HAL Id: hal-00939737https://hal.archives-ouvertes.fr/hal-00939737

Submitted on 30 Jan 2014

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Fault-tolerant control design for trajectory tracking indriver assistance systems

Balázs Németh, Peter Gaspar, Jozsef Bokor, Olivier Sename, Luc Dugard

To cite this version:Balázs Németh, Peter Gaspar, Jozsef Bokor, Olivier Sename, Luc Dugard. Fault-tolerant control de-sign for trajectory tracking in driver assistance systems. SAFEPROCESS 2012 - 8th IFAC Symposiumon Fault Detection, Supervision and Safety for Technical Processes, Aug 2012, Mexico City, Mexico.pp.186-191, �10.3182/20120829-3-MX-2028.00102�. �hal-00939737�

Fault-tolerant control design for trajectorytracking in driver assistance systems ?

Balazs Nemeth∗, Peter Gaspar∗, Jozsef Bokor∗,Olivier Sename∗∗, Luc Dugard∗∗

∗ Computer and Automation Research Institute, Hungarian Academyof Sciences, Hungary; E-mail: {bnemeth;gaspar;bokor}@sztaki.hu

∗∗ GIPSA-lab, Grenoble Institute of Technology, FranceE-mail: {olivier.sename;luc.dugard}@gipsa-lab.grenoble-inp.fr

Abstract: The paper proposes a control system with the brake and the steering for developinga driver assistance system. The purpose is to design a cruise control method to track theroad geometry with a predefined velocity and guarantee the road stability of the vehiclesimultaneously. An actuator selection method is developed in the control design, in which theactuator limits, energy requirements and vehicle operations are taken into consideration. Themethod is extended with a fault-tolerant feature based on a robust LPV method, into which theactuator selection procedure and the detected fault information are incorporated. The operationof the reconfigurable control system is illustrated through various vehicle manoeuvres.

Keywords: fault-tolerant control; reconfiguration; fault detection; linear parameter varyingcontrol; robust control; autonomous systems.

1. INTRODUCTION AND MOTIVATION

The purpose of trajectory tracking is to follow a roadgeometry with a velocity defined by the driver and guaran-tee the road stability of the vehicle simultaneously. Sincethe actuators affect the same dynamics of the vehicle, inthe operation of control systems interference or conflictsmay occur between the control components. In the controldesign the interaction between the actuators must be takeninto consideration and a coordination between them mustbe achieved. An integrated control system is designed insuch a way that the effects of a control system on othervehicle functions are taken into consideration in the designprocess.

The demand for vehicle control methodologies includingseveral control components arises at several research cen-ters and automotive suppliers. Recently, important surveypapers have also been presented in this topic, see e.g. Yuet al. (2008). A vehicle control with four-wheel-distributedsteering and four-wheel-distributed traction/braking sys-tems was proposed by Ono et al. (2006). A yaw stabilitycontrol system in which an active torque distribution anddifferential braking systems were used was proposed byZhang et al. (2009). Differential braking and front steeringto enhance the vehicle yaw stability and the lateral vehicledynamics was proposed by Doumiati et al. (2010). Anintegrated control that involves both four-wheel steeringand yaw moment control was proposed by Jianyong et al.(2007). Active steering and suspension controllers werealso integrated to improve yaw and roll stability Poussot-

? The research was supported by the Hungarian National Officefor Research and Technology through the project ”Innovation ofdistributed driver assistance systems for a commercial vehicles plat-form” (TECH 08 2/2-2008-0088).

Vassal et al. (2011). A global chassis control involving anactive suspension and ABS was proposed by Gaspar et al.(2010); Zin et al. (2008). The driveline system and thebrake were integrated in Rajamani et al. (2000). A possibleintegration of the brake, steering and suspension systemwas presented by Trachtler (2004).

The paper proposes a control system with two activecomponents for developing a driver assistance system. Thepurpose of the control is to generate control inputs, such asthe steering angle and the difference in brake forces. Sinceboth the actuators affect the lateral dynamics of the vehi-cle, in the control design a balance and priority betweenthem must be achieved. An actuator selection method isapplied in the control design. Moreover, detected faultinformation is also considered in order to guarantee thereconfigurable and fault-tolerant operation of the vehicle.

The paper is organized as follows: in Section 2 the vehiclemodel and the longitudinal-lateral trajectory tracking areformalized. In Section 3 the closed-loop interconnectionstructure is formalized and an actuator selection method isapplied. In Section 4 the architecture of the control systemand the fault-tolerant control are presented. In Section 5simulation results are presented.

2. VEHICLE MODEL FOR THE TRAJECTORYTRACKING

In the design of trajectory-tracking assistance systems itis necessary to guarantee that the vehicle must performthe desired motion of the driver. The control system ofthe lateral vehicle dynamics assists the driver in trackingroad geometry. It has advantages in critical situations, inwhich the driver is not able to ensure vehicle stability. Intrajectory tracking the vehicle is moving in the entire plane

of the road, thus both the longitudinal and the lateraldynamics must be taken into consideration as Figure 1shows.

α1 + δ

α2

β ξ

l1l2

Xgl

Ygl

Xv

Yv

ψ

yvygl

Mbr Fl

Fig. 1. Lateral dynamic model of vehicle

Two actuators are used in the system, i.e., the front-wheelsteering angle δ and the differential brake torque Mbr. Inmost of the lateral control problems, the lateral dynamicsof the vehicle can be approximated by the linear bicyclemodel of the vehicle:

Jψ = C1l1αf − C2l2αr +Mbr (1a)

mv(ψ + β) = C1αf + C2αr (1b)

where m is the mass, J is the yaw-inertia of the vehicle,l1 and l2 are geometric parameters, C1, C2 are corneringstiffnesses, ψ is the yaw rate of the vehicle, β is the side-slip angle. Moreover, αf = −β+δ−l1 ∙ψ/v and αr = −β+l2 ∙ ψ/v are the tyre side slip angles at the front and rear,respectively.

Two control systems will be designed based on the statespace representation of the vehicle:

x = Ax+Bu (2)

where the state vector consists of the yaw-rate and the

side-slip angle of the vehicle x =[ψ β

]T. In the brake

control case the input of the system is u = Mbr, while inthe steering control case the input is u = δ. The measuredoutput of both systems is the yaw-rate, y = ψ.

This approach is suitable in the decentralized control con-cept, where the components are designed independently.The advantage of this solution is that the componentswith their sensors and actuators can be designed by thesuppliers independently. Since the controllers guaranteeperformances only locally, the stability and performancesof the entire closed-loop system must also be guaranteed.It is required to perform an analysis step in the robustcontrol framework on a global level.

3. CONTROL DESIGN BASED ON WEIGHTINGFUNCTIONS

3.1 Performance specifications

In the driver assistance system the performance is theminimization of the tracking error of the yaw-rate

z1 = [ψref − ψ]T → min! (3)

where ψref is the reference yaw rate defined by the driver.The reference yaw-rate of the controller can be calculatedfrom the steering wheel angle, see Pacejka (2004).

Simultaneously, actuator saturations must be avoided. Themaximum control input of the steering is determined byits physical construction limits, while in the case of thebraking system the constraints are determined by the tyre-road adhesion. These constraints will be built into theweighting strategy applied in the control design. The otherperformance of the system in terms of the control input isformalized as

z2 = |u| → min! (4)

The control design is based on a weighting strategy, whichis formalized through a closed-loop interconnection struc-ture, see Figure 2. In the trajectory tracking problemthe yaw-rate reference signal is introduced in order toguarantee the tracking of the road geometry: R = ψref .The role of the weighting functions is to define perfor-mance specifications, reflect disturbances and uncertainty.Since the coordination between the actuators and creatingpriority between them are in the focus of the paper, inthe following the design of the weighting functions foractuators is presented.

G

K ( ρ )

W p

W nw n

F d W w

Δ

z 1

Δ

P

K

u

yR

W actz 2

ρ

W u

Fig. 2. Closed-loop interconnection structure

3.2 Weighting function for the actuators

In this section an actuator selection method is developedin the control design, in which the actuator limits, energyrequirements and vehicle operations are taken into consid-eration. Since the steering angle and the brake momentactuators affect the same dynamics of the vehicle, a bal-ance between them must be achieved.

First the steering operation is analyzed. Steering has aconstruction limit, i.e., the value of front-wheel steeringcan not exceed an upper bound. In order to avoid a steeringlimit differential braking must be increased. During drivingthe steering angle is used to handle the lateral dynamics.Moreover, during close to the limit of skidding steering isalso preferred to the brake.

Second the brake intervention is considered. The brakemoment is limited by the adhesion value between the roadand the tire. It is necessary to prevent the skidding of tires,thus in case of skidding the differential braking must be re-duced, while the yaw-motion of vehicle must be controlledby front-wheel steering. By using differential braking thevelocity of the vehicle is decreased. Thus, during drivingthe use of differential braking must be avoided and front-wheel steering is preferred. During deceleration, however,

the brake is already being used, thus the lateral dynamicsis handled by the braking for practical reasons.

Two weighting factors ρst, ρbr are introduced in order totake into consideration the influence of the steering and thebrake moment. These are built into the weighting functionsapplied to the control design. The weighting for the frontwheel steering and that for the brake yaw-moment are

Wact,st = ρst/δmax (5a)

Wact,Mbr = ρbr/Mbrmax (5b)

respectively, where δmax is determined by the construc-tional maximum of the steering system, while Mbrmax isthe maximum of the brake yaw-moment. Figure 3 showsthe characteristics of the weighting factors.

|δ|δ2

δ1

ρst

1

0

Fl

Fl, 1Fl, 2

(a) Steering

α

α2

α1

ρbr

1

0

Fl

Fl, 1Fl, 2

(b) Brake yaw-moment

Fig. 3. Selection of weights ρst, ρbr

In the case of driving the front wheel steering is actuated,which is determined by factor ρst, see Figure 3(a). Thevalue is reduced between δ1 and δ2, which represents theconstructional criterion of the steering system. In thecase of braking the tyre longitudinal slip angle affectsfactor ρbr, see Figure 3(b). In this interval differentialbraking is preferred for practical reasons. Reducing tyreskidding requires an interval. Therefore two parameters aredesigned: α1 and α2 are applied to prevent the skidding oftyres. An interval to prevent chattering between steeringand differential braking: Fl,1 and Fl,2 is also required.

In the following it is assumed that the longitudinal slip andthe longitudinal force are measured or estimated, theseweighting factors are available during the journey. Themodel, which is the basis of the control design, is an LPVform and the control design is based on the LPV method.The purpose of the quadratic LPV design method is tochoose the parameter-varying controller K(ρ) in such away that the resulting closed-loop system is quadraticallystable and the induced L2 norm from the disturbance andthe performances is less than the value γ. Stability andperformance are guaranteed by the design procedure, seeBokor and Balas (2005); Packard and Balas (1997); Wuet al. (1996).

4. DESIGN OF THE FAULT-TOLERANT CONTROLSYSTEM

4.1 Architecture of the control system

The purpose of control design is to calculate the necessaryfront steering angle and brake yaw moment. The design ofthis upper level controller is based on the LPV method.The designed longitudinal force and brake yaw momentare distributed between the four wheels of the vehicle.

Moreover, a third layer is also necessary since the requiredcontrol forces must be tracked by using a low-level con-troller. This controller transforms the wheel forces and thevalues of the steering angle into a real physical parameterof the actuator. These components are implemented byElectronic Control Units (ECUs).

The design of a low-level steering controller might usemore specific techniques that fit the specific nonlinearproperties of the actuator. The steer-by-wire front steeringsystem transforms the steering angle into a real physicalparameter of the actuator. The real physical input of thesystem is the Pulse Width Modulated (PWM) signal of theelectric servo motor, which moves the rack. The physicalconstruction of electric steering has several variations, seee.g. Claeys et al. (1999). Figure 4 shows the architectureof the low-level steering controller.

motor position

PWM

Low

leve

lEC

U

δ

DESIRED Stee

ring

mot

or

Wor

mge

ar

Stee

ring

mec

hani

sm

rack position

δ

REAL

Fig. 4. The low-level driveline control structure

The architecture of the controlled supervisory system isshown in Figure 5.

controller

mea

sure

dsi

gnal

s

Wheel forcedistribution

Mbr

δ

Fi

Supervisory

Steercontroller

Brakecontroller

ρst ρbr

VEHICLE

FDI filter

κ

Fig. 5. Architecture of control system

In the fault-tolerant scheme fault detection and isolation(FDI) filters for actuators are assumed to be used. In thispaper two kinds of actuator faults are considered: the faultof the steering control system and the fault of the brakingcircuits. There may be various fault scenarios, e.g theleakage of the hydraulic systems in the braking or steeringservo, or the steering mechanism becomes jammed. The

different changes in the operation of an actuator make itpossible to realize the detection of a fault.

The filters are able to detect different types of faultsin the operation of the actuators. An H∞ method todesign a fault detection and isolation (FDI) LPV filterwas presented by Edelmayer et al. (1997). The geometricapproaches often lead to successful detection filter design,for details see Bokor and Balas (2004). The selection of theperformance weights in the design of FDI filters has beenapplied to vehicle systems, see in Gaspar et al. (2012). Thispaper focuses only on the design of fault-tolerant controland it is assumed that the FDI filters have been designedand they are available.

4.2 Modification of the weighting functions

Two actuators are operated in cooperation in order toprovide a reconfigurable fault-tolerant control system. Incase of a detected fault either the brake yaw moment Mbror the front wheel steering δ can be changed with similardynamic effects.

When a fault occurs in the operation of the steeringsystem, all the lateral control tasks must be realized byusing the braking system with the generation of the brakeyaw moment Mbr. If fatal error occurs in the operationof the steering system the weight of steering is masked:ρst = 0.

When a fault occurs in the operation of a brake circuitthe actuated brake yaw-moment is reduced. Moreover, thereduction of the brake yaw-moment is asymmetric. Forexample, in the case of a fault of a brake circuit on theleft-hand side of the vehicle, the generated positive brakeyaw-moment is reduced, or it is zero. In this case steeringis activated to substitute for the actuation of brakingand provide trajectory tracking. However, the negativeMbr can be realized by the healthy right-hand-side brakecircuits. Consequently, the weight of braking ρbr dependson the sign of the desired Mbr. In the case of a left-hand-side brake circuit fault, positive Mbr is not allowed,therefore ρbr = 0. However, if Mbr < 0 then ρbr > 0. Theactual modification of ρbr is based on a design parameter:ρbr,new = κi ∙ ρbrm where κi is a weighting factor.

4.3 Quadratic stability of the entire control system

The stability of the individual controllers is guaranteed bythe design method. The global control system contains twocontrollers, the brake and the steering. The global systemuses two scheduling variables ρ = [ρbr, ρst]. According toFigure 3, these factors have limits. When these controllersare used simultaneously it is necessary to guarantee thestability of the global closed-loop system.

A common Lyapunov function for the closed-loop sys-tems must exist. The following affine parameter-dependentclosed-loop system is given, see Scherer and Weiland(2000); Boyd et al. (1997):

x(t) = A(ρ) x(t). (6)

where A(ρ) = A0+ ρ1A1+ ...ρ4A4. For the stability of thesystem (6) it is necessary to guarantee that all trajectoriesof system A converge to zero as t → ∞. A sufficientcondition for this is the existence of a quadratic function

V (ξ) = ξTPξ, P > 0, which decreases along every nonzerotrajectory of (6). If there exists such a P , then (6) issaid to be quadratically stable and V is called a quadraticLyapunov function. The necessary and sufficient conditionfor quadratic stability of system (6) for all of Ai is

ATcl,iP + PAcl,i < 0; P > 0; i = 1, . . . n (7)

Therefore it is necessary to find a V common Lyapunovfunction for all of the closed-loop systems which canguarantee the global stability of the systems in everyscheduling variable.

The matrices of the closed-loop system Acl,i are computedusing the next formula:

Acl,i =

[A+B2DciC2i B2Cci

BciC2 Aci

]

(8)

where A, B2, C2 are the state space representation of theplant, Aci, Bci, Cci,Dci are the state-space representationsof the controllers. The aim is to find a solution to P >0. To analyze the global stability of the LTI systems,

ρbr

ρst

1

1

0

vertex of convex hull

Fig. 6. Convex hull of LTI systems

Co{A1, . . . A4} is covered by the convex hull of finitelymany matrices Acl,i. According to the system, the convexhull contains 4 LTI systems, see Figure 6. For the analysisof global stability this convex hull can be used.

5. SIMULATION RESULTS

In this section the fault tolerance of the control system isillustrated through simulation examples. Several softwarepackages are used for the design and analysis of thecontrolled system. The control design is performed byusing the Matlab/Simulink software. The verification ofthe designed controller is performed by using the CarSimsoftware. In this package the model of the actual roadvehicle dynamics is represented with high accuracy.

The vehicle is traveling along a predefined road, while theintegrated control system supports the driver to guaranteetrajectory tracking. During the simulations different faultsoccur and these faulty cases are compared with a healthysimulation. A typical E-Class automobile is applied inthe simulation. The mass of the 6-gear car is 2023 kg,its engine power is 300 kW (402 hp). The width of thetrack is 1605 mm and the wheel-base is 3165 mm. Inthe simulation examples the vehicle is traveling along asection of Waterford Michigan Race Track, which is shownin Figure 7(a). The velocity of the vehicle changes alongits route as Figure 7(b) shows.

In the first simulation a steering fault occurs in thecontrolled system. Note that the driver assistance systemis not able to modify front wheel steering angle, but the

-200 -150 -100 -50 0 50 100 150 200-200

-150

-100

-50

0

50

100

(a) Road course

1500 1600 1700 1800 1900 2000 2100 2200 230045

50

55

60

65

70

75

80

85

90

Station (m)

Vel

ocity

(km

/h)

(b) Velocity of the vehicle

Fig. 7. Trajectories of vehicles

driver can steer the front wheels. The control systemactuates only brake yaw-moment Mbr. Figure 8 shows thefaulty simulation case compared with a healthy one. Thelateral error of the system and the yaw-rate tracking areillustrated in Figure 8(a) and Figure 8(b). The integratedcontrol system can tolerate a steering fault, the lateralerror and the yaw-rate of faulty simulation results are closeto the healthy cases. The largest difference is at the lastbend. In this bend the longitudinal slip of the wheels reach−1, while in the fault-free case it can be reduced using theactuation of the front wheel steering. The reason for theskidding is the increased brake pressures, compared to thefault-free case, see Figure 8(e) and Figure 8(f). In Figure8(c) and Figure 8(d) the steering and braking actuationsof the controller are shown. If a fault occurs in the steeringthe actuation ofMbr and the brake pressures are increased.Figures 8(g) and Figures 8(h) illustrate the change in theweighting ρ of controllers. In the case of a steering faultthe weight of steering ρst is equal to zero, while the weightof braking is influenced by skidding.

In the second simulation example one of the rear brakecircuits fails. In Figure 9(a) the effect of brake faults isshown. In the first bend the vehicle turns right, whichmeans that the rear right-hand-side wheel brake is ac-tuated to perform the maneuver. Therefore rear right-hand-side brake circuit fault increases the lateral error.In the case of bends to the left the fault of the rear left-hand-side wheel circuit increases the lateral error. Figure9(b) illustrates the steering wheel angle, which is actuatedby the driver. It can be seen that the fault in the brakesystem necessitates faster and more intensive interventionby the driver. A deterioration of the braking effect inducesan increase in the front wheel steering to perform themaneuver, see Figure 9(c). If a fault occurs in the brakethe actuated Mbr moment has a limitation, as shown inSection 4. In the case of a left-hand-side brake circuit faultthe vehicle is not turned anti clockwise, therefore positiveMbr is not allowed and vice versa. The actuated brake-yaw moments can be seen in Figure 9(d). Figures 9(e) and9(f) show the actuated brake pressures, which prove thelimitation of the brake-yaw moment.

In the third simulation example all of the rear brakecircuits have leakage. This situation is compared to a fault-free case and an uncontrolled situation. Figure 10(a) showsthe lateral errors of the vehicle in the three cases. Thelateral error of the vehicle increases because of faults andthe faulty controlled system tracks the trajectory more ac-curately than the uncontrolled vehicle. The steering wheelangle and the front wheel steering angle are illustrated inFigures 10(c) and (d), respectively. The fault of the brake-

1500 1600 1700 1800 1900 2000 2100 2200 2300-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Station (m)

Late

ral e

rror

(m

)

HealthySteer fault

(a) Lateral error

1500 1600 1700 1800 1900 2000 2100 2200 2300-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Station (m)

Yaw

-rat

e (r

ad/s

)

HealthySteer fault

(b) Yaw-rate of vehicle

1500 1600 1700 1800 1900 2000 2100 2200 2300-50

-40

-30

-20

-10

0

10

20

30

40

50

Station (m)

δ (d

eg)

HealthySteer fault

(c) Front wheel steering angle

1500 1600 1700 1800 1900 2000 2100 2200 2300-100

-80

-60

-40

-20

0

20

40

Station (m)

Mbr

(kN

m)

HealthySteer fault

(d) Braking torque Mbr

1500 1600 1700 1800 1900 2000 2100 2200 23000

20

40

60

80

100

120

140

160

180

200

Station (m)

brak

e pr

essu

re (

bar)

Front leftFront rightRear leftRear right

(e) Brake pressures (fault)

1500 1600 1700 1800 1900 2000 2100 2200 23000

20

40

60

80

100

120

140

160

180

200

Station (m)

brak

e pr

essu

re (

bar)

Front leftFront rightRear leftRear right

(f) Brake pressures (fault-free)

1500 1600 1700 1800 1900 2000 2100 2200 2300

0

0.2

0.4

0.6

0.8

1

1.2

Station (m)

ρ w

eigh

t

ρst

ρbr

(g) Weighting ρ (fault)

1500 1600 1700 1800 1900 2000 2100 2200 2300

0

0.2

0.4

0.6

0.8

1

1.2

Station (m)

ρ w

eigh

t

ρst

ρbr

(h) Weighting ρ (fault-free)

Fig. 8. Steering fault compared to the fault-free integratedcontrol

yaw moment affects the increased actuation of the frontwheel steering.

6. CONCLUSION

The paper has proposed the design of a supervisory in-tegrated reconfigurable driver assistance system which isable to track road geometry. The actuators of the controlsystem are the front-wheel steering and the brake yaw-moment. The paper extends the control design with anactuator selection procedure, which is built in the design ofthe supervisor of the system. The control design of actua-tors is based on the robust optimal LPV method, in whichboth performance specifications and model uncertaintiesare taken into consideration. The quadratic stability of theclosed-loop LPV system, which contains the individuallydesigned controllers, is guaranteed by a common Lyapunovfunction. A possible realization of the required controlsystem has also been presented. The integrated system

1500 1600 1700 1800 1900 2000 2100 2200 2300-3

-2

-1

0

1

2

3

4

Station (m)

Late

ral e

rror

(m

)

HealthyRear left faultRear right fault

(a) Lateral error

1500 1600 1700 1800 1900 2000 2100 2200 2300-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Station (m)

Yaw

-rat

e (r

ad/s

)

HealthyRear left faultRear right fault

(b) Yaw-rate of vehicle

1500 1600 1700 1800 1900 2000 2100 2200 2300-400

-300

-200

-100

0

100

200

300

400

Station (m)

Ste

erin

g w

heel

ang

le (

deg)

HealthyRear left faultRear right fault

(c) Steering wheel

1500 1600 1700 1800 1900 2000 2100 2200 2300-25

-20

-15

-10

-5

0

5

10

15

20

25

Station (m)

Mbr

(kN

m)

HealthyRear left faultRear right fault

(d) Braking torque Mbr

1500 1600 1700 1800 1900 2000 2100 2200 23000

50

100

150

200

250

300

Station (m)

brak

e pr

essu

re (

bar)

Front leftFront rightRear leftRear right

(e) Brake pressures (fault in theleft brake circuit)

1500 1600 1700 1800 1900 2000 2100 2200 23000

50

100

150

200

250

300

Station (m)

brak

e pr

essu

re (

bar)

Front leftFront rightRear leftRear right

(f) Brake pressures (fault in theright brake circuit)

Fig. 9. Comparison of a fault in the left-hand-side brakecircuit with a fault in the right-hand-side brake circuit

1500 1600 1700 1800 1900 2000 2100 2200 2300-3

-2

-1

0

1

2

3

4

5

Station (m)

Late

ral e

rror

(m

)

HealthyBrake faultUncontrolled

(a) Lateral error

1500 1600 1700 1800 1900 2000 2100 2200 2300-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Station (m)

Yaw

-rat

e (r

ad/s

)

HealthyRear faultUncontrolled

(b) Yaw-rate of vehicle

1500 1600 1700 1800 1900 2000 2100 2200 2300-400

-300

-200

-100

0

100

200

300

400

Station (m)

Ste

erin

g w

heel

ang

le (

deg)

HealthyRear faultUncontrolled

(c) Steering wheel

1500 1600 1700 1800 1900 2000 2100 2200 2300-50

-40

-30

-20

-10

0

10

20

30

40

50

Station (m)

δ (d

eg)

HealthyRear faultUncontrolled

(d) Front wheel steering angle

Fig. 10. Comparison of the faults in the rear brake circuitswith the fault-free integrated control

makes it possible to achieve a reconfigurable and fault-tolerant system. The fault-tolerance of the controlled sys-tem is demonstrated through simulation examples. It canbe established that the designed integrated supervisorycontrol system tolerates steering and braking faults by

using the proposed weighting strategy and realizes theactuator reconfiguration effectively.

REFERENCES

Bokor, J. and Balas, G. (2004). Detection filter design for LPVsystems - a geometric approach. Automatica, 40, 511–518.

Bokor, J. and Balas, G. (2005). Linear parameter varying systems:A geometric theory and applications. 16th IFAC World Congress,Prague.

Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V. (1997).Linear Matrix Inequalities in System and Control Theory. Societyfor Industrial and Applied Mathematics, Philadelphia.

Claeys, X., de Wit, C.C., and Bechart, H. (1999). Modeling andcontrol of steering actuator for heavy duty vehicle. EuropeenControl Conference ECC’99.

Doumiati, M., Sename, O., Martinez, J., Dugard, L., and Poussot-Vassal, C. (2010). Gain-scheduled LPV/Hinf controller basedon direct yaw moment and active steering for vehicle handlingimprovements. 49th Conf. on Decision and Control, 6427 – 6432.

Edelmayer, A., Bokor, J., Szigeti, F., and Keviczky, L. (1997).Robust detection filter design in the presence of time-varyingsystem perturbations. Automatica, 33(3), 471–475.

Gaspar, P., Szabo, Z., and Bokor, J. (2012). Lpv design of fault-tolerant control for road vehicles. International Journal of AppliedMathematics and Computer Science, 22(1), 173–182.

Gaspar, P., Szabo, Z., Bokor, J., Sename, O., and Dugard, L.(2010). Design of a reconfigurable global chassis control. FISITACongress, Budapest.

Jianyong, W., Houjun, T., Shaoyuan, L., and Wan, F. (2007).Improvement of vehicle handling and stability by integratedcontrol of four wheel steering and direct yaw moment. Proc. 26thChinese Control Conference, Zhangjiajie.

Ono, E., Hattori, Y., Muragishi, Y., and Koibuchi, K. (2006). Vehicledynamics integrated control for four-wheel-distributed steeringand four-wheel-distributed traction/braking systems. VehicleSystem Dynamics, 44:2.

Pacejka, H.B. (2004). Tyre and vehicle dynamics. ElsevierButterworth-Heinemann, Oxford.

Packard, A. and Balas, G. (1997). Theory and application oflinear parameter varying control techniques. American ControlConference, Workshop I, Albuquerque, New Mexico.

Poussot-Vassal, C., Sename, O., Dugard, L., Gaspar, P., Szabo,Z., and Bokor, J. (2011). Attitude and handling improvementsthrough gain-scheduled suspensions and brakes control. ControlEngineering Practice, 19(3), 252–263.

Rajamani, R., Tan, H., Law, B., and Zhang, W. (2000). Demonstra-tion of integrated longitudinal and lateral control for the operationof automated vehicles in platoons. Trans. on Control SystemsTechnology, 8, 695–708.

Scherer, C. and Weiland, S. (2000). Lecture Notes DISC Courseon Linear Matrix Inequalities in Control. Delft University ofTechnology, Delft, Netherlands.

Trachtler, A. (2004). Integrated vehicle dynamics control using activebrake, steering and suspension systems. International Journal ofVehicle Design, 36, 1–12.

Wu, F., Yang, X.H., Packard, A., and Becker, G. (1996). Induced l2-norm control for LPV systems with bounded parameter variationrates. International Journal of Nonlinear and Robust Control, 6,983–998.

Yu, F., Li, D., and Crolla, D. (2008). Integrated vehicle dynamicscontrol: State-of-the art review. IEEE Vehicle Power and Propul-sion Conference, Harbin, China.

Zhang, S., Zhang, T., and Zhou, S. (2009). Vehicle stability controlstrategy based on active torque distribution and differential brak-ing. Int. Conference on Measuring Technology and MechatronicsAutomation.

Zin, A., Sename, O., Gaspar, P., Szabo, Z., Dugard, L., and Bokor, J.(2008). An LPV/Hinf active suspension control for global chassistechnology: Design and performance analysis. Vehicle SystemDynamics, 46, 889–912.