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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012 3441

A New Control Architecture for Robust Controllersin Rear Electric Traction Passenger HEVs

Rafael Coronel Bueno Sampaio, Student Member, IEEE, André Carmona Hernandes, Member, IEEE,Vinicius do Valle Magalhães Fernandes, Student Member, IEEE, Marcelo Becker, Member, IEEE, and

Adriano Almeida Gonçalves Siqueira, Member, IEEE

Abstract—It is well known that control systems are the coreof electronic differential systems (EDSs) in electric vehicles(EVs)/hybrid HEVs (HEVs). However, conventional closed-loopcontrol architectures do not completely match the needed abilityto reject noises/disturbances, especially regarding the input ac-celeration signal incoming from the driver’s commands, whichmakes the EDS (in this case) ineffective. Due to this, in thispaper, a novel EDS control architecture is proposed to offer anew approach for the traction system that can be used witha great variety of controllers (e.g., classic, artificial intelligence(AI)-based, and modern/robust theory). In addition to this, a modi-fied proportional–integral derivative (PID) controller, an AI-basedneuro-fuzzy controller, and a robust optimal H∞ controller weredesigned and evaluated to observe and evaluate the versatilityof the novel architecture. Kinematic and dynamic models of thevehicle are briefly introduced. Then, simulated and experimentalresults were presented and discussed. A Hybrid Electric Vehicle inLow Scale (HELVIS)-Sim simulation environment was employedto the preliminary analysis of the proposed EDS architecture.Later, the EDS itself was embedded in a dSpace 1103 high-performance interface board so that real-time control of the rearwheels of the HELVIS platform was successfully achieved.

Index Terms—Control architecture, control system, electronicdifferential system (EDS), hybrid electric vehicle (HEV), hybridelectric vehicle in low scale (HELVIS) mini-HEV.

I. INTRODUCTION

BASED ON the global warming issue and the potentialdepletion of oil resources worldwide and following our

tradition of carrying out research focused on mobile roboticsfor transportation systems [1], we recently started studies onthe substitution of conventional oil-based vehicles by hybridelectric vehicles (HEVs) [2], [3]. Important institutes [4]–[6]and industries all over the world are investigating new tech-nologies in this field and searching for skilled manpower re-sources, which is still very scarce. Grounded on that idea, weare giving the opportunity for undergraduate and graduatedstudents to be in touch with HEV technologies, becoming one

Manuscript received December 9, 2011; revised April 24, 2012; acceptedJune 11, 2012. Date of publication July 12, 2012; date of current versionOctober 12, 2012. This work was supported in part by the Brazilian ElectricityRegulatory Agency, by Companhia Paulista de Força e Luz, and by Fundaçãopara o Incremento da Pesquisa e do Aperfeiçoamento Industrial. The review ofthis paper was coordinated by Prof. M. Krishnamurthy.

The authors are with the University of São Paulo, 13566-590 São Carlos,Brazil (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2012.2208486

of the first universities in South America to have a real line ofresearch currently running in this area. The “Electric WheelsProject” is supported by the Brazilian Electricity RegulatoryAgency (ANNEL) and the Innovation Center of the State ofSão Paulo Energy Distributor (CPFL). One of the aims ofthe group is to bring new technologies to the developmentof electromechanical wheels to replace conventional wheels inpreexisting passenger vehicles, turning them into series HEVs.Concrete results of such research were recently published [7],which has strengthened the group, encouraging the launch ofthe project, the design of a mini-HEV named Hybrid ElectricVehicle In Low Scale (HELVIS) [8], and the implementationof a parametric vehicular simulator named HELVIS-Sim [9],all of which have significantly expedited researches on HEVs,especially regarding the design and evaluation of two-wheel-drive/rear-wheel-drive (2WD/RWD) electronic differentialsystems (EDSs) [10], [11] for passenger EVs/HEVs [12]. Fur-thermore, such tools have proven to be valuable opportunitiesto encourage researchers and enthusiasts to develop a newgeneration of cleaner vehicles for the new century [13].

Many works in the literature bring relevant results for theEDS problem. When it comes to numerical analysis, the workin [14] and [15] must be highlighted. Other works proposedeither classic and nonrobust controller approaches [16] or verysimple plant models [17], [18]. A magnetic flow algorithm wasproposed in [19], whereas observers were proposed in [20].The use of artificial intelligence (AI)-based controllers wasdescribed in [21] and [22]. In addition to accurate models ofthe vehicle and the power train, the core of a well-designedEDS lies in the following: 1) the control system’s ability toquickly and properly apply corrective actions and 2) its robust-ness against noises/disturbances/uncertainties. Maneuverabilityand stability are considered as direct functions of these twovariables. Thus, the vehicle can ultimately follow AckermanGeometry and minimize the slip phenomena [7], [23]. Thiswork focuses on the design and both simulated and experimen-tal evaluation of an EDS for a rear electric traction HEV thatcan be used with a great variety of control systems. In this case,the optimal H∞ robust controller for a HELVIS EDS has shownto be highly effective [12]. However, the robust control theorydemands that the control architecture (and, thus, the EDS ar-chitecture) be rearranged. Thus, this work also proposes a newcontrol architecture to match the EDS problem for the optimalH∞ controller [24]–[27], which consequently allows the useof other control systems of different proposes. It is expectedthat such a novel architecture leads to the improvement of the

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3442 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

Fig. 1. Body diagram of a front-steering rear-traction hybrid electric passen-ger vehicle.

TABLE ITABLE OF THE VARIABLES INVOLVED IN THE MODEL

EDS for a wide class of vehicles, including passenger cars.Thus, to show how in-depth and versatile the novel EDS moduleis in terms of performance and operability, two more distinctcontrol approaches were also tested: One classical modifiedproportional–integral derivative (PID) controller is outlined[28], [29], as is one neuro-fuzzy control system [30]–[33].

At the end, simulated and experimental results, which areboth performed in HELVIS-Sim simulation environment andHELVIS mini-HEV, are presented and analyzed, respectively.

II. ELECTRONIC DIFFERENTIAL SYSTEM

PROBLEM STATEMENT

A. Vehicle Dynamic and Kinematic Modeling

The EDS formulation is based on a 2-D rigid body dynamicmodel [7]. Fig. 1 shows the body diagram of a front-steeringrear-traction hybrid electric passenger vehicle, and Table Ishows all parameters that are involved in such a model.

From the free body diagram of the vehicle, it results inthe following dynamic equations that represent the kinematicbehavior of the car:

V̇cgx =VcgyΩcg −μg

L

(l2 cos δ1

2+

l2 cos δ22

+ l1

)

+1m

(P3(t)

Vcgx +bΩcg

2

+P4(t)

Vcgx − bΩcg

2

)

− CψF sinδ1m

(δ1 −

Vcgy + l1Ωcg

Vcgx +bΩcg

2

)

− CψF sin δ2m

(δ2 −

Vcgy + l1Ωcg

Vcgx − bΩcg

2

)(1)

V̇cgy = − VcgyΩcg −2VcgxCψR

m

(Vcgy − l2Ωcg

V 2cgx − b2

4 Ωcg

)

− μgl22L

(sin δ1 + sin δ2)

+CψF cos δ1

m

(δ1 −

Vcgy + l1Ωcg

Vcgx + b2Ωcg

)

+CψF cos δ2

m

(δ2 −

Vcgy + l1Ωcg

Vcgxb2Ωcg

)(2)

Ω̇cg =μmgbl2

4LIz(cos δ2 − cos δ1)−

μmgl1l22LIz

(sin δ1 + sin δ2)

+b

2Iz

(P3(t)

Vcgx +bΩcg

2

− P4(t)

Vcgx − bΩcg

2

)

+CψF

Iz

(δ2 −

Vcgy + l1Ωcg

Vcgx − bΩcg

2

)(l1 cos δ2 +

b

2sin δ2

)

+CψF

Iz

(δ1 −

Vcgy + l1Ωcg

Vcgx +bΩcg

2

)(l1 cos δ1

b

2sin δ1

)

+2Vcgxl2CψR

Iz

(Vcgy − l2Ωcg

V 2cgx − b2

4Ωcg

). (3)

The aforementioned equations are solved from the amount ofpower individually applied to both rear actuators and therefore,in practice, show how the control action will change the dy-namic behavior of the vehicle. Exclusively considering the EDSproblem, the desired angular velocities for both rear wheelsmust to be calculated, and it can be obtained from two ofthe kinematic parameters, i.e., the velocity of the car Vx andthe maneuver radius Rcg, respectively. The first parameter canbe extracted from (1), and the second can be calculated fromthe steering angles, which are related to Ackerman Geometry,whose formalism is described in [23]. Finally, the calculatedangular velocities of both rear wheels can be determined byusing [7]

ω3 =Vcg

Rcgr

[√R2

cg − l22 −b

2

](4)

ω4 =Vcg

Rcgr

[√R2

cg − l22 +b

2

]. (5)

One important aspect is that, regardless of the dynamicmodel ability to predict the vehicle’s accelerations from the

SAMPAIO et al.: CONTROL FOR ROBUST CONTROLLER IN REAR ELECTRIC TRACTION PASSENGER HEV 3443

power that is applied to each wheel (which is very useful to sim-ulation evaluation), it represents only an indirect measurement.In practical terms, the vehicle speed can be easily read from thecontroller-area-network bus network embedded in the real-scalecar. The maneuver radius can be estimated by placing an inertialmeasurement unit (IMU) close to the center of gravity (CG) ofthe vehicle. Real-time IMU reading ensures the accuracy of thesystem, even at small slip situations. This procedure is feasibleand has been commonly accomplished in many experiments inthe “SENA Project” at Mobile Robotics Laboratory [1]. Suchsensor fusion has proven to be useful and has been widely usedin many mechatronics applications, including transportationsystems.

III. CONTROL SYSTEM DESIGN AND THE NEW

CONTROL ARCHITECTURE

The most important element of the EDS design is the controlsystem that acts over the adjustment of the electric wheelangular speeds. It is essential that the control system quicklyprovides the actuators with the correct amount of current toproduce the least possible error and the least overshoot sothat the wheel can roll without sliding. A great variety ofcontrol approaches based on different techniques match theEDS problem [14]–[22]. Thus, in this work, three differentcontrol approaches have been proposed [7], as follows:

1) classic approach, through the use of the modified PIDequations;

2) AI approach, through the use of the neuro-fuzzycontroller;

3) robust approach, through the use of the optimal H∞controller.

A. Modified Classic PID Controller

The implementation of a modified PID controller considersthe rearrangement of the recurrence equations for a discretePID controller, as described in [28], to improve the quality ofthe process response. One weighting variable is added to theproportional gain, and filters are implemented into both deriva-tive and integrative terms [29]. It also considers the positionalform with backward difference approximation to the integrativeterm (I) and Tustin approximation to derivative term (D), whosecontrol laws for proportional, integrative, and derivative termscan be represented by

P (k)=Kp [βr(k)−y(k)] (6)

I(k)=I(k−1)+KpT

Tie(k−1) (7)

D(k)=2Td−TN

2Td+TND(k−1)+

2KpTdN

2Td+TN(y(k)−y(k−1)) .

(8)

respectively.Variable Kp is related to the proportional action, Ti refers to

the integral action, and Td is related to the derivative action.Variable r(k) is the reference (desired) value, y(k) is the

Fig. 2. Body diagram of the design of the neuro-fuzzy controller.

process output signal, and e(k) refers to the error. Variable Tis the sample time, and N is a scalar such that the realizabilityof the controller is ensured. (In practice, values in the intervalof 3 ≤ N ≤ 20 are commonly used.) Proportional action finetuning is achieved by inserting a parameter β over the referencesignal [28] so that considerable improvement in both steady-state error and transitory response is observed.

The reset-windup effect occurs over the integrative actionand could be suppressed through the implementation of an anti-reset-windup filter [28]. Regarding the derivative action, it canalso present an unexpected behavior regarding the system’sstability in determined circumstances, e.g., high frequencies.At this point, derivative contribution adds a rising gain to theplant, which is commonly referenced as the quick derivateeffect. In this case, an anti-quick derivate filter is implementedto decrease the closed-loop gain. It turns out that, from thederivative part in the PID controller (8), the presence of onepole in the infinity is observed, which implies the indefinitegrowth of the derivative gain as the frequency raises. That turnsthe system significantly unstable due to the saturation of thecontrol output. The anti-quick derivate filter aims to add a poleto the derivative equation to improve the controllability of theplant.

B. AI-Based Neuro-Fuzzy Controller

The design of a neuro-fuzzy controller is based on twodistinct and very well-defined stages [30] and is inspired incombining the benefits of the knowledge extraction provided bythe fuzzy logic plus the low computational cost offered by theartificial neural networks (ANNs), which yield a very efficientclass of controllers.

The first stage regards the design of a fuzzy controller,involving fuzzification, inference, and defuzzification, whichoriginates a fuzzy control surface, consisting of two inputand one output variables. The second stage consists of theprocess of training a neural network that can learn how thefuzzy controller behaves. Fig. 2 shows all distinct parts thatcompose the design of the neuro-fuzzy controller. Phase (A)comprehends the establishment of the rule base, fuzzification,inference, and defuzzification so that the fuzzy control surfaceis generated (B). The vectors containing all data that define


Fig. 3. Rules matrix established to the electric wheels control.

the fuzzy control surface are then sent to the ANN (C). It isexpected that the neural network can reproduce the very samefuzzy control surface (D).

1) Fuzzification, Inference, and Defuzzification: Fuzzylogic executes a rule-based controller, instead of a model-basedcontroller. This approach is useful because, even if a reliablemodel is available, nonlinearities often raise in maneuvers [7].The controller inputs are the angular speed error E and itsderivative dE. The control action defines the output dU . Fuzzi-fication involves the representation and the decision makingbased on linguistic notations, as for inputs (E, dE) and outputs(dU). In our work, it is determined through the followingvariables:

1) NL: negative large;2) NM: negative medium;3) NS: negative small;4) Z: zero;5) PS: positive small;6) PM: positive medium;7) PL: positive large.

Gaussian functions were used to represent the membershipfunctions for E, dE, and dU because, when compared withother shapes (trapezoidal and triangular), they presented thebest response. The Mandani method was used to the inferenceprocess, and a set of 49 rules was established, as shown inFig. 3. The decision-making procedure was based on thoserules. Each combination between each value of E and dEcorresponds to a particular control level dU .

The MAX-MIN composition and CG method were used inthe defuzzification process [33]. Thus, the final result of thedesign of a fuzzy controller is shown in Fig. 4.

2) Feedforward ANN Training Process: ANNs present asatisfactory performance in terms of low computing cost. Inparticular, feedforward ANN are indicated in classificationproblems, where each input vector is associated to an outputvector [30]. This affirmation perfectly meets the problem ofcontrolling the electric wheels since there is a correspondingcontrol output dU to each couple error derivative E − dE.Thereby, a four-layered feedforward ANN was designed with(Nc/2) + 3 hidden layers, where Nc is the number of inputs.

Fig. 4. Fuzzy control surface as the result of the fuzzy design.

Fig. 5. Obtained fuzzy control surface. (a) Reproduced surface after thetraining process of the feedforward ANN.

Such configuration presents superior performance, comparedwith a three-layered feedforward ANN regarding the num-ber of parameters that are necessary for the training pro-cess. Regarding the NN inputs and outputs, a pair of inputsx = (x

(k)1 , x

(k)2 ) was considered, representing error E and its

derivative dE. In addition, the output y = y(k)1 , representing

the increase/decrease in the control action [32], was alsoconsidered. A MATLAB toolbox was used, employing theLevenberg–Marquardt algorithm. It is important to highlightthat the training performance was in compliance with meansquare error (MSE) criteria.

3) Neuro-Fuzzy Controller: When the ANN training pro-cess is well succeeded, both control surfaces must be verysimilar. (Remember that the fuzzy control surface was recon-structed by the ANN.) Fig. 5(a) shows the fuzzy control surfaceitself, obtained from the implementation of the fuzzy controller,whereas Fig. 5(b) shows the surface provided by the ANN afterthe training process. It is clear that the four-layered feedforwardneural network has reconstructed the original surface. This indi-cates that the ANN could successfully learn how to eventuallyprovide the EDS with the proper control actions, as if it is incharge of an essentially fuzzy-based controller.

The accuracy of the ANN can be quantified by comparingthe then-reconstructed control surface and the original controlsurface obtained by the fuzzy system. The MSE criteria wasused to compute an mean error value of e ≈ 5 · 10−5.


Fig. 6. Augmented plant of the EDS module, representing the transfer func-tion Tzw .

C. Robust Optimal H∞ Controller

The synthesis of the optimal H∞ controller was based on[24]–[27], considering the fact that the plant is stabilizable anddetectable. Thus, the resulting augmented plant Gap, i.e., therespective block diagram, is shown in Fig. 6.

The γ-iteration algorithm was employed, aided by a Matlabtoolbox, through which the γ value is reduced until the optimalvalue of γopt is achieved so that at the end of the procedure,both error and control action weighting functions (We and Wu,respectively) and controller K(s) itself are obtained. Thus, thenorm of the closed-loop transfer function Tzw between w andz1,2 must satisfy the following condition:

Tzw =

∥∥∥∥ WeSWuKS

∥∥∥∥∞

=

∥∥∥∥ WeSWuR

∥∥∥∥∞

< γ (9)

where We and Wu represent the weighting functions of con-troller K. Values from γmin = 0.05 to γmax = 150 were usedfor the iterative process. The value of γ achieved is 0.1366,which is in compliance to the optimal H∞ and aims to minimizethe norm of the transfer function Tzw. The sensitivity functionwas given by S, whereas R is the transfer function between thecontrol action and the reference input. To guarantee stabilityand robustness relative to disturbances/noises/uncertainties, it isnecessary that the gains of S are low at low frequencies, so thatnoise/disturbance rejection can be guaranteed, i.e., |WeS| ≤ 1.On the other hand, R gains must be low at high frequenciesto achieve the same noise rejection level, i.e., |WuR| ≤ 1.The previous two robustness criteria are directly related tothe following: 1) stability against model parametric variations;2) stationary error → 0; 3) robustness, even with open-loopuncertainties and variations; and 4) robustness against noisesthat are inserted into the plant. The sensitivity function mustideally satisfy peak sensitivity Ms and bandwidth ωb so thatthe following relation must be respected:

|S(s)| ≤∣∣∣∣∣ s

sMs

+ ωb

∣∣∣∣∣ . (10)

The closed-loop value for the bandwidth is such that ωb ≈ωn. In addition, for a good control design, it is desirable that Ms

does not reach high values. Values for both bandwidth and peaksensitivity are empirically chosen, observing the frequencyresponses and the natural frequency of the plant. Thus, thebest values are Ms = 160 and ωb = 50. Thus, both weighting

Fig. 7. Unsuitable feedback block diagram due to the high ability of noiserejection by the H∞ controller.

functions obtained through the γ-iteration algorithm and therobustness criteria are given by

We(s) =0.00625s+ 50

s+ 0.05(11)

Wu(s) =s+ 1

0.1s+ 9 · 108 . (12)

From (11) and (12), and all previous described procedures,the following controller K is achieved:

K(s) =5.103s2 + 4.592 · 1010s+ 1.714 · 1011

s3 + 7776s2 + 3.061 · 107 + 1.508 · 106 . (13)

D. New Control Architecture

Generally, the driver’s throttle input is intuitively added tothe control signal in an attempt to simply superimpose thecontrol actions computed by the EDS. Such control architectureand strategy were proposed in [18] and are shown in Fig. 7.In the case of HELVIS EDS, the H∞ controller acts as afilter, degrading the driver’s acceleration input and turning anyattempt to impose new acceleration commands into noise [12].

Fig. 8 shows the exploded view of the proposed architecture,which matches the EDS application with robust controllers.The kinematics block calculates the desired left and right rearangular speeds [ωd

l ωdr ]

T based on reading the states of the statevector [V̇x V̇y Ω̇x Vx Vy Ωx x y z]T .

In practice, the driver’s throttle command β is considered asthe representation of the desired speed of the vehicle (which, inturn, represents the angular speeds of the wheels). Similar to thecalculus of the desired angular speeds based on the speed of thecar Vx and on the maneuver radius (through reading data fromIMU), the kinematics block calculates βr and βl using (4) and(5). These results are used to provide the controllers with βr

and βl as if they were the reference values ([ωdl ωd

r ]T ) since Vx

in both equations is represented by β. The states of the speedsare provided by the dynamics block from both voltage andcurrent [icl i

cr e

cr e

cl ]T delivered to the motors, which allows the

estimation of the power involved [Pl Pr]T for each wheel. As

for the IMU data, it provides the EDS with real measurements,regardless of a possible tire slipping, which makes the overallsystem more accurate and robust.

The control loop is then rearranged, so that the throttle inputis the signal with highest priority. However, the subtraction ofthe desired speeds, which is provided by the kinematics and


Fig. 8. Novel EDS control architecture proposed in this work.

based on the dynamics of the vehicle, ensures that the driver’sthrottle command is assured. Thus, in practice, the controllersenses the resulting error

e = 2βl,r − ωdl,r − ωc

l,r (14)

where [ωcl ω

cr]

T is the vector with the measured values for bothrear wheel angular speeds.

The efficiency of the new proposed control architectureover the conventional control architecture could be attestedin a bench test experiment where the performance of bothapproaches could be evaluated. As this paper is related andfocused on robust controllers, both the new architecture and theconventional architecture were submitted to such experimentwith the optimal H∞ controller in charge of the EDS, whereasthe driver input command was subject to observation. Fig. 9shows that, in fact, the throttle input is rejected as noise, whenthe architecture of Fig. 7 is employed. Indeed, any attemptto request new acceleration inputs (continuous curve) willbe degraded (dotted curve) since it is considered an externaldisturbance. Regardless of the magnitude of the throttle inputcommand, the H∞ controller always acts to minimize suchdisturbance, converging the throttle signal to a minimum value.

That is, the architecture proposed in Fig. 7 cannot be ulti-mately applied to our case. The figure still shows that the pro-posed architecture in this work preserves the throttle command

Fig. 9. Behavior of the throttle input signal using the novel proposed HELVIScontrol architecture.

Fig. 10. HELVIS mini-HEV 2WD/RWD series platform.

imposed by the driver, which is input intact to the kinematicsblock (dashed curve).

IV. SIMULATION AND EXPERIMENTAL TOOLS

All following tests concerning the proposed architecture forthe EDS and the three control approaches are first evaluated in asimulation environment and then analyzed through experimen-tal tests. Thus, a simulation toolbox and a low-scale HEV arepresented next.

A. HELVIS Mini-HEV Platform

As both dynamic and kinematic models for the vehicle areparametrized and the calculus of the desired angular speedsare essentially linear, which allows the scalability of the EDSmodule, all experimental tests were extended to a mini-HEVplatform named HELVIS, which has been successfully con-structed and has been presented at the VPPC 2011 [8].

The HELVIS platform, which is shown in Fig. 10, is a low-scale rear electric traction series HEV endowed with a steeringmechanism (which is in compliance with Ackerman Geome-try). The vehicles’ EDS is part of a 2WD/RWD electric drivetrain [11], composed by two dc motors, each with planetarygears that can deliver 10 W of power to each rear wheels.The general architecture of the HELVIS drive train is shown inFig. 11. It can be classified as a series hybrid drive train since anelectrical coupler handles the power incoming from two distinctsources, which are, in this case, the battery and the generator[10]. In this configuration, the electronic control unit deals with


Fig. 11. General architecture and physical parameters of the series-hybridHELVIS mini-platform.

TABLE IIHELVIS CONSTRUCTIVE PARAMETERS

many functional tasks, e.g., incoming data from sensors, batterystate of charge, integrated circuit engine revolutions per minute,and obviously, EDS powering and data processing. Some ofthe most important constructive parameters of the HELVISplatform are listed in Table II.

B. HELVIS-Sim Simulation Environment

In the case of EVs/HEVs, a simulation tool can be even moreuseful if one considers the fact that EV/HEV component partsare not easy to obtain since those types of vehicles are not astrivial as conventional vehicles are. In this context, a simulationtool can aid engineers and students in the development andmanufacturing of specific pieces for general, as well as for aspecific function in an EV/HEV. Henceforth, a useful Simulink-based simulator named HELVIS-Sim is briefly presented [9].HELVIS-Sim is a parametric simulator that emulates, amongmany other functions, the HELVIS platform EDS module. Inaddition, as the simulation architecture is basically constructedover a set of blocks, Simulink perfectly fits this project sinceit eases the insertion of brand new blocks as well as theintegration to our dSpace real-time interface board to run theexperimental evaluation of HELVIS-Sim [8]. In this paper,the focus is on the control of the EDS module. HELVIS-Simconsiders the driver’s input commands, both vehicle dynam-ics and kinematics, sensors, actuators, control systems, signalconditioning, and other functions. It is important to emphasizethat this simulator allows users to experience different classesof controllers in the torque split-up problem.

Fig. 12. General architecture and functional blocks of HELVIS-Sim simula-tion environment.

The HELVIS-Sim EDS architecture is shown in Fig. 12. Inthis figure, one may observe that the EDS-related modules aredisplayed, such as torque and wheel speed calculation, controlsystem, motor dynamics, kinematics and dynamics, driver’scommands, and steering mechanism.

V. EVALUATION OF RESULTS FOR THE ELECTRONIC

DIFFERENTIAL SYSTEM CONTROL

AND NEW ARCHITECTURE

Since bench tests have proved the efficiency of the newcontrol architecture over the conventional control architecture,the EDS has been set up with the proposed architecture. Then,it was submitted to both simulated and experimental tests. TheEDS performance could be evaluated while the three previouslydesigned controllers were individually applied.

Two situations were observed for both simulation and exper-imental tests as follows:

1) Case I: acceleration of the platform from 0 to 2 m/s withboth side steering and maximum steering angles;

2) Case II: gradual attenuation of the acceleration percent-age from 2 m/s, following sinusoidal pattern with bothside steering and maximum steering angles.

A. Results Achieved From the HELVIS-Sim

1) Case I—Acceleration of the Platform From 0 to 2 m/sWith Both Side Steering and Maximum Steering Angles:Fig. 13 shows the results obtained from the control of the EDSby the modified PID controller, where it is visible that thesystem adjusts the rear wheel speeds as the maneuver occurs.One may also observe a minimum value for the steady-stateerror and quick response. Fig. 14 shows the expanded view ofthe response of the rear wheel angular speeds.

Fig. 15 shows the response of the process of control ofthe EDS by the neuro-fuzzy controller. A millisecond-order


Fig. 13. HELVIS-SIM simulation response for the proposed EDS module,adjusted by the modified PID controller, to a constant speed and steeringmaneuver.

Fig. 14. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the modified PID controller, to a constantspeed and steering maneuver.

Fig. 15. HELVIS-SIM simulation response for the proposed EDS module, ad-justed by the neuro-fuzzy controller, to a constant speed and steering maneuver.

response delay occurs as the steering maneuver runs, althoughthe steady-state error is not present. Fig. 16 shows the expandedview of the response of the rear wheel angular speeds.

Fig. 17 shows the results of the control of the EDS bythe optimal H∞ controller. Both steady-state error and timedelay are not sensed as the vehicle is subject to steering. Theexpanded view of the response of the rear wheel angular speedscan be observed in Fig. 18.

2) Case II—Gradual Attenuation of the Acceleration Per-centage From 2 m/s, Following a Sinusoidal Pattern With Both

Fig. 16. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the neuro-fuzzy controller, to a constantspeed and steering maneuver.

Fig. 17. HELVIS-SIM simulation response for the proposed EDS module,adjusted by the optimal H∞ controller, to a constant speed and steeringmaneuver.

Fig. 18. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the optimal H∞ controller, to a constantspeed and steering maneuver.

Side Steering and Maximum Steering Angles: Fig. 19 showsthe responses of the adjustment of both rear wheel angularspeeds by the modified PID controller during the steeringmaneuver. Both steady-state error and response delay are notobservable. The expanded view of the response of the rearwheel angular speeds can be observed in Fig. 20.

Fig. 21 shows the results of the control of the EDS by neuro-fuzzy controller during the steering maneuver as well as thespeed variation. A millisecond-order delay is noted. As a resultof it, a very small steady-state error is also perceptible. Fig. 22


Fig. 19. HELVIS-SIM simulation response for the proposed EDS module,adjusted by the modified PID controller, to a speed on sinusoidal pattern andsteering maneuver.

Fig. 20. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the modified PID controller, to a speed onthe sinusoidal pattern and steering maneuver.

Fig. 21. HELVIS-SIM simulation response for the proposed EDS module,adjusted by the neuro-fuzzy controller, to a speed on the sinusoidal pattern andsteering maneuver.

shows the expanded view of the response of the rear wheelangular speeds.

Fig. 23 shows the results obtained from the optimal H∞controller. It is seen that the controller provides high accuracyand quickness in response, which eliminates both steady-stateerror and response delay. Fig. 24 shows the expanded view ofthe response of the rear wheel angular speeds by the optimalH∞ controller.

An important quantitative analysis can be drawn based onTable III data. This table presents the steady-state error, time

Fig. 22. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the neuro-fuzzy controller, to a speed onsinusoidal pattern and steering maneuver.

Fig. 23. HELVIS-SIM simulation response for the proposed EDS module,adjusted by the optimal H∞ controller, to a speed on the sinusoidal pattern andsteering maneuver.

Fig. 24. Expanded view of the HELVIS-SIM simulation response for theproposed EDS module, adjusted by the optimal H∞ controller, to a speed onthe sinusoidal pattern and steering maneuver.

delay, and overshoot mean values acquired in HELVIS-Simsimulations. Such review can reveal important data, which cansignificantly determine the choice of the controller that best fitsthe EDS application. In this case, all three controllers presentsatisfactory values for the three parameters under analysis,although optimal robust H∞ controller performance presentsthe best overview overall. Thus, it can also be concluded thatthe novel proposed architecture perfectly matches the EDSproblem, making it possible to embed different controllers.


TABLE IIICONTROL PERFORMANCE QUANTITATIVE COMPARISON TABLE

IN SIMULATION (MEAN VALUES)

Fig. 25. Experimental response for the HELVIS platform EDS module,adjusted by the modified PID controller, to a constant speed and steeringmaneuver.

B. Experimental Results Achieved From the HELVIS Platform

Experimental results followed the very same inputs pre-viously used to the simulated evaluation of the EDS fromHELVIS-Sim environment. Communication between the realEDS and the control module was achieved by using a high-performance dSpace 1103 optical fiber interface board. Controlof both motors was individually accomplished through twodifferent pulsewidth modulation channels whose duty cycle isof approximately 12 kHz, which is reasonable for a real-timeapplication such as the EDS control.

Once again, the following cases were evaluated.

Case I: Fig. 25 shows the EDS response while the modifiedPID controller adjusts both rear wheel angular speeds. Itis possible to observe that, as the vehicle speed increasesand the vehicle steers, the controller follows the desiredvalues for the calculated/desired angular speeds. Moreover,the EDS alternates the module of the reference signal, asthe vehicle changes the steering direction, which is alsofollowed by the controller.

Fig. 26 shows the expanded view of the response ofboth measured rear wheel angular speeds. It is possible toobserve that, indeed, the modified PID controller appropri-ately responds to the demands of controlling the actuators.It is also observed that both time delay and steady-stateerror are minimum and acceptable.

Fig. 27 shows the behavior of the EDS under the ad-justment of the neuro-fuzzy controller. It is notable thatcontrol of the actuator is satisfactorily accomplished. Lowlevels of steady-state error and overshoot are observed. Theexpanded view in Fig. 28 shows that the control actionsdrive both measured angular speeds to correctly follow thereference as the vehicle’s speed changes and the steeringmaneuver occurs.

Fig. 26. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the modified PID controller, to a constant speedand steering maneuver.

Fig. 27. Experimental response for the HELVIS platform EDS module, ad-justed by the neuro-fuzzy controller, to a constant speed and steering maneuver.

Fig. 28. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the neuro-fuzzy controller, to a constant speedand steering maneuver.

The resulting curves for both rear wheel angular speedscontrolled by the optimal H∞ controller can be observedin Fig. 29. In this case, the noise suppression can be clearlynoted. In particular, in Fig. 30, one may note that, in fact,the optimal H∞ controller is able to reject noises anddisturbances that can be eventually or purposely insertedinto the control plant. Neither steady-state error nor timedelay response are observed. Moreover, high control effortis observed, particularly at low frequencies.


Fig. 29. Experimental response for the HELVIS platform EDS module, ad-justed by the optimal H∞ controller, to a constant speed and steering maneuver.

Fig. 30. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the optimal H∞ controller, to a constant speedand steering maneuver.

Fig. 31. Experimental response for the HELVIS platform EDS module,adjusted by the modified PID controller, to a speed on the sinusoidal patternand steering maneuver.

Case II: Fig. 31 shows the behavior of the EDS under thecontrol of the modified PID controller. As in Case I, it isnoted that the controller provides the EDS with sufficientcontrol actions accordingly to project specifications. Thelow-frequency responses and consequent control effort areshown in Fig. 32, which results in no deterioration in theattempt to maintain the speed of the actuator.

Fig. 33 shows the control responses of the EDS bythe neuro-fuzzy controller. The controller appropriatelyfollows the reference values for the angular speeds, result-

Fig. 32. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the modified PID controller, to a speed onsinusoidal pattern and steering maneuver.

Fig. 33. Experimental response for the HELVIS platform EDS module,adjusted by the neuro-fuzzy controller, to a speed on the sinusoidal pattern andsteering maneuver.

Fig. 34. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the neuro-fuzzy controller, to a speed on thesinusoidal pattern and steering maneuver.

ing in a quasi-zero steady-state error and no significantovershoot levels. When it comes to time delay response,neither is observed (see Fig. 34). The system appropriatelyresponds even at low frequencies, and the control effortalso keeps the wheel speeds in compliance with the correctcalculated speeds.

Finally, Fig. 35 shows the EDS response by applyingthe optimal H∞ controller for the same case. The controlrobustness can be noted, such that the noise that is inserted


Fig. 35. Experimental response for the HELVIS platform EDS module,adjusted by the optimal H∞ controller, to a speed on the sinusoidal patternand steering maneuver.

Fig. 36. Expanded view of the experimental response for the HELVIS plat-form EDS module, adjusted by the optimal H∞ controller, to a speed on thesinusoidal pattern and steering maneuver.

TABLE IVCONTROL PERFORMANCE QUANTITATIVE COMPARISON TABLE

DURING EXPERIMENTS (MEAN VALUES)

into the process is suppressed. The expanded view of thecontrol responses is shown in Fig. 36. It is observed thatH∞ presents a high ability to reject the external distur-bances. Furthermore, control effort and controller precisionlead the EDS to a quasi-zero steady-state error and noovershoot, as well as a very quick time response.

As for the experimental quantitative performance analysis,it is noted from Table IV that all three controllers presentvery satisfactory mean values during experimental tests. Thisfact directly reflects the vehicle performance since the com-bination of low levels of steady-state error, time delay, andovershoot guarantees a more stable and more maneuverablecar. Moreover, it expresses the accuracy of the overall EDSwhile working with the novel proposed architecture, whichproves that it can embed controllers from various classes andapproaches.

VI. CONCLUSION

Both EDS and the new control architecture proposed in thiswork directly and deeply contributes to the development ofEVs/HEVs regarding improvements in the power train/tractionsystem. Although other control approaches can handle the prob-lem of electronic differential control, even with MIMO systems,the focus of this research is to allow the design of an electricwheel, which can independently replace the conventional rearwheel in conventional passenger vehicles.

The proposed architecture is grounded in the fusion betweena high-performance IMU sensor and kinematic and dynamicparametric models, which makes the design of the EDS per-fectly scalable to other four-wheel drive rear traction vehicles.Despite the fact that all tests have been run in a low-scalevehicle, it is feasible to be embedded in a full-scale electricand Ackerman-based rear traction vehicle. Both simulated andexperimental results show that the novel control architecturepresents good results, regardless of the type and nature of thecontroller. Therefore, the resulting EDS system is extremelyflexible in terms of control. Furthermore, it presents a generalin-depth solution to be used with any kind of control system,under any circumstances. In terms of visibility, the proposedarchitecture module allows clear vision of how the informationflows into the context of the EDS module.

As for the HELVIS platform and HELVIS-Sim simulationenvironment, both are concrete contributions of this research.They can potentially help spread the new paradigms of a newand cleaner transportation paradigm.

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Rafael Coronel Bueno Sampaio (S’09) receivedthe B.E. degree in computing/electronic engineeringand the M.Sc. degree in mechanical engineering, in2011, from the University of São Paulo, São Carlos,Brazil, where he is currently working toward thePh.D. degree.

He is currently the Hybrid Electric Vehicle in LowScale Project Team Leader and the Team Leader ofAerial Robots Team with the Mechatronics Labora-tory, University of São Paulo. He is a member of theAutonomous Embedded Navigation System Project.

During his M.Sc. studies, he authored more than ten important papers (includ-ing one chapter of book) involving robust control systems for stabilization ofunmanned aerial vehicles and traction in hybrid electric vehicles. His researchinterests are robust control systems for automobiles and aircraft, includingmodeling high-performance models for control in flight simulators.

André Carmona Hernandes (S’09–M’12) receivedthe B.E. degree in mechatronics engineering, in2009, from the University of São Paulo, São Car-los, Brazil, where he is currently working towardthe M.S. degree, working on probabilistic reasoningusing Bayesian networks.

He is currently the Team Leader of the Au-tonomous Embedded Navigation System Project.His research interests are mobile robots, decisionmaking, and probabilistic reasoning.

Vinicius do Valle Magalhães Fernandes (S’11) iscurrently working toward the degree in mechatronicsengineering with the University of São Paulo, SãoCarlos, Brazil.

Since 2011, he has been working on a projectfor scaled electrical vehicles with the Group ofMechatronics, Mobile Robots Laboratory, Univer-sity of São Paulo. His research interests are mobilerobots, vehicular dynamics, electrical vehicles, andpath planning.

Marcelo Becker (M’05) received the M.Sc. andD.Sc. degrees in mechanical engineering from theState University of Campinas (UNICAMP), Brazil,in 1997 and 2000, respectively.

During his D.Sc. studies, he spent eight months asa Guest Student with the Institute of Robotics, SwissFederal Institute of Technology, Zurich, Zurich,Switzerland. At that time, he was involved in re-search on obstacle avoidance and map-building pro-cedures for indoor mobile robots. From August 2005to July 2006, he was on sabbatical leave with the

Autonomous System Laboratory Swiss Federal Institute of Technology, Lau-sanne, Lausanne, Switzerland, where he was involved in research on obstacleavoidance for indoor and outdoor mobile robots. From 2001 to 2008, he was anAssociate Professor with Pontifical Catholic University of Minas Gerais, (PUCMinas), Belo Horizonte, Brazil. From 2002 to 2005, he was also a co-Head ofthe Mechatronics Engineering Department and of the Robotics and AutomationGroup, PUC Minas. Since 2008, he has been a Professor with the University ofSão Paulo, São Carlos, Brazil. He has authored more than 80 papers in thefields of vehicular dynamics, mechanical design, and mobile robotics in severalconference proceedings and journals. His research interests focus on mobilerobots, inspection robots, vehicular dynamics, design methodologies and tools,and mechanical design applied on robots and mechatronics.

Adriano Almeida Gonçalves Siqueira (M’04) re-ceived the B.E. degree in mechanical engineeringand the Ph.D. degree in electrical engineering fromthe University of São Paulo, São Carlos, Brazil, in1999 and 2004, respectively.

Since 2005, he has been an Associate Profes-sor with the Department of Mechanical Engineer-ing, University of São Paulo. His research interestsare underactuated robots, cooperative robots, robustcontrol, nonlinear control, exoskeletons, and roboticrehabilitation.

Dr. Siqueira was a finalist of the Best Student Paper Award for the 2002 IEEEConference on Decision and Control and a finalist for the 2004 Best StudentPaper Award of the IEEE Conference on Control Applications.

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