
pos
itive
rate
Figure 12 ROC for the 119896-NN classifier
aususp = [1 1 1 0]
aususp = [1 1 0 1]
aususp = [1 0 1 0]
aususp = [0 1 0 1]aususp = [0 0 1 1]
aususp = [1 1 0 0]
10 2 3minus2 minus1minus3
Roll (deg)
minus02
02
06
1
14
Pitc
h (d
eg)
RidingHard brakingAccelerationbrakingLoss of control
Road irregularityCorneringRapid steering
Figure 13 Suspension Adjustment Plane (SAP)
was defined by considering different riding conditions (roadroughness and velocities) Figure 13 shows the SAP withdifferent driving situations and also the proper suspensioncombinations aremarked for each regionWith this plane it ispossible to classify which riding situation occurs (riding perse a road irregularity an accelerationbraking situation or ahard braking)
In Figure 13 the dotted lines delimit the threshold forpitch and roll movements caused by road roughness outsidethose limits it is considered that the experienced movementsare caused by other driving situations The central verti-cal zone includes primarily pitch situations like braking
Table 9119863119862vectors for different driving conditions
Driving situation 119863119862
119904119894
119904119904
119886119906susp
119886119906steer
119886119906braking
Ride 1 0 [0 0 0 0] 0 0Road irregularity 2 0 SAP 0 0Accelerationbraking 3 0 SAP 0 0Hard braking 4 0 SAP 0 0Cornering 5 0 SAP 1 0Rapid steering 6 1 SAP 1 1Loss of control 7 1 [1 1 1 1] 1 1
whereas the horizontal central zone refers to primarily rollmovements like cornering
422 Decision Logic Table 9 presents the proposed valuesfor vector119863
119862at each driving situation
43 Control Layer The performance of the proposed GCCsystem is evaluated and comparedwith two additional controlcases The first case corresponds to an uncontrolled (UC) sys-tem that is it is a vehicle which lacks any control system andis equipped with standard actuators and a passive suspensionsystem The second case corresponds to a vehicle with a setof dynamics controllers without a coordination strategy inDecentralized Controllers (DC) that is a set of controllers areacting simultaneously seeking their own control goals
To evaluate quantitatively the performance at each driv-ing test the Root Mean Square (RMS) value of the signalsis used To have a point of comparison the RMS values ofthe controlled cases (DC and GCC) are normalized with thatobtained by the UC case using
of Improvement
=RMS (119883
119894Passive) minus RMS (119883
119894Controlled)
RMS (119883119894Passive
)
(22)
431 Road Profile with Bump Test For this test two variablesare important (1) vertical acceleration of the sprung mass(119904) Figure 14(a) and (2) pitch angle (120601) Figure 14(b) For the
vertical acceleration Figure 14(a) the GCC system achieves96 of improvement in vibrationmitigationwhen comparedwith the reference case (UC) on the other hand the DCcase achieves 311 During this test the bump it intended toexcite the pitch motion of the vehicle which is also relatedto the comfort of the passengers Figure 14(b) the GCCsystem manages to reduce the pitch motion of the vehicleby 117 whereas the DC case achieves 108 both resultswhen compared with the UC case The main improvementof the control strategy can be seen after the bump (1 secondmark) during that transient response the vehicle reaches astable behavior faster than the reference case
432 Braking Distance Test Two variables are the mostimportant for this test (1) brake distance Figure 15(a) and
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
14 Mathematical Problems in Engineering
GCC
UC
DC
05 1 150Time (s)
minus08
minus04
0
04
08Ve
rtic
al ac
cele
ratio
n (G
rsquos)
(a) Vertical acceleration (119904)
GCC
UC
DC
05 1 150Time (s)
minus04
0
04
08
12
Pitc
h an
gle (
deg
)
(b) Pitch angle (120601)
Figure 14 Road profile with bump test
0
10
20
30
40
50
60
70
Brak
e dist
ance
(m)
1 2 3 4 5 6 70Time (s)
DC (63m)
UC (69m)
GCC (59m)
(a) Brake distance
GCCUC
DC
1 2 3 4 5 6 70Time (s)
0
04
08
12
16
Pitc
h (d
eg)
(b) Pitch angle (120601)
Figure 15 Brake distance test
(2) pitch angle 120601 Figure 15(b) Regarding brake distance thereference case (UC) takes 69m to fully stop whereas thecontrolled cases have improvements of 87 for the DC and145 for the GCC meaning a stop distance of 10m less thanthat of the UC case For the pitch angle the improvementof the DC against the UC was 62 whereas GCC has animprovement of 103 Also in Figure 15(b) it can be seenthat the GCC has less overshoot and shorter stabilizationtime Those oscillations cause loss of grip of the tires andproduce uncomfortable movements for the passengers Evenwhen the improvement indices for both controlled cases aremarginal for the pitch angle the uncomfortable behaviors aresuccessfully attenuated
433 DLC Test Figure 16 shows the vehicle trajectory foreach case It can be observed that the GCC has the smallest119910-coordinate deviation and also its finish is straight whereasfor theUC the119910-coordinate deviation is bigger and at the endits path is divergingTheDC has a performance similar to theUC but at the end the 119910-coordinate deviation is bigger (morenegative) than the other cases
After assessing the vehicle trajectory it is important toanalyze the behavior of the related variables to the vehiclestability such as roll angle (120579) Figure 17(a) and yaw angle(120595) Figure 17(b) Figure 17(a) illustrates that the GCC systemhas less roll movement than the other cases that is 10 lessthan UC also the roll movement has less duration having
GCCUC
DC
50 100 150 200 2500x-coordinate (m)
minus2
minus1
0
1
2
3
4
y-c
oord
inat
e (m
)
Figure 16 Vehicle trajectory for a DLC test
a rapid stabilization For theDC the rollmovement is abruptlycaused by the lack of coordination of the steering and brakingthis causes those oscillations and a deterioration of 89compared to the UC case In Figure 17(b) also the GCCsystem has less yaw motion 125 less than the UC whilethe DC has a deterioration of 4 compared to the UC case
434 FH Test In this test the evaluation starts with theassessment of the vehicle trajectory Figure 18 shows thetrajectory for the three cases As it can be seen the GCCsystem has a smaller turn radius than the other two casesespecially when compared with UC this indicates more
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 15
GCC
UC
DC
1 2 3 4 5 6 70Time (s)
minus2
minus1
0
1
2Ro
ll (d
eg)
(a) Roll angle (120579)
GCC
UCDC
1 2 3 4 5 6 70Time (s)
minus10
minus6
minus2
2
6
Yaw
(deg
)
(b) Yaw angle (120595)
Figure 17 DLC test
GCC
UC
DC
minus5
0
5
10
15
20
25
y-c
oord
inat
e (m
)
20 40 60 80 1000x-coordinate (m)
Figure 18 Vehicle trajectory for FH test
GCC UC
DC1 2 3 4 50
Time (s)
minus4
minus2
0
2
4
Roll
(deg
)
(a) Roll angle (120579)
GCC
UC
DC
1 2 3 4 50Time (s)
minus08
minus04
0
04
08
Late
ral a
cc (
g)
(b) Lateral acceleration ()
Figure 19 FH test
handling capabilities in GCC Also the proposed GCC hasa shorter trajectory which indicates less skidding than othercases
The significant variables are (1) roll angle (120579) Figure 19(a)and (2) lateral acceleration () Figure 19(b) Since theinduced cornering situation by the steering movement isreally similar regardless of the control system the importantfeatures to study are the transient responses of the variablesat the time when the cornering starts and ends FromFigure 19(a) it is evident that in GCC the induced oscillationsby the change of load transfer are better absorbed by thesuspension system that is 7 less oscillations than in the UCcase and 3 less than in DC Regarding lateral accelerationFigure 19(b) GCC has less oscillations when the change of
load takes place even when the improvement is marginal 2with respect to UCThere is no significant improvement withrespect to DC
435 Split 120583-Surface Test This test is designed to evaluatethe ability of a vehicle to remain in control against a criticalsituation It is important to verify how well the vehicleremains in its original path after the braking action startsFigure 20 shows the trajectory of the three Vehicle ControlSystemsThe controlled vehicle with GCC remains in straightline during the whole test whereas UC moves away from theoriginal trajectory On the other hand the vehicle with DCalso manages to remain close to the straight path
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
16 Mathematical Problems in Engineering
GCC
UC
DC
10 20 30 40 50 600x-coordinate (m)
minus1
0
1
2
y-c
oord
inat
e (m
)
Figure 20 Vehicle trajectory for Split 120583-surface braking test
GCC
UC
DC
0
200
400
600
800
Stee
ring
whe
el an
gle (
deg
)
1 2 3 4 50Time (s)
(a) Steering wheel angle (120575)
GCC
UCDC
minus04
minus02
0
02
Late
ral a
ccel
erat
ion
(g)
1 2 3 4 50Time (s)
(b) Lateral acceleration ()
GCC
UC
DC
minus100
minus80
minus60
minus40
minus20
0
20
Yaw
rate
(deg
s)
1 2 3 4 50Time (s)
(c) Yaw rate ()
Figure 21 Split 120583-surface braking test
The important variables for this test are (1) steeringwheel angle (120575) Figure 21(a) (2) lateral acceleration ()Figure 21(b) and (3) yaw rate () Figure 21(c) Figure 21(a)shows that the driver does not affect significantly the steeringwheel angle that is theGCC andDCapproaches can stabilizethe vehicle On the other hand the UC vehicle begins to losecontrol and the driver has to make a huge adjustment to tryto keep the stability of the vehicle It can be noticed that thesteering allocation system takes action increasing the steeringmaneuver for DC this extra movements cause the vehicle todiverge slightly from the original path The steering actionfor GCC is 879 less than UC vehicle while DC has 806less movement Because the lateral acceleration is induced by
the steering action similar results are obtained Figure 21(b)GCC has 887 less lateral acceleration than UC and 101less acceleration than DC
Finally to evaluate the rotational movements of thevehicle in the road the yaw rate is analyzed Figure 21(c)shows that in UC the driver loses completely the vehiclecontrol causing toomuch yawmotion GCC has 98 less yawrate than UC and 96 less than DC
5 Conclusions
A novel Global Chassis Control system was proposed Itcombines fuzzy logic inference systems data-based logic and
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 17
heuristic techniques as classifiers allocation systems andmodel-free controllers also it takes the advantages of a prioriknowledge of a vehicle driving to develop an efficient controlstrategy Also it has the advantage of beingmodular and com-putationally light based on Principal Components Analysisdata reduction was applied Most of the computing is doneoffline the onboard systems only execute the classification ofthe driving situations and calculate the allocation and controlprocedures
The evaluation of the strategy was performedwith severalwell-known tests using CarSim Simulation results showedthat the performance of the Global Chassis Control systemoutperforms the uncontrolled vehicle case and the Decen-tralized Controllers scheme that do not have coordinationfeatures Qualitative and quantitative results of the evaluationdemonstrate the importance of a coordination level whendifferent controllers coexist and interact in an integratedsystem as a vehicle Such coordination level consists in aclassification algorithm based on the 119896-Nearest Neighborclustering technique supported by a Suspension AdjustmentPlane to identify different driving situations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors thank Tecnologico de Monterrey and CONACyTfor their partial support through the Automotive Consortiumresearch chair and PCP 0310 and 0613 bilateral (Mexico-France) projects
References
[1] H Chou and B DrsquoAndrea-Novel ldquoGlobal vehicle control usingdifferential braking torques and active suspension forcesrdquoVehicle System Dynamics vol 43 no 4 pp 261ndash284 2005
[2] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995
[3] TechCast ldquoBubble charts of TechCastrsquos latest results on TRANS-PORTATIONsrdquo Tech Rep TechCast-LLC 2012
[4] WHO ldquoGlobal status report on road safety 2013 supporting adecade of actionrdquo Technical Report World Health Organiza-tion 2013
[5] C J Kahane ldquoLives Saved by vehicle safety technologies andassociated federal motor vehicle safety standards 1960 to 2012passenger cars and LTVs with reviews of 26 FMVSS and theeffectiveness of their associated safety technologies in reducingfatalities injuries and crashesrdquo Tech Rep National HighwayTraffic Safety Administration Washington DC USA 2015
[6] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 1ndash6Harbin China September 2008
[7] N Schilke R Fruechte N Boustany A Karmel B Repa andJ Rillings ldquoIntegrated vehicle controlrdquo in Proceedings of the
International Congress onTransportation Electronics pp 97ndash106Dearborn Mich USA October 1988
[8] T El-Sheikh Concept of global chassis control using modelreference and virtual actuators [PhD thesis] University ofCalifornia Oakland Calif USA 2011
[9] J He Integrated vehicle dynamics control using active steeringdriveline and braking [PhD thesis] University of Leeds LeedsUK 2005
[10] M Valasek O Vaculin and J Kejval ldquoGlobal chassis controlintegration synergy of brake and suspension control for activesafetyrdquo in Proceedings of the 7th International Symposium onAdvanced Vehicle Control pp 495ndash500 Arnhem The Nether-lands 2004
[11] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Senameand L Dugard ldquoGlobal chassis control using braking andsuspension systemsrdquo in Proceedings of the 20th Symposium ofthe International Association for Vehicle System Dynamics pp13ndash17 Berkeley Calif USA August 2007
[12] R D Fruechte A M Karmel J H Rillings N A Schilke NM Boustany and B S Repa ldquoIntegrated vehicle controlrdquo inProceedings of the 39th IEEE Vehicular Technology ConferenceGateway to New Concepts in Vehicular Technology vol 2 pp868ndash877 San Francisco Calif USA May 1989
[13] J Andreasson and T Bunte ldquoGlobal chassis control based oninverse vehicle dynamicsmodelsrdquoVehicle SystemDynamics vol44 supplement 1 pp 321ndash328 2006
[14] O Mokhiamar and M Abe ldquoHow the four wheels shouldshare forces in an optimumcooperative chassis controlrdquoControlEngineering Practice vol 14 no 3 pp 295ndash304 2006
[15] W Cho J Choi C Kim S Choi and K Yi ldquoUnified chassiscontrol for the improvement of agility maneuverability andlateral stabilityrdquo IEEE Transactions on Vehicular Technology vol61 no 3 pp 1008ndash1020 2012
[16] M Ali P Falcone C Olsson and J Sjoberg ldquoPredictive preven-tion of loss of vehicle control for roadway departure avoidancerdquoIEEE Transactions on Intelligent Transportation Systems vol 14no 1 pp 56ndash68 2013
[17] S Sato H Inoue M Tabata and S Inagaki ldquoIntegrated chassiscontrol system for improved vehicle dynamicsrdquo in Proceedingsof the International Symposium on Advanced Vehicle Control(AVEC rsquo92) pp 413ndash418 Yokohama Japan 1992
[18] C Poussot-Vassal Robust multivariable linear parameter vary-ing automotive global chassis control [PhD thesis] InstitutPolytechnique de Grenoble Grenoble France 2008
[19] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011
[20] S Fergani O Sename and L Dugard ldquoPerformances improve-ment through an 119871119875119881 = 119867
infincontrol coordination strategy
involving braking semi-active suspension and steering Sys-temsrdquo in Proceedings of the 51st IEEE Conference on Decisionand Control (CDC rsquo12) pp 4384ndash4389 Maui Hawaii USADecember 2012
[21] T Gordon M Howell and F Brandao ldquoIntegrated controlmethodologies for road vehiclesrdquoVehicle System Dynamics vol40 no 1ndash3 pp 157ndash190 2003
[22] J Nayak B Naik and H Behera ldquoFuzzy C-means (FCM)clustering algorithm a decade review from 2000 to 2014rdquo inComputational Intelligence in Data MiningmdashVolume 2 L CJain H S Behera J K Mandal and D P Mohapatra Eds vol
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
18 Mathematical Problems in Engineering
32 of Smart Innovation Systems and Technologies pp 133ndash149Springer 2015
[23] P Gaspar Z Szabo J Bokor C Poussot-Vassal O Sename andL Dugard ldquoTowards global chassis control by integrating thebrake and suspension systemsrdquo in Proceedings of the 5th IFACSymposium on Advances in Automotive Control pp 563ndash570Pajaro Dunes Calif USA August 2007
[24] A Tavasoli M Naraghi and H Shakeri ldquoOptimized coordina-tion of brakes and active steering for a 4WS passenger carrdquo ISATransactions vol 51 no 5 pp 573ndash583 2012
[25] T Raste R Bauer and P Rieth ldquoGlobal chassis controlchallenges and benefits within the networked chassisrdquo in Pro-ceedings of the FISITA World Automotive Congress MunichGermany 2008
[26] W Chen H Xiao L Liu J W Zu and H Zhou ldquoIntegratedcontrol of vehicle system dynamics theory and experimentrdquoin Advances in Mechatronics chapter 1 InTech Rijeka Croatia2011
[27] R P Good D Kost and G A Cherry ldquoIntroducing a unifiedPCA algorithm for model size reductionrdquo IEEE Transactions onSemiconductor Manufacturing vol 23 no 2 pp 201ndash209 2010
[28] R Isermann Fault-Diagnosis Systems Springer Berlin Ger-many 1st edition 2006
[29] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005
[30] S Krishna S Narayanan and S D Ashok ldquoControl of yawdisturbance using fuzzy logic based yaw stability controllerrdquoInternational Journal of Vehicular Technology vol 2014 ArticleID 754218 10 pages 2014
[31] S Guo S Yang and C Pan ldquoDynamic modeling of magne-torheological damper behaviorsrdquo Journal of Intelligent MaterialSystems and Structures vol 17 no 1 pp 3ndash14 2006
[32] M Doumiati O Sename L Dugard J-J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of