lpv design of fault-tolerant control for road vehicles

Int. J. Appl. Math. Comput. Sci., 2012, Vol. 22, No. 1, 173–182DOI: 10.2478/v10006-012-0013-x

LPV DESIGN OF FAULT–TOLERANT CONTROL FOR ROAD VEHICLES

PETER GASPAR, ZOLTAN SZABO, JOZSEF BOKOR

Systems and Control Laboratory, Computer and Automation Research InstituteHungarian Academy of Sciences, Kende u. 13–17, Budapest, H-1111, Hungary

e-mail: [email protected]

The aim of the paper is to present a supervisory decentralized architecture for the design and development of reconfigurableand fault-tolerant control systems in road vehicles. The performance specifications are guaranteed by local controllers,while the coordination of these components is provided by a supervisor. Since the monitoring components and FDI filtersprovide the supervisor with information about the various vehicle maneuvers and the different fault operations, it is ableto make decisions about necessary interventions into the vehicle motions and guarantee reconfigurable and fault-tolerantoperation of the vehicle. The design of the proposed reconfigurable and fault-tolerant control is based on an LPV methodthat uses monitored scheduling variables during the operation of the vehicle.

Keywords: robust control, fault detection, LPV systems, faut-tolerant control, vehicle dynamics, vehicle control.

1. Introduction and motivation

Recently, there has been a growing demand for vehicleswith ever better driving characteristics in which efficiency,safety and performance are ensured. In line with the re-quirements of the vehicle industry, several performancespecifications are in the focus of research, e.g., improv-ing road holding, passenger comfort, roll and pitch sta-bility, guaranteeing the reliability of vehicle components,reducing fuel consumption and proposing fault-tolerantsolutions (Gillespie, 1992). Integrated vehicle controlmethodologies are in the focus in research centers andautomotive suppliers. The purpose of integrated vehiclecontrol is to combine and supervise all controllable sub-systems affecting vehicle dynamic responses. An inte-grated control system is designed in such a way that theeffects of a control system on other vehicle functions aretaken into consideration in the design process by select-ing various performance specifications. Recently, sev-eral important papers have been presented on this topic(Yu et al., 2008; Gordon et al., 2003; Palkovics andFries, 2001; Trachtler, 2004; Zin et al., 2006).

This paper proposes a multi-layer supervisory archi-tecture for integrated control systems in road vehicles.The supervisor has information about the various vehiclemaneuvers and the different fault operations by monitor-ing components as well as fault-detection and identifica-tion (FDI) filters. For some examples of fault detection

methods in industrial mechatronic products please refer tothe works of, e.g., Muenchhof et al. (2009), Kanev andVerhaegen (2000), Fischer and Isermann (2004) or Theil-liol et al. (2008).

The supervisor is able to make decisions about neces-sary interventions into the vehicle components and guar-antee reconfigurable and fault-tolerant operation of the ve-hicle. In the proposed solution, local controllers are de-signed by taking into consideration the monitoring andfault signals received from the supervisor. The local con-trol components are designed by Linear Parameter Vary-ing (LPV) methods. These are well elaborated and suc-cessfully applied to various industrial problems. It is par-ticularly appealing that nonlinear plants are treated as lin-ear systems with a priori not necessarily known but on-line measurable, time-varying parameters. Hence, it al-lows linear-like control techniques to be applied to non-linear systems.

The structure of the paper is as follows. In Section 2,the architecture of the integrated control is presented. InSection 3, the control-oriented modeling is performed andthe control problem is set. In Section 4, the FDI designand the reconfigurable and fault-tolerant control designbased on an LPV method are presented. Both the FDI de-sign and the operation of the fault-tolerant control systemare illustrated through simulation examples in Section 5.Finally, Section 6 contains concluding remarks.

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174 P. Gaspar et al.

2. Architecture of integrated control

A large number of theoretical problems have occurred inthe design of the architecture of integrated vehicle con-trol. The difficulty in the classical approaches is that thecontrol design leads to hybrid and switching methods witha large number of theoretical problems (e.g., Hencey andAlleyne, 2010; Lu and Filev, 2009). Moreover, global sta-bility and performance are difficult to guarantee. In or-der to implement a safety feature, the operation of a localcontroller must be modified by a supervisory command.However, in this case, the sharing of the responsibility ofthe designers is often unclear.

One remedy for these difficulties is to design a cen-tralized controller which is able to integrate various con-trollable subsystems affecting the vehicle. For exam-ple, in the design of the global chassis control system,the brake, the steering, the anti-roll bars and the suspen-sion systems are integrated. In this method, a sophisti-cated high-complexity and control-oriented model is con-structed, which is augmented with a large number of per-formance specifications. The designed controller calcu-lates the actuator commands based on measured signalsand monitoring components.

This centralized control structure has several advan-tages: the designed controller guarantees performancespecifications and robustness against uncertainties; the so-lution reduces the number of necessary sensors; it im-proves the flexibility of the actuators and avoids unnec-essary duplications. This high-complexity control prob-lem, however, is often difficult to handle, i.e., the morecomplex the vehicle model, the more numerical problemsmight occur. Moreover, this centralized approach is notsuitable for the partial design tasks carried out by vehi-cle component suppliers. Furthermore, if a new compo-nent is added to the system, the entire system must be re-designed.

Aζ

Aβ

Aα

Actuator

Actuator

ActuatorSupervisory control

ComponentsMonitoring

FDI filters

Sensors

Local LocalLocalControllerController Controller

KβKα Kζ

Fig. 1. Multi-layer supervisory architecture of integrated vehi-cle control.

The solution to integrated control proposed by thispaper is to design a high-level controller which is ableto supervise the effects of individual control components

on vehicle dynamics, see the illustration in Fig. 1. Inthis supervisory decentralized control structure, there arelogical relationships between the supervisor and the in-dividually designed controllers. The communication be-tween control components is performed by using the CANbus. The advantage of this solution is that the compo-nents with their sensors and actuators can be designed bythe suppliers independently. The role of the supervisoris to meet performance specifications and avoid interfer-ence and conflict between components. The supervisorperforms the coordination of local controllers based onsignals of the monitoring components and the FDI filters.It determines the various vehicle maneuvers and the dif-ferent fault operations. The communication between thesupervisor and the local components is realized through awell-defined interface, i.e., a set of signals with specificsemantics. Once the interface is fixed after a conceptualdesign of the supervisor, the controllers of the individuallocal components can be designed separately.

The advantage of the proposed architecture for inte-grated vehicle control is that the complexity of the vehiclemodel is divided into several parts. In the formalism ofthe control-oriented model, the messages of the supervisormust be taken into consideration. Consequently, the sig-nals of monitoring components and FDI filters are built inthe performance specifications of the controller by usingparameter-dependent weighting. In this way, the operationof a local controller can be extended to reconfigurable andfault-tolerant functions.

3. Actuator controller design

In this section, a motivation example for an integrated ve-hicle control is presented. The objective of the controldesign is to track a predefined path, guarantee road hold-ing and increase yaw, roll and pitch stability. Four controlcomponents are applied in the system: the active brake,steering, anti-roll bars and the suspension system. In gen-eral, chassis control integrates the active steering and theactive brake. A possible solution to the tracking problemuses active steering. When a rollover is imminent andthis emergency persists, the brake system is activated toreduce the rollover risk. When the brake is used, how-ever, the real path significantly deviates from the desiredpath due to the brake moment, which affects the yaw mo-tion. This deviation must be compensated for by the activesteering system. It is a difficult problem to perform track-ing and rollover prevention at the same time since thesetasks are in conflict with each other. In the paper, chassiscontrol also includes two additional components. Activeanti-roll bars are used to improve roll stability. Road hold-ing and passenger comfort are improved by applying anactive suspension system.


LPV design of fault-tolerant control for road vehicles 175

3.1. LPV models for local controllers. The local con-trollers are designed based on vehicle models with dif-ferent complexity. In what follows, the dynamic mod-els that correspond to the four control components arepresented.

The lateral (yaw and roll) dynamics of the vehicle,which is modelled by a three-body system with a sprungmass ms and two unsprung masses at the front muf andthe rearmur including the wheels and axles, are illustratedin Fig. 2. Ixx, Ixz , Izz are the roll moment of the inertiaof the sprung mass, the yaw-roll product, and the yaw mo-ment of inertia, respectively. The signals are the side slipangle of the sprung mass β, the heading angle ψ, the yawrate ψ, the roll angle φ, the roll rate φ, the roll angle of theunsprung mass at the front axle φt,f and at the rear axleφt,r. δf is the front wheel steering angle, and v is the for-ward velocity. The lateral tire forces in the direction of thewheel ground contact are denoted by Fyf and Fyr. Theroll motion of the sprung mass is damped by suspensionswith damping coefficients bf , br and stiffness coefficientskf , kr. The tire stiffnesses are denoted by kt,f , kt,r. Hereh is the height of CG of the sprung mass and huf , hur arethe heights of CG of the unsprung masses, �w is the half ofthe vehicle width and r is the height of the roll axis fromthe ground.

�

�......................................................

.................................

�

� .................................

�

�

�

�

�..................

..................

...........

� �

roll axis

φ

h · cosφ

r

mu,ig

msg

msay

Fz,l Fz,r

φt,i

z

y

��hu,i

...............

�

�

y

x

........

........

........

.δf

...............

.............

......................... ........

........

........

.

.........................

�

�

�

�

lf

lr

ψ �

� �

� �Fb,fl

Fb,rl Fb,rr

Fb,fr

� vβ

�� 2lwCGs

CGu

Fig. 2. Vehicle model with lateral dynamics.

In vehicle modelling, the motion differential equa-tions are formalized. They are the lateral dynamics, theyaw moment, the roll moment of the sprung mass and theroll moment of the front and the rear unsprung masses.The equations are the following:

mv(β + ψ) −mshφ = Fyf + Fyr, (1)

−Ixzφ+ Izzψ = Fyf lf − Fyrlr + lwΔFb,(2)

(Ixx +msh2)φ − Ixzψ = msghφ+msvh(β + ψ)

− kf (φ− φtf ) − bf (φ− φtf ) + uaf

− kr(φ − φtr) − br(φ− φtr) + uar (3)

−rFyf = mufv(r − huf )(β + ψ) +mufghufφtf

− ktfφtf + kf (φ− φtf )

+ bf (φ− φtf ) + uaf , (4)

−rFyr = murv(r − hur)(β + ψ) −murghurφtr

− ktrφtr + kr(φ− φtr)

+ br(φ− φtr) + uar. (5)

The lateral tire forces Fyf and Fyr are approximatedlinearly to the tire slide slip angles αf and αr, respec-tively: Fyf = μCfαf and Fyr = μCrαr, where μ isthe side force coefficient and Cf and Cr are tire side slipconstants. In stable driving conditions, the tire side slipangle αi can be simplified by substituting sinx ≈ x andcosx ≈ 1. The classic equations for the tire side slipangles are then given as αf = −β + δf − lf · ψ/v andαr = −β + lr · ψ/v.

This structure includes several control mechanisms,which generate control inputs. They are the roll momentsbetween the sprung and unsprung masses generated by theactive anti-roll bars, uaf and uar, the difference in brakeforces between the left and right-hand sides of the vehicleΔFb, and the steering angle δf .

The state space representation of the lateral dynam-ics, which is used in the control design of anti-roll bars, isformalized as follows:

xr = Ar(ρ)xr +Br(ρ)ur, (6)

where the state vector is xr = [β, ψ, φ, φ, φtf , φtr]T . Thecontrol inputs are the roll moments at the front and therear between the sprung and unsprung masses: ur =[uaf , uar]T . The scheduling vector is ρ = [v, μ]T . Furtherdetails on the model structure can be found in the work ofGaspar et al. (2003b).

In the state equation, the matrix Ar depends on theforward velocity of the vehicle v nonlinearly. As a mod-elling assumption, the forward velocity is approximatelyequivalent to the velocity in the longitudinal directionwhile the slide slip angle is small. It is also assumed thatthe forward velocity is available, i.e., it is estimated on-line by using the on-board sensors (Song et al., 2002). Theadhesion coefficient of the vehicle μ depends on the typeof road surface. There are several factors that can affectthe value of the adhesion coefficient, which is a nonlin-ear and time varying function. Several methods have beenproposed for the estimation of the adhesion coefficient andthe side slip angle (de Wit et al., 2003). Since the modelcontains a time-varying adhesion coefficient, an adaptiveobserver-based grey-box identification method has beenproposed for its estimation (Gaspar et al., 2010). Thus,the nonlinear model is transformed into an LPV one in



which nonlinear terms are hidden with a suitably definedscheduling vector ρ. In practice, the components of thescheduling vector are measured or estimated.

In the design of the brake system, the same statespace vector is used. The control input is the brake mo-ment, which is able to generate unilateral brake forces atthe front and the rear wheels at either of the two sidesub = ΔFb,

xr = Ab(ρ)xr +Bb(ρ)ub. (7)

In the design of the steering system The control input isthe steering angle: ud = δf ,

xr = Ar(ρ)xr +Bd(ρ)ud. (8)

The vertical dynamics of the vehicle are modeled bya five-body system with a sprung mass ms, and four un-sprung masses at the front and the rear on the left andright hand sides. The state space representation of verti-cal dynamics, which is used for the control design of thesuspension system, is formalized as follows:

xs = As(ρs)xs +Bs(ρs)us, (9)

where xs = [x1, θ, φ, x2ij , x1, θ, φ, x2ij ]T is the state vec-tor which includes the vertical displacement of the sprungmass, the pitch angle and the roll angle of the sprung mass,the front and rear displacements of the unsprung masseson the left and right hand sides and their derivatives. Thecontrol inputs are generated by the suspension actuators:

us =[ffl, ffr, frl, frr

]T. The state space representation

of an active suspension system is found in the work ofGaspar et al. (2003a).

Throughout modelling, the nonlinear characteristicsin the suspension spring and damper components aretaken into consideration. The relative displacement δxand the relative velocity δx between the sprung mass andthe unsprung mass are assumed to be available. Thusthe scheduling vector is chosen in the following form:ρs = [δx, δx]T .

3.2. Control design based on the LPV method. Theclosed-loop system applied in the design of integratedcontrol includes the feedback structure of the modelG(ρ),the compensator, and elements associated with the un-certainty models and performance objectives. These el-ements define the parameter dependent augmented plantP (). Using the controller K the closed-loop systemM() is given by an LFT structure (see Fig. 3). Thequadratic LPV performance problem is to choose theparameter-varying controller K() in such a way that theresultant closed-loop system M() is quadratically stableand the induced L2 norm from w to z is less than γ, i.e.,

‖M(ρ)‖∞ = infK

sup‖Δ‖2≤1

sup�

sup‖w‖2 �=0

‖z‖2

‖w‖2

< γ. (10)

By assuming an unstructured uncertainty and by apply-ing a weighted small gain approach, the existence of acontroller that solves the quadratic LPV γ-performanceproblem can be expressed as the feasibility of a set ofLMIs, which can be solved numerically (see Packard andBalas, 1997; Wu et al., 1996; Bokor and Balas, 2005). Forthe general case, see the works of Scherer (2001) and Wu(2001).

�

d� e�w

u

z

yP.�/

K.�/

M.�/

Fig. 3. General closed-loop interconnection structure.

In this framework, performance requirements are im-posed by a suitable choice of the weighting functionsWp.The proposed approach realizes the reconfiguration of theperformance objectives by suitable scheduling of theseweighting functions. In what follows, this strategy is de-tailed.

The local components also include units for monitor-ing vehicle operations and FDI filters, and they are ableto detect emergency vehicle operations, various fault op-erations or performance degradations in controllers. Theyalso send messages to the supervisor. In the reconfigurableand fault-tolerant control of the local controller, severalsignals must be monitored and scheduling variables areadded to the scheduling vector in order to improve thesafety of the vehicle.

Below several examples of monitored componentsare presented.

Yaw stability is achieved by limiting the effects of thelateral load transfers. The purpose of the control designis to minimize the lateral acceleration, which is monitoredby a performance signal: za = ay . Unilateral braking isone of the solutions in which brake forces are generated inorder to achieve a stabilizing yaw moment. In the secondsolution, an additional steering angle is generated in orderto reduce the effect of the lateral loads. These solutions,however, require active driver intervention into the motionof the vehicle to keep the vehicle on the road.

Yaw tracking. Another control task is to follow a roadby using a predefined yaw rate (angle). In this case, the



current yaw rate must be monitored and the difference be-tween the reference and the current yaw rate is calculated.The purpose of the control is to minimize the tracking er-ror: zψ = ψcmd − ψref .

Roll stability is achieved by limiting the lateral load trans-fers on both axles to below the levels for wheel lift-off dur-ing various vehicle maneuvers. The lateral load transfer isΔFzy = ktφt, where φt is the monitored roll angle of theunsprung mass. The normalized lateral load transfer is in-troduced: ρR = ΔFzy/mg. The aim of the control designis to reduce the maximum value of the normalized lateralload transfer if it exceeds a predefined critical value.

Pitch stability is achieved by limiting the longitudinalload transfers to below a predefined level during suddenand hard braking. The normalized longitudinal load trans-fer is the normalized value of the pitch angle: ρP =θ/θmax, where θ is the monitored pitch angle and θmax isthe maximal value of the pitch angle. The aim of the con-trol design during braking is to reduce the pitching dynam-ics if the normalized longitudinal load transfer exceeds acritical value.

Road holding is achieved by reducing the normalized sus-pension deflections ρk between the sprung and unsprungmasses at the four corner points of the vehicle. Since in-creasing road holding reduces the passenger comfort inthe design of the suspension system its desired level issubject of a design decision.

4. Design of fault-tolerant LPV control

The fault-tolerant local controllers also require compo-nents for monitoring fault information. Faults in the op-eration of an actuator can be usually detected by usinga built-in self-diagnostic method. In this case, fault in-formation is sent by the actuator itself to the supervisor.When fault information is not achievable, the operation ofan actuator must be monitored. In this case, an FDI com-ponent must be constructed which is able to detect faultor even performance degradation in the actuator. Fast andreliable operation of the actuator is critical. Since fault-tolerant control requires fault information in order to guar-antee performances and modify its operation, an FDI filteris also designed.

4.1. Design of an FDI component. Any reconfigu-ration scheme relies on a suitable FDI component. Thereare a lot of approaches to design a detection filter (Chenand Patton, 1999). The LPV setting, however, narrows theavailable tools.

In contrast to the LTI case, in the LPV frameworkstability cannot be guaranteed in algebraic terms, e.g., byrequiring that the “frozen” LTI systems be stable. Be-sides the technical difficulties of the potential design pro-

cess, this fact implies that algebraic methods of the classi-cal LTI FDI filter design (Gertler, 1998; Varga, 2008) arenot suitable for the LPV setting. In the LPV framework,the only practical solution is to require quadratic stabil-ity, which can be cast as a set of Linear Matrix Inequal-ity (LMI) feasibility problems (Rodrigues et al., 2007).The so-called geometric approach of the FDI meets theserequirements and often leads to successful detection fil-ter design (for details, see Balas et al., 2003; Bokorand Balas, 2004; Edelmayer et al., 2004; Shumsky andZhirabok, 2006).

As a high level approach, the FDI filter design prob-lem can often be cast in the model matching frameworkdepicted in Fig. 4 (Rank and Niemann, 1999).

fdu

G .�/ ryF .�/

W .�/

eC

�

T

Fig. 4. Norm based detector design problem.

The LPV paradigm permits to cast a nonlinear sys-tem as a Linear Time-Varying (LTV) one, i.e., the residualcan be expressed as

r = Truu+ Trdd+ Trff. (11)

Hence, to achieve robustness in the presence of distur-bances and uncertainty, multiobjective optimization-basedFDI schemes can be proposed where an appropriately se-lected performance index has to be chosen to enhance sen-sitivity to the faults and simultaneously attenuate distur-bances: the robust disturbance rejection condition formu-lated as

||Trd||∞ = sup||f ||2=1,ρ∈P

||r||2 (12)

is to be minimized.This is a usual worst-case filtering problem and the

corresponding design criteria can be formulated as a con-vex optimization problem by using LMIs. The main prob-lem here is that the sensitivity and robustness conditionsare conflicting. In the LTI framework, this means that bothsensitivity to faults and insensitivity to unknown inputscannot be achieved at the same frequencies. Faults havingsimilar frequency characteristics as those of disturbancesmight go undetected. While the design problem is non-convex, in general, Henry and Zolghadri (2004) propose ascheme that can handle it by using LMI techniques.

For illustrative purposes, the LPV detection filter de-sign of the active anti-roll bars is sketched. The specific



structure that fits the norm based approach, containing theweighted open-loop system, which includes the yaw-rollmodelG(ρ) and the parameter-dependent FDI filter F (ρ),and elements associated with performance objectives, isdepicted in Fig. 5. In the diagram, u is the control torque,which is generated by anti-roll bars, y is the measured out-put, which contains the lateral acceleration ay and the rollrate φ. The FDI filter takes the measured outputs and thecontrol torques. The control torque is provided to the FDIfilter so that the effect of the control input is attenuatedon residual outputs. In the figure, fa is the actuator faultand fs is the sensor fault. Here ea and es represent theweighted fault estimation errors associated with failures.

fa fs

u

�

�

yra

rs

d

ea

esG .�/

F .�/

Wfa Wfs

Wpa

Wps

Fig. 5. Open loop interconnection structure for FDI filter de-sign.

Wpa and Wps are the fault detection performanceweights, which reflects the relative importance of the dif-ferent frequency domains. These weighting functions canbe considered penalty functions, i.e., the weight shouldbe large in the frequency range in which small errors aredesired (low frequency) to achieve the integral action forfault estimation and small in the range where larger er-rors can be tolerated. The weight Wfa represents the sizeof a possible fault in the actuator channel. The weightWfs takes sensor failure into consideration in the FDI fil-ter design. The augmented plant of the filtering problem

has w =[δf Fb fa fs u

]Tas the disturbance in-

put and e =[ea es

]Tas the performance output, which

are used to evaluate the estimation quality. The design re-quirement for H∞ residual generation is to maximize theeffect of the fault on the residual and simultaneously min-imize the effect of exogenous signals (δf , Fb, u) on theresidual. Further details on the design can be found in thework of Grenaille et al. (2008).

The fault information provided by a fault detectionfilter triggers the control reconfiguration. At the level oflocal control design, the reconfiguration is achieved byscheduling the performance weights by a signal ρD re-lated to the fault information and provided by a fault de-cision block. As a simple example, one might considerρD = fact/fmax, where fact is an estimation of the fail-ure (output of the FDI filter) and fmax is an estimation ofthe maximum value of the potential failure (fatal error).

The value of a possible fault is normalized into the inter-val ρD = [0, 1]. The estimated value fact represents therate of the performance degradation of active components.

4.2. Weighting strategy for reconfiguration. In whatfollows, the choice of the performance weights for theproblems listed in Section 3.2 are detailed.

In order to solve the yaw rate tracking problem in thedesign of the steering system, the command signal must befed forward to the controller (ψcmd). The command signalis a pre-defined yaw rate signal and the performance sig-nal is the tracking error zψ = eψ, which is the differencebetween the actual yaw rate and the yaw rate command.The weighting function for the tracking error is selectedas

Wpe =1ε

(Td1s+ 1)(Td2s+ 1)

, (13)

where Tdi are time constants. Here, it is required thatthe steady state value of the tracking error should be be-low an acceptable limit ε. In the design of the brake sys-tem, the command signal is the difference in brake forceswhile the performance signal is the lateral acceleration:

zb =[ay, ur

]T. The weighting function of the lateral ac-

celeration is selected as

Wpa = Γa(ρR)(Tb1s+ 1)(Tb2s+ 1)

. (14)

Here Γa is a gain, which reflects the relative impor-tance of the lateral acceleration and it is chosen to beparameter-dependent, i.e., the function of ρR. When ρR issmall, i.e., when the vehicle is not in an emergency, Γa issmall, indicating that the LPV control should not focus onminimizing the acceleration. On the other hand, when ρRapproaches the critical value, Γa is large, indicating thatthe control should focus on preventing the rollover. Asthe gain Γa increases, the lateral acceleration decreases,since the active brake affects the lateral acceleration di-rectly. In the control design, the parameter dependence ofthe gain is selected as follows:

Γa(ρR) =1

Ra −Rb(|ρR| −Rb). (15)

Here Rb defines the critical status when the vehicleis close to the rollover situation, and Ra shows how fastthe control should focus on minimizing the lateral acceler-ation. If a fault is detected in the suspension system or inthe anti-roll bars, concerning roll stability their role is sub-stituted by the brake system. In this case, the brake systemis activated at a smaller critical value than in a fault-freecase. Consequently, the brake is activated in a modifiedway and the brake moment is able to assume the role ofthe anti-roll bars or the suspension actuator in which thefault has occurred.



The modified critical values are

Ra,new = Ra − α · ρD, (16)

Rb,new = Rb − α · ρD, (17)

where α is a predefined constant factor. When there is per-formance degradation in the operation of the brake sys-tem, it is not able to create a sufficient yaw moment toimprove roll stability. In this sense, the brake systemis substituted by the steering system. The steering sys-tem receives the fault message from the supervisor andit modifies its operation in such a way that the effects ofthe lateral loads are also reduces. The difficulty in thissolution is that performance degradation also occurs con-cerning the tracking task, since the steering system mustcreate a balance between the tracking and the roll stability.The performance signals used in the suspension design are

zs =[az sd td us

]T.

The goals of the suspension system are to keep theheave accelerations az = q, suspension deflections sd =x1ij − x2ij , wheel travels td = x2ij − wij , and controlinputs small over the desired operation range. The per-formance weighting functions for heave acceleration, sus-pension deflections and pitch angles are selected as

Wp,az = Γaz(ρk)Ts1s+ 1Ts2s+ 1

, (18)

Wp,sd = Γsd(ρk)Ts3s+ 1Ts4s+ 1

, (19)

Wp,θ = Γθ(ρP )Ts5s+ 1Ts6s+ 1

, (20)

where Tsi are time constants. The trade-off between pas-senger comfort and road holding is due to the fact that itis not possible to guarantee them together simultaneously.A large gain Γaz and a small gain Γsd correspond to a de-sign that emphasizes passenger comfort, while choosingΓaz small and Γsd large corresponds to a design that fo-cuses on road holding. The design procedure for an activesuspension system is found in the work of Gaspar et al.(2003a).

The idea of the reconfigurable suspension system isbased on the fact that active suspension systems are usednot only to eliminate the effects of road irregularities butalso to generate roll moments to improve roll stabilityor generate a pitch moment to improve pitch stability.For a reconfigurable suspension system, the parameter-dependent gains are selected as functions of the suspen-sion deflection ρk, the normalized lateral load transfer ρRand the normalized value of the pitch angle ρP . In normalcruising, i.e., when |ρR| < Rs, the suspension system fo-cuses on the conventional performances. If ρk and ρP donot exceed their critical values, the controller must createa balance between passenger comfort and road holding. IfρP exceeds a predefined critical value, the controller mustfocus on pitch moments. If ρk exceeds a critical value,

the controller must focus on suspension deflection. In anemergency, however, i.e., when |ρR| ≥ Rs, the suspen-sion system must reduce the rollover risk, and guarantee-ing passenger comfort (and pitch dynamics) is no longer apriority.

The weights (13),(14),(18)–(20) used in the paperare Proportional-Derivative (PD) components. Their timeconstants and gains reflect the required steady state andtransient behavior of the different signals that describe theperformance specifications.

5. Simulation examples

In the first simulation example, the FDI filter is tested dur-ing a double lane change maneuver. This maneuver isused to avoid an obstacle in an emergency. The maneu-ver has 2.5 m path deviation over 100 m. The size of thepath deviation is chosen to test a real obstacle avoidancein an emergency on a road. The vehicle velocity is 70km/h. The steering angle input is generated according toa human driver. The braking inputs are used to deceleratethe vehicle during the maneuver. The velocity of the ve-hicle is changing from 70 km/h to approximately 64 km/hwhen applying braking forces. The fault scenarios usedin the closed loop simulations are a 10 kNm anti-roll barfault starting from 2 sec and a 0.1 rad/sec sensor fault oc-curring at the 5-th second. The step sensor fault meansthat the φ sensor measures a signal with a constant addi-tive fault. In our case, the step failure demonstrates a lossin effectiveness in the actuator. The time responses duringthe maneuver are illustrated in Fig. 6.

The weighting strategy of the FDI filter is formalizedin the following way. The fault detection performanceweight is selected in such a way that in the low frequencydomain the fault estimation error should be rejected by afactor of 2 for both types of failure. Moreover, the weightsfor fault channels are selected in such a way that the sizeof a possible fault is 10 kNm in the actuator channel andthere is a 0.1 rad/sec sensor failure.

As the lateral acceleration increases during the ma-neuver, the normalized load transfer also increases. Thecontrol torque between −40 kNm and 80 kNm at the frontand rear axles. The fault at the actuator occurs at the 2nd sec at the first actuator. The additive fault occurs atthe measured yaw rate at the 5-th second. The first resid-ual shows the actuator fault and the second one the sensorfault. The effects of the two failures are decoupled andthe residuals give an acceptable estimation of faults in theanti-roll bars and the sensor fault, the time of their occur-rence and their values, see Figs. 6(d) and (h).

In the second simulation example, the supervisorycontroller (solid) is compared with the conventional dis-tributed controller without reconfiguration (dashed). Theheavy vehicle performs a sharp double lane change ma-noeuver, which is defined by the signal yaw-rate. The



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Fig. 6. Time responses to double lane change maneuver in the operation of the FDI filter: steering angle (a), lateral acceleration (b),yaw rate (c), residual with an actuator fault (d), roll moment at the front (e), brake force at the left (f), roll rate (g), residual witha sensor fault (h).

maneuver has a 4 m path deviation over 100 m. The ve-locity of the vehicle is 120 km/h. The example presentsthe integration of several components in order to followa predefined path and guarantee roll and yaw stability si-multaneously. Figure 7 shows the time responses of thecontrolled system.

In the example, the fault-tolerant control system inwhich there is a float failure in the active anti-roll bar atthe front is examined, (see Fig. 7(c)). During the faultyoperation, this component is not able to generate a stabi-lizing moment to balance the overturning moment. Thesupervisory control system uses fault information from anFDI filter, which monitors the operation of the active anti-roll bars.

The control design is based on the LPV methodsince it is able to handle the parameter dependence inthe weighting strategy and guarantee that the designedcontroller meets the performance specifications. The in-tegration is carried out through the parameter-dependentweighting function used in the design of the brake. Thebrake activates and generates a yaw moment in order to re-duce the influence of the lateral loads, (see Figs. 7(d) and(h). When there is a failure in the front anti-roll bar, thebraking lasts longer and the forces are greater than in thefault free case. Consequently, a greater steering angle isgenerated by the supervisory scheme to follow the prede-fined path and guarantee yaw/roll stability, see Fig. 7(a).The brake forces required by the control system are of im-pulsive nature for the conventional case while for the su-pervisory controller braking lasts longer. The deviation ofthe current yaw rate from the reference yaw rate is greater

in the conventional case than in the supervisory case, (seeFig. 7(f)).

6. Conclusions

In the paper, a multi-layer supervisory architecture forthe design and development of integrated vehicle con-trol systems has been proposed. The local controllersare designed independently by taking into considerationthe monitoring and fault signals by using LPV methods.In this architecture, the supervisor is able to make deci-sions about necessary interventions and guarantee recon-figurable and fault-tolerant operation of the vehicle.

As an illustration, integrated control is proposed fortracking the path of the vehicle, guaranteeing road hold-ing, and improving pitch and roll stability. In a cruisingmode the centralized solution when all the control com-ponents are designed together usually results in more bal-anced control actions. However, examples show that thedistributed control system is less sensitive to fault opera-tions than the centralized control.

Acknowledgment

The research was supported by the Hungarian NationalOffice for Research and Technology through the projectInnovation of distributed driver assistance systems fora commercial vehicles platform (TECH 08 2/2-2008-0088), and by the Control Engineering Research Groupof the HAS at the Budapest University of Technology andEconomics.



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Peter Gaspar received both the M.Sc. and Ph.D.degrees from the Faculty of Mechanical Engi-neering, Budapest University of Technology andEconomics, in 1985 and 1997, respectively, andthe D.Sc. degree in control from the HungarianAcademy of Sciences (HAS) in 2007. Since 1990he has been a research advisor in the Systemsand Control Laboratory of the Computer and Au-tomation Research Institute, HAS. He is the headof the Vehicle Dynamics and Control Research

Group. He is also a professor at the Control and Transport Automa-tion Department, Budapest University of Technology and Economics.His research interests include linear and nonlinear systems, robust con-trol, multi-objective control, system identification and identification forcontrol. His industrial work has involved mechanical systems, vehiclestructures and vehicle control.

Zoltan Szabo obtained his Ph.D. degree in ap-plied mathematics from Eotvos Lorand Univer-sity, Budapest, in 2003, and the D.Sc. degree incontrol from the Hungarian Academy of Sciences(HAS) in 2011. Since 1996 he has been withthe Systems and Control Laboratory (SCL) of theComputer and Automation Institute, HAS. Cur-rently he is a research advisor of the SCL. Hisresearch interests include multivariable systemsand robust control, system identification, fault

detection with applications in power systems safety operations and alsoin the control of mechanical and vehicle structures. He is presently in-volved in activities related to reconfigurable control and control of linearhybrid systems.

Jozsef Bokor received the Dr.Tech. and laterthe Ph.D. degree in automation from the Tech-nical University of Budapest, and the D.Sc. de-gree from the Hungarian Academy of Sciencesin 1990. He was elected a corresponding mem-ber and later a full member of the HungarianAcademy of Sciences in 1999 and 2002, respec-tively. Currently he is a research director ofthe Computer and Automation Research Insti-tute, Hungarian Academy of Sciences, where he

is also the head of the Systems and Control Laboratory. He is a professorand the head of the Control and Transportation Automation Department,Faculty of Transportation Engineering, Budapest University of Technol-ogy and Economics. His research interest includes multivariable systemsand robust control, system identification, fault detection with applica-tions in power systems safety operations, and also the control of roadand aerial vehicles and mechanical structures.

Received: 17 January 2011Revised: 18 June 2011


lpv design of fault-tolerant control for road vehicles

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