confidentiel jusqu’au septembre 2009 - insa...

PROJET DE FIN D’ÉTUDE

Sylvain TARDY

Mécatronique

ACTIVE STEERING FOR VEHICLE

STABILITY CONTROL

Août 2007

Réalisé avec :

Cranfield University Automotive Department School of Engineering Cranfield University Bedford MK43 0AL, UK

Jaguar Land Rover Doctor Robert Williams Jaguar Cars Ltd, Abbey Road, Whitley Coventry CV3 4LF, UK

Confidentiel jusqu’au 1er septembre 2009

Active Steering for Vehicle Stability Control S. Tardy

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CRANFIELD UNIVERSITY

SCHOOL OF ENGINEERING

MSc THESIS *

Academic Year 2006-2007

S. TARDY

Active Steering for Vehicle Stability Control

Supervisor: Professor N. Vaughan

August 2007

This thesis is submitted in partial fulfilment of the requirements

for the degree of Master of Science

© Cranfield University 2007. All rights reserved. No part of this publication may

be reproduced without the written permission of the copyright owner.


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* Ce projet a été effectué au cours d’un Double Diplôme à l’Université de Cranfield en

Angleterre – MSc Automotive Product Engineering


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ABSTRACT

In this Thesis “Active Steering for Vehicle Stability Control”, the area of investigation

is introduced as well as the project aim and objectives. This study, based on simulations

using the tool IPG CarMaker, intends to provide relevant recommendations for Jaguar

Land Rover regarding the use of Active Front Steering and Rear Wheel Steering from a

stability control point of view.

After a requirement capture to define the controllers’ objectives, two control strategies

aiming to improve the vehicle stability – yaw rate feedback control and minimization of

the derivative of the lateral speed – have been investigated. To evaluate the potential of

each controller applied to Active Front Steering and Rear Wheel Steering, several tests

have been carried out. Time histories and RMS value analyses have been used to

compare the performance. It has been found that a high bandwidth actuator is needed to

remove oscillations due to a counter action of the driver. Moreover, the two active

steering devices have shown a great potential to improve the vehicle stability by

reducing overshoots and providing lower settling times. The potential to reject external

disturbances has also been noticed. It has been pointed that a minimization of the lateral

speed derivative strategy was not appropriate for Active Front Steering.

The capabilities of Active Front Steering and Rear Wheel Steering to improve the

handing behaviour have also been considered. It has been demonstrated that both were

able to track either a two degree of freedom or a neutral steering reference model in

spite of the vehicle stability could be impaired close to the handling limit.

Finally, recommendations have been proposed concerning the use of active steering

systems. There is not one best system: Rear Wheel Steering enhances the stability in

most of the situations while Active Front Steering is efficient to reject external

disturbances.

ABSTRACT


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ACKNOWLEDGEMENT

Firstly, I would like to thank my supervisor, Professor Nick Vaughan, for his continual

support and guidance throughout this project. I would also like to express my gratitude

for his availability to answer all my “last questions”.

Moreover, I would to address many thanks to Jaguar Land Rover, and particularly Drs

Robert Williams and Matthew Hancock for their support and for having given me the

opportunity to work on this very interesting project.

In addition, I would like to thank Mr Leung Tin and Dr David Purdy for their

constructive advices as well as Dr James Marco from the Automotive Department for

his help and advices during the requirement capture.

I am also grateful to Mr Charles Glide and the IPG CarMaker Service Team for their

assistance about IPG CarMaker.

Thanks are also due to my classmate Imanol Olazarri working on Torque Vectoring

Differential for the mutual assistance we gave to each other.

Finally I would like to thank my family for all their support over the last year in

everything I did.

ACKNOWLEDGEMENT


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LIST OF CONTENTS

ABSTRACT ..................................................................................................................... i

ACKNOWLEDGEMENT ............................................................................................. ii

LIST OF CONTENTS .................................................................................................. iii

LIST OF FIGURES..................................................................................................... viii

LIST OF TABLES........................................................................................................ xii

NOMENCLATURE .................................................................................................... xiii

1 INTRODUCTION .................................................................................................. 1

1.1 Topic Area............................................................................................................... 1

1.2 Active Steering ........................................................................................................ 1

1.3 Research Activity, Objectives ................................................................................. 2

1.3.1 Project Description .................................................................................................. 2

1.3.2 Objectives................................................................................................................ 2

1.4 Layout of the Report................................................................................................ 4

2 ACTIVE STEERING............................................................................................. 5

2.1 Rear Wheel Steering and Four Wheel Steering....................................................... 5

2.1.1 The Necessity of Four Wheel Steering.................................................................... 5

2.1.2 Classification of the Control Methods..................................................................... 6

2.1.2.1 Control Schemes ............................................................................................. 6

2.1.2.2 Control Strategies........................................................................................... 7

2.1.3 Open Loop and Closed Loop................................................................................... 8

2.1.4 Open Loop, Feed-forward Structure........................................................................ 9

2.1.4.1 Vehicle Speed Function Based........................................................................ 9

2.1.4.2 Steer Angle Function Based.......................................................................... 10

2.1.4.3 Other Approaches......................................................................................... 11

2.1.5 Closed Loop Structure........................................................................................... 12

2.1.5.1 Basic Yaw Rate Feedback Controller........................................................... 12

2.1.5.2 Reference Model Strategy............................................................................. 13

2.1.5.3 H-Infinity Controller..................................................................................... 14

2.1.5.4 Mixed H-Infinity and H-2 Controller............................................................ 15

LIST OF CONTENTS


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2.1.5.5 Limited State Feedback Controller............................................................... 16

2.1.5.6 Fuzzy Logic Controller ................................................................................. 17

2.1.5.7 Time Delay Controller .................................................................................. 17

2.2 Active Four Wheel Steering – Dual Steering Scheme........................................... 18

2.3 Active Front Steering ............................................................................................ 19

2.3.1 Description ............................................................................................................ 19

2.3.2 Control Strategies .................................................................................................. 20

2.4 Closing Comments ................................................................................................ 21

3 SIMULATION ENVIRONMENT...................................................................... 22

3.1 IPG CarMaker ....................................................................................................... 22

3.2 IPG CarMaker for Simulink .................................................................................. 23

4 REQUIREMENT CAPTURE ............................................................................. 25

4.1 Level, Primary Actors and Scope.......................................................................... 25

4.2 Use Case ................................................................................................................ 26

4.3 Objectives for the Systems .................................................................................... 28

4.4 Test Scenarios........................................................................................................ 29


5 VEHICLE MODEL AND VALIDATION......................................................... 30

5.1 Three Degree of Freedom Handling Model .......................................................... 30

5.1.1 Presentation ........................................................................................................... 30

5.1.2 Model Verification ................................................................................................ 30

5.1.2.1 Tyre Characteristics ..................................................................................... 30

5.1.2.2 Vehicle Step Response .................................................................................. 31

5.1.2.3 Vehicle Characterisation .............................................................................. 32

5.2 IPG CarMaker Vehicle Model............................................................................... 33

5.2.1 CarMaker Axis Systems ........................................................................................ 33

5.2.2 General Layout ...................................................................................................... 34

5.2.3 Steering Subsystem ............................................................................................... 36

5.2.4 Kinematics Subsystem........................................................................................... 36

5.2.5 Forces Subsystem.................................................................................................. 37

5.2.5.1 Presentation.................................................................................................. 37

5.2.5.2 Tyre Model.................................................................................................... 37


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5.2.6 Implementation...................................................................................................... 38

5.3 3-DOF Handling Model vs. Carmaker Model....................................................... 38


6 YAW RATE CONTROL FOR STABILITY IMPROVEMENTS .................. 40

6.1 Design Structure .................................................................................................... 40

6.1.1 Rear Wheel Steering.............................................................................................. 40

6.1.2 Active Front Steering ............................................................................................ 41

6.1.3 Reference Yaw Rate .............................................................................................. 42

6.2 System Adaptation for CarMaker.......................................................................... 44



6.2.2.1 First Attempt ................................................................................................. 46

6.2.2.2 Final Design ................................................................................................. 47

6.3 Controller Tuning .................................................................................................. 47

6.4 Integration of the Actuator .................................................................................... 48

6.4.1 Actuator Model...................................................................................................... 48

6.4.2 Influence of the Bandwidth ................................................................................... 49

6.4.2.1 Bandwidth Analysis Without Driver in the Loop .......................................... 49

6.4.2.2 Bandwidth Analysis With Driver in the Loop ............................................... 50

6.5 Performance Analysis............................................................................................ 55

6.5.1 Test 1: Step Steer Input Without Driver Control................................................... 55

6.5.2 Test 2: Step Steer Input With Driver Control........................................................ 58

6.5.3 Test 3: Accelerating and Turning .......................................................................... 59

6.5.4 Test 4: Braking and Turning.................................................................................. 62

6.5.5 Test 5: Split-µ Braking .......................................................................................... 64

6.5.6 Double Lane Change ............................................................................................. 65

6.5.6.1 Test 6: ISO Double Lane Change ................................................................. 65

6.5.6.2 Test 7: High Speed Double Lane Change..................................................... 67

6.5.7 Side Wind.............................................................................................................. 69

6.5.7.1 Test 8: Side Wind Without Driver Control ................................................... 69

6.5.7.2 Test 9: Side Wind With Driver Control ........................................................ 71



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7 DERIVATIVE OF THE LATERAL VELOCITY CONTROL FOR

STABILITY IMPROVEMENTS................................................................................ 74

7.1 Design Structure .................................................................................................... 74



7.2 System Adaptation for CarMaker.......................................................................... 76

7.3 Integration of the Actuator .................................................................................... 77

7.4 Controller Tuning .................................................................................................. 77

7.5 Performance Analysis............................................................................................ 77

7.5.1 Test 1: Step Steer Input Without Driver Control................................................... 78

7.5.2 Test 2: Step Steer Input With Driver Control........................................................ 80

7.5.3 Test 3: Accelerating and Turning .......................................................................... 81

7.5.4 Test 4: Braking and Turning.................................................................................. 83

7.5.5 Test 5: Split-µ Braking .......................................................................................... 84

7.5.6 Double Lane Change ............................................................................................. 84

7.5.6.1 Test 6: ISO Double Lane Change ................................................................. 84

7.5.6.2 Test 7: High Speed Double Line Change...................................................... 86

7.5.7 Side Wind.............................................................................................................. 87

7.5.7.1 Test 8: Side Wind Without Driver Control ................................................... 87

7.5.7.2 Test 9: Side Wind With Driver Control ........................................................ 89


8 COMPARISON OF THE TWO CONTROL STRATEGIES.......................... 92

8.1 Test 1: Step Steer Input Without Driver Control................................................... 93

8.2 Test 2: Step Steer Input With Driver Control........................................................ 93

8.3 Test 3: Accelerating and Turning .......................................................................... 94

8.4 Test 4: Braking and Turning.................................................................................. 96

8.5 Test 6: ISO Double Lane Change.......................................................................... 96

8.6 Test 7: High Speed Double Lane Change ............................................................. 97

8.7 Test 8: Side Wind Without Driver Control ........................................................... 98

8.8 Test 9: Side Wind With Driver Control................................................................. 99

8.9 Closing Comments .............................................................................................. 100


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9 YAW MOMENT CONTROL FOR HANDLING IMPROVEMENTS ........ 101

9.1 Two Degree of Freedom Linear Model Objective .............................................. 101

9.1.1 Reference Model ................................................................................................. 101

9.1.1.1 Concept ....................................................................................................... 101

9.1.1.2 Pure Time Delay ......................................................................................... 102

9.1.1.3 Saturation ................................................................................................... 102

9.1.2 Performance Analysis.......................................................................................... 103

9.1.2.1 Cornering Performance at Constant Speed................................................ 104

9.1.2.2 Step Steer Inputs ......................................................................................... 104

9.1.2.3 Double Step Steer ....................................................................................... 108

9.1.2.4 High Speed Double Lane Change – Test 7 ................................................. 108

9.1.2.5 Accelerating and Turning – Test 3 ............................................................. 111

9.2 Neutral Steering Objective .................................................................................. 112

9.2.1 Reference Model ................................................................................................. 112

9.2.2 Performance Analysis.......................................................................................... 113

9.3 Closing Comments .............................................................................................. 114

10 CONCLUSIONS................................................................................................. 115

10.1 Influence of the Actuator, Interaction with the Driver ........................................ 115

10.2 Stability Improvement ......................................................................................... 115

10.3 Handling Behaviour Improvement ...................................................................... 116

10.4 Recommendations: “AFS or RWS?”................................................................... 117

10.5 Future Work ........................................................................................................ 117

REFERENCES ........................................................................................................... 119

APPENDIX A: VEHICLE DATA ............................................................................ 123

APPENDIX B: 3 DEGREE OF FREEDOM HANDLING MODEL..................... 125

APPENDIX C: TEST SCENARIOS......................................................................... 129


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LIST OF FIGURES

Figure 1: Transient Response of FWS Vehicle to Stepwise Steering Input [1] ............... 5

Figure 2: Transient Response of 4WS Vehicle to Stepwise Steering Input [1] ............... 6

Figure 3: Block Diagram of Single Steering Scheme [2]................................................. 7

Figure 4: Block Diagram of Dual Steering Scheme [2] ................................................... 7

Figure 5: Open Loop Control ........................................................................................... 8

Figure 6: Closed Loop Control - Feed-forward / Feed-back Structure [4]....................... 9

Figure 7: Steering Characteristics of Mazda 4WS [3].................................................... 10

Figure 8: Rear Wheel Steer Angle: Function of the Steering Wheel Angle [1]............. 10

Figure 9: Configuration of a Closed Loop 4WS System [7] .......................................... 12

Figure 10: Feedback Contribution Scheme [4] .............................................................. 14

Figure 11: 2-DOF System with H-Infinity Controller [11] ............................................ 15

Figure 12: Structure of the Feedback Compensator [11] ............................................... 15

Figure 13: Other Configuration of a RWS Controller using H-Infinity Theory [7]....... 15

Figure 14: Multi-Objective Control Synthesis Framework [13] .................................... 16

Figure 15: General Structure of a Two-Input FZ-PID Controller [15]........................... 17

Figure 16: Active 4WS Controller Layout [17].............................................................. 18

Figure 17: Full Order Observer Layout [18] .................................................................. 19

Figure 18: Active 4WS Observer Layout, Driver-Vehicle System [17] ........................ 19

Figure 19: Principle of the Angle Superposition [20] - [21] .......................................... 20

Figure 20: Simulation Environment [25] ....................................................................... 22

Figure 21: Interface IPG CarMaker – Simulink [25] ..................................................... 23

Figure 22: Scope for the Use Case ................................................................................. 26

Figure 23: Tyre Lateral Properties.................................................................................. 31

Figure 24: Step Responses - 3-DOF Model ................................................................... 31

Figure 25: Yaw Rate Time Responses - 3-DOF Model ................................................. 32

Figure 26: Yaw rate vs. Forward Speed - 3-DOF Model ............................................... 32

Figure 27: Understeer Diagram - 3-DOF Model ............................................................ 33

Figure 28: CarMaker Axis Systems [28]........................................................................ 34

Figure 29: ISO Sign Convention .................................................................................... 34

LIST OF FIGURES


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Figure 30: CarMaker Model in Simulink - Layout......................................................... 34

Figure 31: CarMaker Vehicle Model.............................................................................. 35

Figure 32: IPG CarMaker Car And Trailer Subsystem .................................................. 35

Figure 33: Interface of the Steering System [27] ........................................................... 36

Figure 34: Steering System [27]..................................................................................... 36

Figure 35: IPG CarMaker Forces Subsystem................................................................. 37

Figure 36: Structure of the Tyre Model [27] .................................................................. 37

Figure 37: Comparison IPG CarMaker/3-DOF Model - Yaw Rate Response ............... 39

Figure 38: Yaw Moment Controller Structure for RWS................................................ 41

Figure 39: Yaw Moment Controller Structure for AFS ................................................. 41

Figure 40: Lookup Table for Reference Yaw Rate ........................................................ 43

Figure 41: Reference Model Subsystem - Lookup Table............................................... 43

Figure 42: Reference Yaw Rate Time History for a Step Steer Input............................ 43

Figure 43: Definition of the Tow Angle and the Rotation rz [27]................................... 44

Figure 44: RWS Implementation in the CarMaker Model ............................................. 45

Figure 45: CarMaker Yaw Moment Controller Layout for RWS .................................. 45

Figure 46: AFS Controller at the Steering Column........................................................ 46

Figure 47: AFS at the Steering Column - Controller Layout ......................................... 46

Figure 48: CarMaker Yaw Moment Controller Layout for AFS ................................... 47

Figure 49: Actuator Model Subsystem........................................................................... 48

Figure 50: Actuator Bandwidth Influence - Step Steer Input......................................... 49

Figure 51: Time Histories: Basic vs. Optimized Driver Model ..................................... 51

Figure 52: Time Histories: Bandwidth and Controller Tuning ...................................... 53

Figure 53: Step Steer Input - Test 1 - Yaw Rate Control ............................................... 55

Figure 54: Time Histories - Test 1 - Yaw Rate Control ................................................. 56

Figure 55: Sideslip Phase Plane - Test 1 - Yaw Rate Control........................................ 57

Figure 56: Vehicle Trajectory - Test 1 - Yaw Rate Control........................................... 57

Figure 57: AFS vs. Passive Vehicle in IPG Movie - Test 1 - Yaw Rate Control........... 57



Figure 60: RWS vs. Passive Vehicle in IPG Movie - Test 3 - Yaw Rate Control ......... 61



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Figure 62: Steering Wheel Angle and Forward Velocity - Test 4 - Yaw Rate Control . 62












Figure 74: Wind Disturbances - Test 9........................................................................... 71




Figure 78: Derivative of the Lateral Velocity Controller Structure for RWS................ 75

Figure 79: Derivative of the Lateral Velocity Controller Structure for AFS ................. 76

Figure 80: CarMaker Derivative of the Lateral Velocity Controller Layout for RWS .. 76

Figure 81: Time Histories - Test 1 - Derivative of the Lateral Velocity Control........... 78

Figure 82: Sideslip Phase Plane - Test 1 - Derivative of the Lateral Velocity Control . 79

Figure 83: Vehicle Trajectory - Test 1 - Derivative of the Lateral Velocity Control..... 79






Figure 89: RWS vs. Passive Vehicle in IPG Movie - Test 6 - Derivative of the Lateral

Velocity Control ..................................................................................................... 84




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Figure 92: AFS vs. Passive Vehicle in IPG Movie - Test 6 - Derivative of the Lateral



Figure 94: AFS vs. RWS - Test 7 - Derivative of the Lateral Velocity Control ............ 87





Figure 99: AFS vs. Passive Vehicle in IPG Movie - Test 9 - Derivative of the Lateral


Figure 100: Roll Angle Time Response - Test 3 - Controller Comparison.................... 95

Figure 101: Vehicle Body Sideslip Angle, Vehicle Heading and Direction of Motion. 99

Figure 102: Two Degree of Freedom Reference Model with Saturation ..................... 103

Figure 103: Understeer Diagram with the 3-DOF Model - 2-DOF Reference Model . 104

Figure 104: Yaw Rate Time Response with 3-DOF Vehicle Model - 0.03rad Step Steer

Input - 2-DOF Reference Model .......................................................................... 105

Figure 105: Yaw Rate Response with CarMaker Vehicle Model - 0.03rad Step Steer

Input - 2-DOF Reference Model .......................................................................... 105

Figure 106: Time Histories - 0.03rad Step Steer - 2-DOF Reference Model............... 106

Figure 107: Yaw Rate Response with 3-DOF Vehicle Model - 0.08rad Step Steer - 2-

DOF Reference Model ......................................................................................... 107

Figure 108: Yaw Rate Response with 3-DOF Vehicle Model - Double Step Steer Input -

2-DOF Reference Model ...................................................................................... 108

Figure 109: Time Histories - Test 7 - 2-DOF Reference Model .................................. 109

Figure 110: Vehicle Trajectory - Test 7 - 2-DOF Reference Model ............................ 110

Figure 111: Yaw Rate and Vehicle Trajectory - Test 6 - 2-DOF Reference Model .... 110

Figure 112: Time Histories - Test 3 - 2-DOF Reference Model .................................. 112

Figure 113: Yaw Rate vs. Steer Angle - Vx=70km/h - Neutral Steering Target ......... 113

Figure 114: Yaw Rate vs. Steer Angle - Vx=140km/h - Neutral Steering Target ....... 113

Figure 115: Structure of the 3-DOF Model - 2WS....................................................... 125

Figure 116: 3-DOF Vehicle Model .............................................................................. 126

Figure 117: Tyre Force in the Vehicle Coordinate System.......................................... 128


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LIST OF TABLES

Table 1: Use Case ........................................................................................................... 27

Table 2: P+I Controllers’ Parameters - Yaw Rate Feedback Control ............................ 48

Table 3: P+I Controllers’ Parameters after Actuator Integration - Yaw Rate Feedback

Control .................................................................................................................... 54

Table 4: P+I Controllers’ Parameters - Derivative of the Lateral Velocity Control ...... 77

Table 5 : RMS Value Comparison - Test 1 .................................................................... 93





Table 10 : RMS Value Comparison - Test 7 .................................................................. 97

Table 11 : RMS Value Comparison - Test 8 .................................................................. 98

Table 12 : RMS Value Comparison - Test 9 ................................................................ 100

Table 13: P+I Controllers’ Parameters - 2-DOF Reference Model.............................. 103

Table 14: Data Sheet Test 1.......................................................................................... 129









LIST OF TABLES


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NOMENCLATURE

Notation

a - distance from the vehicle C.G. to the front axle

ay - vehicle lateral acceleration

b - distance from the vehicle C.G. to the rear axle

Cf, Cr - front, rear tyre stiffness

Cφf, Cφr - front, rear suspension roll damping

D(s) - pure delay transfer function

Fs - aerodynamic disturbances

Fyi - lateral tyre force

Fzi - vertical tyre force

G(s) - controller transfer function

h - distance from sprung mass C.G. to the roll axis

hf, hr - height of front, rear roll centre

huf, hur - height of front, rear unsprung mass C.G.

H(s) - actuator transfer function

Ixx - sprung mass moment of inertia about the roll axis

Ixz - sprung mass product of inertia about the roll and yaw axes

Izz - sprung mass moment of inertia about the yaw axis

l - vehicle wheelbase

lfs, lfr - distance from the sprung mass C.G. to the front, rear axle

Kφf, Kφr - front, rear suspension roll stiffness

m - vehicle mass

ms - sprung mass

muf, mur - front, rear unsprung mass

P - controller proportional gain

g - acceleration due to gravity

r - yaw rate

rref - reference yaw rate

rz - wheel orientation around vertical axis

Sh - plysteer – horizontal shift

NOMENCLATURE


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Sv - conicity forces – vertical shift

t - vehicle track

Td - pure time delay

Ti - controller integral time constant

U - set point for the actuator

Vx - vehicle forward velocity

Vy - vehicle lateral velocity

α - side slip angle

β - vehicle body sideslip angle

γs - static camber angle

γ - dynamic camber angle

δfactive - active part of the front steer angle

δf, δr - front, rear steer angle

δsw - steering wheel angle

η - lateral deviation from straight ahead path

θf, θr - front, rear steering pinion rotation angle

µ - road/tyre friction coefficient

µHi - adjustable road/tyre friction coefficient

τ0 - actuator time constant

φ - roll angle

Acronyms

4WS - Four Wheel Steering

AFS - Active Front Steering

C.G. - Centre of Gravity

DOF - Degree of Freedom

FWS - Front Wheel Steering

GUI - Graphical User Interface

LQR - Linear Quadratic Regulator

RMS - Root Mean Square

RWS - Rear Wheel Steering

TVD - Torque Vectoring Differential


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1 INTRODUCTION

1.1 Topic Area

Safety and comfort are key points for the automotive industry for several decades. Car

manufacturers have particularly made remarkable efforts to improve the vehicle

behaviour. Several intelligent stability and handling control systems have been

developed and are now common devices in mass production vehicles. Most of these

systems use brake intervention at individual front and/or rear wheels and/or reduce

engine power in order to generate yaw moments to improve the vehicle stability when it

could be impaired. Active Baking System (ABS) or Electronic Stability Program (ESP)

are certainly the most famous and widespread systems.

Over a period of time, alternatives have appeared to improve the vehicle handling and

the overall safety by working through the cornering forces. Manufacturers are

particularly attentive to these alternatives since they could not deteriorate the driver

enjoyment – often said impaired with actual stability control devices. Active steering is

one of these alternatives.

1.2 Active Steering

Several researches have demonstrated the efficiency of active steering to improve the

vehicle stability. Active steering is a generic name containing Active Front Steering

(AFS), Rear Wheel Steering (RWS) and Active Four Wheel Steering (Active 4WS). A

particular attention has to be paid to these acronyms since confusions happen

frequently. AFS consists of adding a steer angle at the front wheels in complement to

the driver steer action. RWS provides the steer of the rear wheels while the front is

steered via a traditional passive system controlled by the driver. Active 4WS is a

combination of AFS and RWS: the rear wheels are steered on the demand of an

electronic system, the front wheel steering is a superposition of the driver action and an


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active component. Note that Active 4WS is different to Four Wheel Steering (4WS)

which includes Passive Rear Wheel Steering, RWS and Active 4WS.

Whatever the method of active steering, this could help to reduce the delay in the

generation of cornering forces as well as permit the vehicle path and behaviour to be

controlled. The two main state variables that an active steering system could influence

are the body sideslip angle and the yaw rate. A relevant control of one of these variables

improves the overall vehicle behaviour.

4WS systems have been widely studied for more than twenty years and passive 4WS

systems have been integrated in mass production vehicles a few years ago. Several

advantages of 4WS and AFS are claimed to enhance the manoeuvrability at low speed,

improve the handling at high speed and improve the driving safety.

1.3 Research Activity, Objectives

1.3.1 Project Description

Jaguar Land Rover has always given lots of emphasis on the comfort, the performance,

the driver enjoyment and the safety of their vehicles. Therefore, stability control

systems are becoming an important aspect of their research works and the company is

continuously considering new possibilities. Planning the launch of a new saloon vehicle

in a near future, JLR is paying attention to three new stability control systems: AFS,

RWS and Torque Vectoring Differential (TVD) which could be fitted in this vehicle. A

second project aiming to investigate TVD has been carried in parallel to this one by I.

Olazarri.

1.3.2 Objectives

The aim of this project is to provide a review of AFS and RWS as vehicle stability

control devices and investigate their benefits for a new vehicle. The main part of this

project consists of simulations to evaluate the performance of each system. The

simulation tool IPG CarMaker is used for such a purpose. Along this lines appear

different objectives which can be regrouped in three major tasks:


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• Design of the controller

- Define the objectives of each control system by performing a

requirement capture.

- Draw up a list of test scenarios which show the objectives being

achieved – or not.

- Develop a basic vehicle model to become familiar with the vehicle

dynamics.

- Define control strategy(ies) applicable for both AFS and RWS.

- Build up a model of the actuator – at a higher level.

- Implement the active systems in IPG CarMaker via Simulink.

• Carried out simulations

- Perform basic simulations in Simulink and CarMaker to verify the

vehicle model.

- Tune the controller to achieve the best response.

- Investigate the influence of the actuator on the performance of the

systems.

- Carried out simulations based on the test scenarios defined in a first stage

of the project to evaluate the potential and benefits of each system.

• Get recommendations

- Get relevant conclusions about the capabilities of the systems to improve

the vehicle stability.

- Compare AFS and RWS with TVD – in collaboration with I. Olazarri.

- Formulate recommendations for JLR regarding the use of AFS or RWS

for a new vehicle.


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1.4 Layout of the Report

This report consists on ten major chapters. This first chapter introduces the project and

its objectives. A review of the existing control methods for RWS is then presented. A

short description of Active 4WS and AFS is also included. Next, the simulation

environment is briefly introduced in a third chapter. The fourth chapter presents a

requirement capture to define the objectives of the active steering systems while

Chapter 5 describes the vehicle models. Then, two controller strategies – yaw rate

feedback control and derivative of the lateral velocity control – which aim to improve

the vehicle stability are developed for both AFS and RWS, tested and compared in

Chapters 6, 7 and 8. In Chapter 9 is investigated a new control strategy to improve the

handling behaviour. Finally, conclusions as well recommendations for future

development work are stated in a last chapter.


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2 ACTIVE STEERING

With the objective to become more confident with the area of investigation, this section

is a literature review of previous studies performed on active steering. It has been

chosen to focus this review on the control methods for RWS. However, a brief

introduction to Active 4WS and AFS is also provided.

2.1 Rear Wheel Steering and Four Wheel Steering

2.1.1 The Necessity of Four Wheel Steering

In order to understand why 4WS is needed, the steering characteristics of a Front Wheel

Steering (FWS) vehicle must first be analysed. Sano et al [1] did a relevant study in this

area: their work is referenced in lots of other studies. They sequenced the series of

motions generating the turning of a FWS vehicle as illustrated in Figure 1.

Figure 1: Transient Response of FWS Vehicle to Stepwise Steering Input [1]

The transient response is divided in two phases: the first, resulting from the lateral

forces generated at the front tyres, corresponds to the rotation around the Centre of

Gravity (C.G.) and generates the yaw motion. The second is a consequence of the first:

the yaw motion involves lateral forces at the rear tyres and, combined with the front

ones engage the rotation around the turning centre. As mentioned by Sano et al, the


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overall vehicle rotation is subject to a delay mainly due to vehicle forward speed and

vehicle inertia.

Thereby, appears the requirement of 4WS. For a 4WS vehicle, no sideslip angle is

needed to generate the lateral forces at the rear tyres as the rear wheels are turned. Sano

et al sequenced the transient response of a 4WS vehicle as represented in Figure 2.

Figure 2: Transient Response of 4WS Vehicle to Stepwise Steering Input [1]

If the rear wheels are correctly controlled to set the steady state sideslip angles equal to

zero, the rotation around the C.G. is not needed anymore. In this way the steering

response is considerably improved by decreasing consequently the delay mentioned

previously.

The necessity of 4WS is so highlighted. The aim of the next sections is to provide a

review of existing methods to control a 4WS system.

2.1.2 Classification of the Control Methods

Lots of different methods to control the steer angles of a 4WS vehicle have been

proposed and reported by the literature. Before describing and analysing these methods,

it is necessary to classify them. Nikzad and Naraghi [2] proposed a relevant

classification into Schemes and Strategies.

2.1.2.1 Control Schemes

The Control Scheme rests on the number of steering angles that are controlled. It can be

a “Single Steering Scheme” – Figure 3, or a “Dual Steering Scheme” – Figure 4.


- 7 -

Figure 3: Block Diagram of Single Steering

Scheme [2]

Figure 4: Block Diagram of Dual Steering Scheme [2]

The former is the simplest as it controls only one state variable - generally yaw rate,

lateral speed or sideslip angle. For a conventional 4WS vehicle, only the rear wheels are

controlled, the front ones are actuated by the driver. Hence the name of RWS which

refers to active RWS coupled with a conventional FWS system.

The Dual Steering Scheme consists of controlling both the front and rear wheels which

gives the possibility to control two state variables. Hence is explained the name Active

4WS which refers to a combination of front and rear active steering systems. This

scheme is more advanced and is the purpose of several researches nowadays.

2.1.2.2 Control Strategies

The Control Strategy is “a method to set the final control policy” [2]. Niksad and

Naraghi divided the existing strategies into three categories: Zero Side Slip, Zero Yaw

Rate and Reference Model.

The Zero Side Slip strategy consists of setting the steady state value of the sideslip

angle to zero. It leads to reduce the lateral motion, improve the manoeuvrability and

reduce the phase by increasing the yaw rate [1].This strategy can be inappropriate at

high speed as it tends to reduce the vehicle stability.

In opposition to the previous strategy, the Zero Yaw Rate strategy minimizes the yaw

rate but increases the lateral velocity. This tends to reduce the rotational motion and

increase the lateral one which could be preferable for high speed manoeuvres [2].


- 8 -

The third strategy proposed by Niksad et al – Reference Model – is a combination of the

previous two and considers a reference model to be tracked. Generally, the reference

model is only influenced by the front steer angle and does not consider the controlled

state variables. Niksad and Naraghi showed that a reference model can lead to less

transient vibration with more reliability. Moreover, the use of a reference model with

Dual Steering Scheme gives the best handling response but it is a complex control

device – details in Section 2.2.

2.1.3 Open Loop and Closed Loop

As all controlled system, two methods exist to control the rear wheel steer angle.

The first one, open loop control or feed-forward control – Figure 5 (a) – has been

largely investigated. In this case, the driver, which can be included within the loop,

plays the role of the feedback. Therefore it is preferable to call this control method feed

forward instead of open loop as a closed loop is created by the driver – Figure 5 (b) [3].

Figure 5: Open Loop Control

In case of disturbances, the driver must react and steer the steering wheel to involve the

actuation of the rear wheels via the controller. In this way, it is a passive rear wheel

steering strategy since nothing occurs as long as the driver does not turn the front

wheels.

The second configuration, closed loop control, consists both in feed forward and

feedback compensation. This arrangement has been illustrated by Pascali [4] – Figure 6.

The motion is corrected even if there is no action provided by the driver. This

configuration is an active control.

(a)

(b)


- 9 -

Figure 6: Closed Loop Control - Feed-forward / Feed-back Structure [4]

These two methods have been largely investigated in the past. They are further

presented in the next sections.

2.1.4 Open Loop, Feed-forward Structure

The feed-forward compensation has been the first structure to be integrated in mass

production vehicles as it rests on simple algorithms and mechanical devices to steer the

rear wheels. Two main feed-forward strategies exist: “Vehicle Speed Function Based”

and “Steer Angle Function Based”.

2.1.4.1 Vehicle Speed Function Based

2.1.4.1.1 Description

Sano et al [1] proposed a simple open loop strategy to keep the steady state body

sideslip angle equals to zero:

1r fKδ δ=

with

2

2

1

x

f

x

r

VlC

mba

VlC

mab

K

+

+−

= (1)

This algorithm has been used in lots of other studies as it gives relevant results and is

quite simple.

The steering ratio between front and rear depends on the vehicle speed. This algorithm

is so called “Vehicle Speed Function Based”. At low speed, the rear wheels are turned

out of phase to the front ones which improves the manoeuvrability by reducing the

turning diameter. At high speed, the rear wheels turn in the same direction as the front

-


- 10 -

wheels improving the handling behaviour and the stability. Despite these characteristics,

the implementation complexity is slightly increased by the use of a speed sensor.

2.1.4.1.2 Commercial Applications

This control strategy has been used by Mazda to develop the system Mazda 4WS

integrated for example in the Mazda 626. It uses both a speed sensing system and the

front steer angle to control the rear wheels. The steering characteristic is shown in

Figure 7.

Regarding the practical implementation, a shaft

from the front rack actuates a servo valve and,

coupled with the controller, procures the

motion of the rear tie rod via a hydraulic

actuator [3].

The Vehicle Speed Function Based is also used

in Quadrasteer, a 4WS system developed by

Delphi for General Motors. It is difficult to find

relevant information about this system which

may be protected by confidentiality.

Figure 7: Steering Characteristics of

Mazda 4WS [3]

2.1.4.2 Steer Angle Function Based

2.1.4.2.1 Description

Sano et al proposed another control strategy

called “Steer Angle Function Based” where

the rear wheels are controlled as a function of

the magnitude of the steering wheel input – at

low speed, this input is large whereas it is

very small at high speed. The steering ratio is

set regarding this consideration. Figure 8

illustrates the control law given by Sano et al.

In opposition to the Vehicle Speed Function

Based, this control strategy does not require a

speed sensor system.

Figure 8: Rear Wheel Steer Angle: Function

of the Steering Wheel Angle [1]


- 11 -

2.1.4.2.2 Commercial Application

The Steer Angle Function Based was used in the Honda 4WS system [3]. In 1987, this

system was the first 4WS system integrated in a mass production vehicle: the Honda

Prelude. From a practical aspect, the rear steering system is actuated mechanically via a

shaft form the front steering system and a gearbox to achieved the desired ratio.

2.1.4.3 Other Approaches

Naclecz and Bindemann [5] proposed four simple rear wheel control algorithms which

are still referenced today by several works. All these algorithms are based on the front

and rear steering pinion rotation angle - respectively θf and θr. Two of them are

interesting: the first one considers the angular and velocity rotation of the steering

wheel, r

K and r

T are two constants:

swf δθ = and rswrswr TK ⋅−⋅= δδθ & (2)

The second, called “Advance 4WS” controls the rotation of both the front and rear

steering pinions:

fswswf T⋅+= δδθ & and rswrswr TK ⋅−⋅= δδθ & (3)

Naclecz and Bindemann compared the performance of these controllers with a FWS

system by using their own 3 Degree of Freedom (DOF) model. They concluded that the

four 4WS systems provide better handling performance, the advance 4WS is the best

one.

More recently, Morgando et al [6] have investigated a control logic system based on a

feed-forward structure with the objective to limit the number of parameters used in the

controller. They developed a Reference Model strategy and concluded that feed-forward

structure involves instantaneous vehicle control and gives quicker response than a

closed loop controller. Nevertheless, a feed-forward structure reaches its limits when

the vehicle is subjected to a lateral acceleration higher than 0.6g. In this situation the

linear approximation – particularly the tyre – is not acceptable. In this way, the authors

advocated a closed loop control logic.


- 12 -

2.1.5 Closed Loop Structure

Closed loop control appears as more advanced and more complex than open loop

control. However, it allows the considerable improvement of the system performance

and provides a better rejection of disturbances. Closed loop control refers to active

control: the rear wheels are steered even if the driver does not procure any action.

A common integration layout of a closed loop controller was proposed by Akita [7]; it is

given in Figure 9.

Figure 9: Configuration of a Closed Loop 4WS System [7]

2.1.5.1 Basic Yaw Rate Feedback Controller

One of the first RWS closed loop controllers was proposed by Whitehead [8] in 1988

and is still used as a reference nowadays. The algorithm developed by Whitehead uses a

yaw rate feedback as well as the front steer angle to control the rear wheel steer angle:

f

r

f

xr

f

xr

x

rC

Cr

VC

aC

V

b

C

mVδδ −

+−= (4)

This control law tends to produce zero sideslip angle during a steady state cornering. In

this, there are no needs to measure the sideslip angle. By comparing, the performance of

this controller with the performance of the Vehicle Speed Function Based controller

proposed by Sano, Whitehead demonstrated that closed loop control improves the

vehicle stability at high speed after a sudden steering input - the steering overshoot is

reduced. Moreover, he showed that his approach allows a significant reduction of the

phase lags in the lateral response improving the handling performance.

Xia and Law [9] did quite a similar study by comparing the performance of open loop

control – Vehicle Speed Function Based controller proposed by Sano et al, closed loop


- 13 -

control – algorithm proposed by Whitehead, and a FWS system. They evaluated “the

collision avoidance performance during combined hard braking and severe steering”

with a non-linear 5-DOF vehicle model. The authors noticed that, because of a strong

oversteering behaviour of the 4WS vehicles, a larger steering input, and so a higher

driver workload is needed for the two 4WS systems to achieve the same yaw rate as the

FWS vehicle. Under 4° steering input, the yaw rate responses are similar for the open

and closed loop systems. However, above 4°, the non-linearity of the tyres highlights

better performances for the closed loop system - higher yaw rate. Xia and Law’s

conclusions were similar to those obtained by Whitehead a couple of years before.

Lee [10] did an interesting work to compare open and closed loop controller by

including the driver in the loop. By achieving computed and “on the road” simulations,

Lee observed that the performance achievable with a 4WS vehicle (both open loop and

closed loop) in high speed change lane change manoeuvre are not significant for an

experienced driver in comparison with a FWS vehicle. In this way, Lee reconsidered the

conclusions got by Xia and Whitehead. However, this must be considered warily as the

Lee’s study relies on a specific experienced driver model.

More recently, researches have been focused on more sophisticated closed loop

controllers using advanced control algorithms. Some of them are presented in the next

section.

2.1.5.2 Reference Model Strategy

Pascali et al [4] investigated the use of the reference model strategy to improve the

vehicle handling and comfort. They developed a target controller with the objective to

reach the best handling performance. The layout of their controller is represented in

Figure 10.


- 14 -

Figure 10: Feedback Contribution Scheme [4]

It consists on a feed forward / feedback compensations aiming to nullify the transient

and steady state sideslip angle as well as reducing the time response of the system. In

Figure 10, “X” relates a virtual state variable. Moreover, the virtual model is a non-

linear bicycle model and the controller rests on Linear Quadratic Regulator (LQR)

theory. Pascali et al showed that the handling performance could be improved

significantly. However, the main point of their results is that the handling performances

are considerably affect by the accuracy of the reference model and so let believe the

potential tuning of the handling performance via a reference model.

2.1.5.3 H-Infinity Controller

Hirano et al [11] developed a controller using an H-Infinity (H-∞) theory to design the

feedback compensator – C2(s) in Figure 11 and 12. This compensator aims to track a

desired yaw rate – R– in opposition to the controller proposed by Whitehead which

aims to keep the sideslip angle equal to zero. In order to improve the vehicle behaviour

in the entire handling domain, the authors considered also an adaptive logic – Figure 12

– to reduce the yaw rate when the tyres reach the limit of adhesion and are not able to

generate enough lateral forces for the demanded yaw rate. Their experimentation has

illustrated the potential improvements of controllability and stability generated by such

a controller if the tracked yaw rate is well defined.


- 15 -

Figure 11: 2-DOF System with H-

Infinity Controller [11]

Figure 12: Structure of the Feedback Compensator [11]

P(s): Plant (Vehicle Dynamics) C1(s): Feed forward Compensator P0(s): Reference Model R0: Desired Yaw Rate

Figure 13 is another H-∞ controller layout proposed by Akita et al [7]. The steering

wheel angle, the yaw rate, and the lateral acceleration are the vehicle states which are

used to control the rear wheels. To improve the stability, the yaw rate and the lateral

acceleration are used as feedback and compared to reference states.

Figure 13: Other Configuration of a RWS Controller using H-Infinity Theory [7]

Lv, Chen and Li [12] have also investigated the use H-∞ control method by studying a

Multi-Objective H-∞ controller. In their work, the yaw rate is the only feedback signal

which reduces considerably the cost of implementation. They showed that, as expressed

by Hirano, the handling performance can be improved particularly at high speed.

2.1.5.4 Mixed H-Infinity and H-2 Controller

The H-∞ controller is well known for its robustness but involves important control

effort. Another control algorithm, the H-2, is well appropriated for real system.

However, stability and robustness of an H-2 controller can be deteriorated in cases of

uncertainties – quite common in the vehicle application with wind, surface roughness or

braking. In this way, You and Jeong [13] proposed a “mixed H-2/H-∞ multi-objective


- 16 -

synthesis with pole constraint on the basis of full state feedback applying Linear Matrix

Inequality”. A base of their controller is illustrated in Figure 14. They demonstrated that

such a controller can be robust, achieve good performance – attenuation of severe

disturbances, and also improve the vehicle stability. Nevertheless, as mentioned by Lv

et al, it needs more state variables to work. The You and Jeong’s approach requires a

measure of the sideslip angle which is difficult to achieve for a low cost.

Figure 14: Multi-Objective Control Synthesis Framework [13]

2.1.5.5 Limited State Feedback Controller

This problem of measurement has been highlighted in several studies. Generally,

feedback controls are done with full state feedback information and so rest on the

perfect measurement of these state variables. This is not often true in practice where

signals are often associated with noise. A pertinent approach has been developed by El-

Nashar et al [14]. They proposed a Limited State Feedback system by using the Kalman

filter algorithm. This algorithm allows the prediction of the state by combining the

extrapolated past value and the observed value. This method takes into consideration the

practical limitations of the feedback signal measurement. By comparing their system

with a LQR feedback gain system and a conventional 2WS system, they found that a

Limited State Feedback system generates the same performance as the classical LQR

feedback gain system. Nevertheless, the former is more practical as it reduces the

measurement work and sensor devices. In this way, the authors reconsidered most of the

RWS controllers proposed at this time.


- 17 -

2.1.5.6 Fuzzy Logic Controller

Ozatay, Unlusoy and Yildirim [15] investigated the use of the Fuzzy Logic with a two

input Fuzzy PID controller – Figure 15.

Figure 15: General Structure of a Two-Input FZ-PID Controller [15]

They demonstrated that both the steady state cornering behaviour and the lane change

manoeuvre stability can be improved by reducing the sideslip angle and improving the

response time of the yaw rate in comparison to a FWS vehicle. The main advantage of

their controller is to allow poor implementation of the controller gain without impairing

the stability of the system.

2.1.5.7 Time Delay Controller

Nikzad and Naraghi [16] investigated the differences between a LQR and a Time Delay

Controller with a 3-DOF non-linear handling model. The authors underlined clearly that

the use of LQR is not possible for a dual steering scheme whereas time delay controller

can be use for both single and dual steering schemes. Nikzad and Naraghi showed that

for a single steering scheme the time delay controller involves a yaw rate response

closer to the reference needed and a better handling behaviour than the LQR controller.

Moreover, the time delay controller with the dual steering scheme rejects well all

disturbances. Deeper investigations of the time delay controller are needed to

characterise well the influence of the delay factor, particularly for the dual steering

scheme.


- 18 -

2.2 Active Four Wheel Steering – Dual Steering Scheme

First of all, as said before, Active 4WS refers to an active system which controls both

front and rear steer angles. It can be also referred as Dual Steering Scheme.

Active 4WS has been studied by Aga et al [17] with a 2-DOF vehicle model. They have

developed a first controller to control both yaw rate and sideslip angle as illustrated in

Figure 16.

Figure 16: Active 4WS Controller Layout [17]

Their simulations showed that the yaw rate and the sideslip angle responses are faster

than a “conventional” open loop 4WS system. However, the lateral acceleration is

reduced which is not appreciable for a driver point of view. They demonstrated also that

with a dual steering scheme the yaw rate feedback dominates: the sideslip angle

feedback has very small influence. Thereby, they had developed a second controller

taking the roll motion (hence a 3-DOF model) for the second motion instead of the

sideslip angle. Such a controller confers a smooth response for the roll angle –

enhancement of the comfort, but tends to reduce the yaw rate. The work achieved by Ag

et al shows that different feedback configurations are possible. They have lots of

influence on the handling behaviour and involve often some compromises.

Palkovics [18] has also investigated Active 4WS in 1992: both front and rear wheels are

steered via a control unit which has the steering wheel angle and the lateral acceleration

as inputs. He used a Full Order Observer method to estimate the yaw rate and the side

sleep angle from the lateral acceleration as shown in Figure 17.


- 19 -

Figure 17: Full Order Observer Layout [18]

In this way, he used the simplest variable to measure – lateral acceleration – and avoids

measuring the sideslip angle. Moreover, the Palkovics’ work was based on a reference

model strategy where the real vehicle had to follow a virtual reference model. He also

included the driver in the model as illustrated in Figure 18 where the complete driver-

vehicle system is represented.

Figure 18: Active 4WS Observer Layout, Driver-Vehicle System [17]

The main conclusion obtained by Palkovics is that, with a full order observer, the design

parameters of the controller are crucial regarding the system performance: a

configuration very performing for a given vehicle can become unstable if a simple

parameter as the tyre stiffness is slightly changed. In regards to the weakness of this

controller, Palkovics advices the use of robust controller or adaptive controller for

Active 4WS.

2.3 Active Front Steering

2.3.1 Description

Active Front Steering – commonly called AFS – consists of superposing a controlled

angle to the steering wheel angle as represented in Figure 19. Indeed, from the steering

wheel driver’s command δsw is added an active component δfactive via a planetary gear

set. This additional degree of freedom enables a continuous and driving dependent


- 20 -

adaptation of the steering characteristics. Features like steering comfort, driver work

load and steering dynamics are optimized; stabilizing steering intervention can also be

performed.

The permanent mechanical connection between the steering wheel and the wheels

remains. Therefore, it is important to notice that AFS must not be considered as a steer-

by-wire device – not permitted by the law at this day.

Figure 19: Principle of the Angle Superposition [20] - [21]

The first AFS system has been developed by ZF Lenksysteme and BMW [19] and

introduced in the new BMW 5-series in 2003. Klier et al. from ZF Lenksysteme [20] -

[21] presented the main features and characteristics of their system. These papers are

very interesting and formative as this system is the first to be integrated in a

commercialized vehicle. The practical implementation is not presented here, however it

could be refer to [20] - [21] for further details.

2.3.2 Control Strategies

Several studies have been done on AFS [22 to 25]. Most of them used a reference

model strategy – this concept will be further presented in Section 2.1.5.2.

Oraby et al [22] proposed the controller which consists on a feed forward/feedback

controller using the LQR theory to obtain the optimal design. Other investigations have

been carried out with the same controller structure, using H-∞ control theory [23], or the

sliding mode technique [24] to enhance the robustness.

All the studies showed that AFS is very interesting at low and moderate lateral

acceleration by improving considerably the handling characteristics.


- 21 -

2.4 Closing Comments

To conclude this review, several important observations and conclusions have to be

highlighted. First, two main categories of controller layouts have been investigated in

the literature: the feed forward compensation which exploits the driver’s steering wheel

angle as system input, and the feedback compensation which uses state variables of the

vehicle as input. The former has already been integrated in passenger cars, but it cannot

be considered as an active device. A combination of the two compensations – feed

forward/feedback – appears as the best configuration for RWS controllers. This method

of active control can provide high performance: stability, responsiveness, robustness

and reliability.

The literature does not allow the identification of the best configuration for these feed

forward/feedback structures. Indeed, a relevant comparison of the different controllers

has not been studied. Provide its own comparison and conclusions is also delicate as all

the investigated controllers rest on different assumptions, dynamic models and are

always the result of compromises. However, the use of simple compensator –

Proportional Integral – may give very relevant results in spite of the utilisation of

advance theories, as LQR or H-∞ theories would improve the controller robustness.

Moreover, integrated a reference model into the loop is also interesting and necessary.

A desired steering response can therefore be achieved and tune the handling

performance becomes possible.


- 22 -

3 SIMULATION ENVIRONMENT

The simulation environment is a key aspect of this study. The aim of this section is to

provide a brief introduction to this environment. Firstly, IPG Carmaker is introduced,

and then its interaction with Matlab/Simulink is discussed.

3.1 IPG CarMaker

The software IPG CarMaker, a tool for vehicle dynamics simulation, is used to carry out

the simulations of this project. IPG CarMaker is a “Virtual Vehicle Environment” which

includes vehicle models – IPG Car, driver models – IPG Driver, and road models – IPG

Road. Other virtual models are included and closely related as represented in Figure 20.

Figure 20: Simulation Environment [25]

The software incorporates also the CarMaker Interface Toolbox which contains the

Graphical User Interface (GUI) to set simulation parameters. The toolbox contains an

instrument window to view the most important information – from a driver’s

perspective – during a simulation, IPG Control to plot and view the results of a

simulation, and IPG Movie to render 3-D animations.

Note that CarMaker User’s Guide [26], CarMaker Reference Manual [27] and

CarMaker Programmer’s Guide [28], have been fundamental resources during the entire

project.

(Reproduced with the permission of IPG Automotive GmbH)


- 23 -

3.2 IPG CarMaker for Simulink

IPG CarMaker provides also a connection with Matlab/Simulink – IPG CarMaker for

Simulink, where the CarMaker features are added to Simulink via S-Function

implementations. This interface CarMaker/Simulink is represented in Figure 21.

Figure 21: Interface IPG CarMaker – Simulink [25]

The CarMaker environment executes an advanced Simulink model of the vehicle – see

Section 5.2 – and the driver. In this configuration, CarMaker accounts for the conductor

of the simulation process via the “Sync_In” / “Sync_Out” variables in Simulink.

CarMaker is also where are defined vehicle parameters, test scenarios, driver

characteristics, and all the other data needed for a simulation.

To ensure the interaction between Simulink and CarMaker, several functions are added

in the Simulink library as “Read CM Dict” which allows Simulink to access and import

CarMaker variables in Simulink, or “Define CM Dict” and “Write CM Dict” to define

and write Simulink variables in the CarMaker dictionary.

In spite of CarMaker is a very performing simulation tool, some constraints have to be

highlighted since they have influences on the study. Indeed, first of all, most of the

CarMaker blocks in Simulink are locked S-functions and cannot be accessed by the user

(Reproduced with the permission of IPG Automotive GmbH)


- 24 -

which reduces the possibilities to implement new systems without creating a new block.

Moreover, the vehicle model in Simulink cannot be linearized and so frequency or root

locus analyses are not conceivable. Furthermore, the tool IPG Control, which is used to

plot simulations results, does not allow the displaying of results from two different

simulations in a same window. Therefore, all the results have to be imported – cmread

function, and processed in Matlab to provide relevant comparisons. Note that as

CarMaker is a real simulation environment, the vehicle is necessarily immobile at the

beginning of a simulation: a period of acceleration is always needed. This uninteresting

part of the simulation has also to be removed during the data processing in Matlab.


- 25 -

4 REQUIREMENT CAPTURE

The objective of this section is to draw up specifications for the systems under study -

AFS and RWS. The use of a requirement capture aims to consider most of the important

aspects and to highlight crucial questions for the design. The main principles of a

Requirement Capture for automotive systems have been developed by Gebhard [29].

The requirement capture undertook here is a functional one since the requirement is

“directly connected with the behaviour of the intended system” [29]. A functional

requirement capture defines the problem and gives answer to “Why this system?” and

“What has it to do?” The capture is carried out by writing a Use Case as proposed by

Alistair Cockburn [30]. The task is so divided in three main stages:

- Definition of the level of investigation, the primary actors and the scope.

- Writing of the Use Case.

- Getting useful conclusions regarding the objectives of the system.

4.1 Level, Primary Actors and Scope

Before writing the Use Case, the level of investigation, the primary actors and the scope

must be clearly defined. The investigation is done at a higher level as the studies is

“model based”. The primary actor “who initiates an interaction with the system to

accomplish some goals” [30], is obviously the driver. The scope, which defines the

boundaries of the system, allows the identification of “what is really the system under

discussion?” It is obtained by defining the elements surrounding the system. Figure 22

illustrates the scope definition and the interacting elements. Note that, in order to

achieve a performing Use Case, all considerations have to be included even if they will

not be used during the design process.


- 26 -

Figure 22: Scope for the Use Case

In Figure 22, the environment includes the road, external disturbances as the wind, the

temperature, etc. This figure shows that the system under consideration is the steering

system and the related controller which interact with several external elements and the

driver.

4.2 Use Case

The scope being clearly defined, the requirement capture leads to write a Use Case as

illustrated in Table 1. Lots of ways are conceivable to write a Use Case but it has been

chosen to present it in a Table as suggested by Alistair Cockburn. This Use Case is

applicable for both AFS and RWS since the two systems must responds to the same

requirement for a relevant comparison.

Note that a complete Use Case would also consider alternative and error flow. However,

regarding the aim of this study, these flows are not essential. Therefore, only the main

flow has been considered.

Longitudinal speed sensor

Steering wheel angle sensor

Environment

Electro-mechanical actuator

Yaw rate sensor

SCOPE

SYSTEM

Driver

PRIMARY ACTOR

Lateral acceleration sensor


- 27 -

Table 1: Use Case

USE CASE Improve the vehicle stability, expand the handling region

Context of Use Reduction or loss of the stability at high speed

Scope Active Steering Control System

Level Summary

System Steering system

Primary Actor Driver

Stakeholder & Interests Stakeholder Interests

Driver

Follow a given direction Feel responsive, accurate Less under/oversteering Low steering work

Car manufacturer Customer satisfaction

Preconditions None

Minimal Guarantees Driver always kept informed Rely to the driver, always able to turn the vehicle, minimal turning characteristics

Success Guarantees

Vehicle follows the desired path Vehicle more stable Vehicle less under/oversteering No delay Good feedback feeling

Trigger Predefined state variables are verified

Description Step Action

1 Driver turns the steering wheel

2 System validates driver request

3 System verifies all the data needed for the reference model (forward speed, steer input) if existing

4 System measures and verifies a predefined state variable

5 System compares the state variable with the one given by the reference model or another source

6 System generates corrective action

7 Vehicle follows the required path

Extensions Step Action

3a Sensor, controller failure

3a1 Use a backup strategy

6a Saturation of the actuator

6a1 Provide the maximum possible correction

7a Saturation of the tyres (cannot generate the desired lateral forces)

Data Variations /


- 28 -

4.3 Objectives for the Systems

The Use Case presented above has allowed the consideration of several aspects which

should have not been regards with a simple approach. It constitutes a solid guide to

define the objectives and goals for the two systems.

First of all, it is important to remind that, as inquired by Jaguar Land Rover, the system

objectives have to be defined for applications in the high speed range – low speed

manoeuvrability is not considered in this study. As AFS and RWS have to be compared,

they have to respond to the same objectives. Therefore, in the following discussion the

two systems will be grouped into a single name: active steering.

An active steering system may have two distinct objectives:

- Improve the vehicle stability during transient response – better damped, lower

settling time – and keep the steady state behaviour as closer as possible to the

passive vehicle to not influence driver feeling and enjoyment.

- Improve the vehicle handling and stability by achieving a desired steering

response – e.g. neutral steering or less understeering.

Whatever the objective, several goals in a lower level remain similar and they are:

- Reduce the phase lag in the lateral acceleration and yaw rate response. Indeed,

when the vehicle forward speed increases, delays in the lateral acceleration and

the yaw rate increase consequently. This implies a driver work to advance the

phase lead in the steering control. This work load has to be reduced.

- Reduce the vehicle body sideslip angle to fix it as closer as possible to zero.

However, as mentioned in Section 2.1.1, this angle must not be zero for a FWS

steering vehicle.

- Provide better response near the limit of adhesion. The increasing of lateral

acceleration during cornering involves a raise of the lateral forces in the tyre.

This force gets saturated resulting in the decreasing in the tyre stiffness. The

forces in the tyre have to be managed better.

- Reduce the driver work load and so enhance his comfort.


- 29 -

4.4 Test Scenarios

The enumeration of these diverse objectives shows that active steering systems aim to

improve the vehicle handling and stability of the vehicle comparing to the passive

vehicle. In this way, a list of test scenarios is defined in order to carry out numerous

simulations to evaluate and compare the systems performance. They have to show the

goals and objectives being achieved by representing real situation as closer as possible.

These scenarios, which are listed below, aspire to represent frequent situations met by

drivers in the real world.

- Test 1: Step steer input without driver control

- Test 2: Step steer input with driver control

- Test 3: Accelerating and turning

- Test 4: Braking and turning

- Test 5: Split-µ braking

- Test 6: ISO double lane change

- Test 7: High speed double lane change

- Test 8: Side wind disturbances without driver control

- Test 9: Side wind disturbances with driver control

All the tests have been implemented in IPG CarMaker. A data sheet of each test is

enclosed in Appendix C; they are also further presented in Section 6.5.


This preliminary part of the study is very important. The Use Case has allowed a clear

definition of the scope and the various interactions with the surrounding elements.

Several points have also been highlighted during the preparation of the Use Case which

has led to a complete and relevant definition of the objectives for the active steering

systems.


- 30 -

5 VEHICLE MODEL AND VALIDATION

In this chapter, the 3-DOF handling model is introduced. Some typical results are then

displayed to verify the model. Finally, the IPG CarMaker vehicle model is presented

and compared with the 3-DOF model.

5.1 Three Degree of Freedom Handling Model

5.1.1 Presentation

A 3-DOF handling model was developed in Simulink to facilitate some part of the

investigation and to ensure an understanding of the vehicle dynamics background. The

implementation of such a model has allowed a crossed verification with the vehicle

model in CarMaker.

The main features of this model are:

- 3-DOF: longitudinal, yaw and roll motions

- Non-linear tyre model

- Lateral weight transfer

A more detailed description and the derivation of the model can be found in Appendix

B, vehicle parameters are given in Appendix A.

5.1.2 Model Verification

Since the lateral vehicle performance varies consequently with the forward speed and

the linear and non-linear regions can influence significantly the handling behaviour, it is

important to understand and characterize the vehicle response before the design of the

AFS and RWS controllers. This analysis is carried out with the 3-DOF model by using

Matlab/Simulink.

5.1.2.1 Tyre Characteristics

An illustration of saturation phenomena of tyres is given in Figure 23. It can be seen

that as expected for small tyre slip angle, the relation between slip angle and lateral


- 31 -

forces is linear. For larger slip angles –

above around 3°, the tyre attempts to

generate a lateral force which exceeds

its limit of adhesion and so the tyre get

saturated making the relation between

slip angle and lateral force non-linear.

It is noticeable that the non-linear

phenomena may become significant

and cannot be neglected.

Figure 23: Tyre Lateral Properties

5.1.2.2 Vehicle Step Response

The vehicle step responses of yaw rate (a), lateral acceleration (b), and body sideslip

angle (c) are represented in Figure 24. A 3D mesh representation is used to characterize

the step responses of the model. For each graph, the steer input was maintained to 0.02

rad while the vehicle forward velocity varied from 10 to 50 m/s.

Figure 24: Step Responses - 3-DOF Model

(a) (b)

(c)


- 32 -

The three graphs illustrate well that the vehicle response is impaired when the speed

increases. Indeed, when increasing the forward speed, the vehicle becomes less

responsive, less damped and slower to achieve its steady state. That means the more the

forward speed is the more the vehicle stability is deteriorated.

5.1.2.3 Vehicle Characterisation

Figure 25 represents the yaw rate time response for the non-linear 3-DOF model where

it is compared with the linear 3-DOF and the equivalent neutral steering vehicle. The

vehicle forward speed was 140 km/h for a step steer input of 0.02 rad. This time

response is a typical response of an understeering vehicle: the yaw rate is lower than the

neutral steering yaw rate.

Figure 25: Yaw Rate Time Responses - 3-DOF

Model

Figure 26: Yaw rate vs. Forward Speed - 3-DOF

Model

Figure 26 gives the yaw rate as a function of the forward speed for both the linear and

non-linear 3-DOF. This characterises the cornering performance during slow

acceleration. The longitudinal acceleration was set to 1 m/s2

while the steer input was

kept to 0.02 rad. The vehicle’s understeering behaviour is noticeable too: the yaw rate

for both the linear and non-linear models are inferior to the reference neutral steering

yaw rate when the longitudinal speed is increased. Moreover, the effect of the non-

linearity can be also observed. When the non-linearity region is reached – around 30

m/s, the tyre cannot generate more forces. Therefore, the yaw rate reaches a limit

instead of continuing to increase for the linear model.


- 33 -

Another interesting graph to characterise the handing performance and visualize the

effect of the tyre saturation is given in Figure 27 where the steering angle is plotted

versus the lateral acceleration. The steering angle rate change is 0.01 m/s at a forward

speed of 140 km/h.

Figure 27: Understeer Diagram - 3-DOF Model

It can be seen in that, when the lateral acceleration exceed approximately 6m/s2, the

non-linearity of the model influences a lot the steering characteristics. The non-linear

model cannot achieve a lateral acceleration more than about 9 m/s2 while the linear

model can attain all range of lateral acceleration. Therefore, the tyre saturation due to a

non-linear model limits the handling performance.

5.2 IPG CarMaker Vehicle Model

5.2.1 CarMaker Axis Systems

In CarMaker, three main axis systems are used – see Figure 28:

- Frame Fr0: CarMaker inertial axis system – fixed origin, (0.X.Y) is the

horizontal driving plane, and (Z) directed upwards.

- Frame Fr1: axis system of the vehicle where which respect the ISO sign

convention where (X) points the forward driving direction, (Y) the left, and (Z)

directed upwards. The ISO sign convention is illustrated in Figure 29 .


- 34 -

- Frame Fr2: carrier axis system where (O) is the centre of the wheels, (X) the

forward driving direction, (Y) is along the wheel spin axis and (Z) directed

upwards.

Figure 28: CarMaker Axis Systems [28]

Figure 29: ISO Sign Convention

The definition of these coordinate systems is important for the continuation of the study.

Nevertheless, caution has to be paid since the 3-DOF model has been developed with

the SAE sign convention.

5.2.2 General Layout

The CarMaker’s model in Simulink is made up of subsystems containing a chain of

individual blocks. The first layer is shown in Figure 30. The blocks “CM_FIRST” and

“CM_LAST” are used for the interface and the synchronization with CarMaker, the

second block is the driver model and the third is the vehicle model.

Figure 30: CarMaker Model in Simulink - Layout

When the model is executed, all the chain has to be executed in order. The blocks are

“direct feed through” and run with a fixed step size of 1 ms. These blocks do not have

continuous states: the state variables are integrated using CarMaker internal solver. The

blocks of the deeper layer are S-functions and are not accessible from the user.


- 35 -

Changes in the Simulink model are done by overriding signals and disabling unneeded

internal CarMaker functionalities; replacement, removal or reorder of CarMaker blocks

is not possible.

The entire Simulink model must be understood to be confident with the simulation

environment. However, the main interest here is the “Vehicle” block since AFS and

RWS subsystems will be set in this block. The “Vehicle” block is divided in three

subsystems as represented in Figure 31. The most important for this study is the

“CarAndTrailer” subsystem.

Figure 31: CarMaker Vehicle Model

The “CarAndTrailer” block is formed of five subsystems as shown in Figure 32. The

first three blocks are the most important for the implementation of AFS and RWS. Note

that the “Kinetics” block, which has the forces acting on the vehicle as inputs,

calculates the vehicle motion.

Figure 32: IPG CarMaker Car And Trailer Subsystem


- 36 -

5.2.3 Steering Subsystem

The “Steering” system interacts with the “DrivMan” which simulates the human

interactions with the vehicles. It obviously also interrelates with the vehicle suspension

module as represented in Figure 33.

Figure 33: Interface of the Steering System [27]

The system used for the project is a “Steer by Angle” model where the steering wheel

angle is transformed to translational quantities - Figure 34. This basic model simulates a

rack steering system where all the elements are considered stiff. The steering ratio is not

constant, only the average ratio is accessible for the user. Position, velocity and

acceleration are considered in the model.

Figure 34: Steering System [27]

5.2.4 Kinematics Subsystem

The “Kinematics” subsystem is a part of the suspension model. It describes the

movements of the wheels due to the steer action and compression. It includes also the

compliance. Two sources of movement closely linked can be distinguished: the steering

kinematics and the suspension kinematics. The one of interest for the purpose of the

study is mainly the former. In CarMaker, each wheel position and orientation – 3

translations and 3 rotations – are defined in the coordinate systems “Frame Fr2”.


- 37 -

5.2.5 Forces Subsystem

5.2.5.1 Presentation

As shown in Figure 35, the “Forces”

subsystem is compounded of three systems:

- “Vehicle Forces”: derives all the

forces acting on the vehicle as

aerodynamic forces or loads.

- “Tires”: derives the forces at each

tyre, the aligning torque and the slip

angle. This block is further

presented in Section 5.2.5.2.

- “External Suspension Forces”:

derives the external forces acting on

the suspension system – springs,

dampers, stabilizer components.

Figure 35: IPG CarMaker Forces Subsystem

5.2.5.2 Tyre Model

The overall structure of the CarMaker tyre model is represented in Figure 36.

Figure 36: Structure of the Tyre Model [27]

Besides the inputs and outputs listed in the

Figure, they are:

- : velocity vector in the tyre-road

contact point

- : velocity of the tyre belt in the tyre-

road contact point

- : tyre forces in the tyre-road contact

point

- : torques in the tyre-road contact point.

The tyre model is so formulated for the tyre-road contact point and aims to calculate the

tyre forces and torques as a function of lateral and longitudinal slip angles, normal

forces in the tyre contact point, camber angle and tyre/road friction coefficient. The


- 38 -

calculation is done by using the Pacejka’s Magic Formula. More information about the

implementation of the Magic Formula can be found in the IPG CarMaker Reference

Manual [27].

5.2.6 Implementation

The vehicle parameters made available from JLR were set in IPG CarMaker by using

the CarMaker “Luxury Car” model as a starting point. These parameters, enclosed in

Appendix A, were defined in the CarMaker Vehicle Data Set windows. The tyre

specifications were set by using the “DT_225_60R15” CarMaker tyre model as a

guideline.

5.3 3-DOF Handling Model vs. Carmaker Model

The 3-DOF handling model has been compared with the model tuned in IPG CarMaker.

In order to make the simulations in the two environments as closer as possible, the steer

angle at the wheel was estimated in CarMaker by taking the average of the right and left

front wheels orientation for a steering wheel input of 20°. This angle was then defined

as the input in the 3-DOF Simulink model with a ramp function.

The yaw rate response has been drawn in Matlab for each model at four different

forward speeds as shown in Figure 37. Note that the yaw rate response for the

CarMaker model was imported and processed in Matlab.

(a)

(b)


- 39 -

(c)

(d)

Figure 37: Comparison IPG CarMaker/3-DOF Model - Yaw Rate Response

The steady state yaw rate error generated by the 3-DOF was estimated for each speed as

a percentage of the steady state yaw rate obtained in CarMaker. This error is +4% at 50

km/h - Figure 37 (a), +0.4% at 90 km/h (b), -2.5% at 110 km/h (c), and -6.3% at 140

km/h (d). Such a divergence, both transient and steady state, can be explained by

differences in tyre models for each vehicle and the parameters used: the tyre model in

CarMaker is a parametric model where only few parameters can be set by the user while

the tyre model of the 3-DOF vehicle model is based on the “Magic Formula” and

parameters estimated for a sedan vehicle.

However, the error involved by the 3-DOF model is acceptable as it is less than 6.5%,

close to the error considered in the definition of the settling time.


The work achieved within this section has defined the vehicle model used in CarMaker

for the simulation as well as a 3-DOF handling model which has led to a better

understanding of the vehicle dynamics principles. Simple tests carried out with this 3-

DOF model have verified and characterized the vehicle response. Is has been seen that

the non-linearity influence consequently the vehicle lateral performance. Comparisons

in the yaw rate responses between the 3-DOF handling model and the model in

CarMaker have verified the validity of the two models since they have provided quite

similar responses.


- 40 -

6 YAW RATE CONTROL FOR STABILITY IMPROVEMENTS

The literature review presented in Chapter 2 has shown that yaw rate is the state

variable which is the most often controlled in active steering systems whatever the

controller structure – either feed forward or feedback. Moreover, a reference model to

be tracked has been mentioned as necessary. Therefore, the controller developed in this

chapter is a yaw rate feedback controller coupled with a reference model. The controller

design and its implementation are presented. Then, the influence of the actuator and its

bandwidth are discussed. Finally, the performances of the controller are analysed for

both AFS and RWS.

6.1 Design Structure

The yaw rate feedback controller developed here aims to fulfil the first objective

discussed in Section 4.3: improve the vehicle stability during the transient response. The

steady state behaviour has to be kept as closer as possible to the passive vehicle in order

to not influence the overall vehicle response and so maintain the driver feeling and

enjoyment. The use of a reference model involves the combination of the feed forward

and feedback paths – see Section 2.1.3 – in a simple layout. Thus, the advantages of

feed forward and feedback are chunk: achievement of a desired dynamics characteristics

and rejection of external disturbances.

6.1.1 Rear Wheel Steering

The RWS yaw moment control system illustrated in Figure 38 is divided in two parts: a

reference model – presented in Section 6.1.3, and a yaw rate feedback controller. The

later compares the vehicle’s actual yaw rate r with the reference yaw rate r_ref. Then by

applying a proportional and integral control – P+I controller – to the difference in these

rates, the set point U for the active steering actuator is determined. The active steer

angle Delta_r for the rear wheels comes from the active steering actuator – see Section

6.4 – which executes the RWS controller command.


- 41 -

Figure 38: Yaw Moment Controller Structure for RWS

The P+I controller used is led by the following transfer function:

⋅

⋅+⋅=

sTi

sTiPsG

1)( (5)

It has been chosen to use a P+I controller rather than more advanced control theory

since it is a simple controller well know for its performance and reliability.

Note that the driver and his resulting loop are not presented in Figure 38.

6.1.2 Active Front Steering

The AFS yaw moment control layout – Figure 39 – is very similar to the RWS one.

However, instead of steering the rear wheels, the active component Delta_f Active is

added to the driver steer demand Delta_f Demand to steer the front wheels. The action

Delta_f Active is decided by a feedback contribution evaluating the gap between the

reference and the measured yaw rate.

Figure 39: Yaw Moment Controller Structure for AFS


- 42 -

6.1.3 Reference Yaw Rate

The discussion here is applied to AFS, but it would have been similar for RWS. The

yaw rate target definition is an important part of the controller design. Different

approaches have been investigated. In a first time, a 2-DOF linear bicycle model of the

passive vehicle has been considered to generate the reference yaw rate. However at

moderate speed, this 2-DOF model provides a lower settling time than the passive

vehicle if the linearized cornering stiffness is not precisely estimated. Therefore, in such

a situation, the performance of the active vehicle would have been impaired. On the

other hand, when the vehicle is in the non-linear region at high speed, the 2-DOF

reference model gives a better transient response – both settling time and overshoot –

that the passive vehicle. However, the steady state yaw rate given by the reference

model is much higher than the one generated by the passive vehicle. Thus, the second

objective of the controller – keep the steady state yaw rate of the active vehicle close to

the passive vehicle – would have never been achieved. Besides, in situation of strong

non-linearity, the reference yaw rate is too ambitious and involves the “spin out” of the

vehicle. Indeed, the active system “asks” for higher tyre forces to increase the yaw rate

but the tyres already saturated cannot generate lateral forces anymore.

Furthermore, with such considerations, a neutral steering reference model has been

dismissed as it would have involved higher steady state yaw rate than the 2-DOF model

and so a premature loss of vehicle control.

These two attempts show that the matching of the steady state yaw rate of the passive

vehicle in the non-linear region is a demanding constraint and difficult to achieve since

all the simple models do not account the non-linearity. Considering that the active

systems have to be analysed at high speed and so often close to the non-linear region,

error is the steady state yaw rate cannot be accepted. Therefore, it has finally been

chosen to use a lookup table to match correctly the steady state yaw rate of the passive

vehicle. This lookup table, shown in Figure 40, was computed from points

corresponding to the steady state yaw rate of the passive vehicle for a given forward

speed and a steer angle demand.


- 43 -

In order to reduce the size of the table, this one has been built up for positive steer

angles only. The sign of the yaw rate is then attributed in function of the steer demand.

The table has been built for the speed varying from 15 m/s (50 km/h) – the controller is

not active under this speed – to 45 m/s (160 km/h) and steer angle demand at the wheels

from 0 to 0.22 rad (i.e. 0 to 220º at the steering wheel). The implementation of the

reference model subsystem in Simulink is illustrated in Figure 41. The lookup table

function in Simulink achieves interpolations to determine the precise output for a given

steer angle and forward speed when the inputs are within the definition scope,

extrapolation are done when the inputs are without the definition scope.

Figure 40: Lookup Table for Reference Yaw Rate

Figure 41: Reference Model Subsystem - Lookup

Table

With such a lookup table, the reference yaw rate is constant – at speed and constant

steer angle – without any transient response. It allows the perfect matching of the steady

state behaviour of the passive vehicle. Figure 42 is an illustration of the reference yaw

rate and the yaw rate responses of the passive FWS vehicle for a 0.035 rad steer angle

input at 40 m/s. Note that this graph has been drawn in IPG Control.

Figure 42: Reference Yaw Rate Time History for a Step Steer Input


- 44 -

It has been noticed that the reference yaw rate varies slightly in the steady state region.

This is due to the small change of vehicle forward speed Vx. The use of a lookup

involves some negative aspects: it does not consider changes on the vehicle parameters

or changes on the road/tyre friction coefficient which could be quite depreciable. Thus,

a lookup strategy may appear as a coarse approach. However, this strategy has been

considered as the most efficient regarding the objective of the controller.

6.2 System Adaptation for CarMaker

The generic layouts presented in Section 6.1 have to be adjusted for the integration in

IPG CarMaker by using accessible variables. The aim of the two following sections is to

describe how AFS and RWS have been implemented in CarMaker.


The vehicle model used in CarMaker is a FWS vehicle. Therefore, the rear suspension

kinematics and the Simulink model are not implemented to steer the rear wheels. In

order to integrate the steering of the rear wheel, the Kinematics and Forces Subsystems

should have been entirely redeveloped and replaced. However, by investigating

examples provided by IPG Automotive GmbH, an alternative has been found by

overwriting some accessible variables of the model.

As described in Section 5.2.4, each wheel is characterized by six degrees of freedom in

a local coordinate system. The degree of freedom which is on interest here is the wheel

rotation around the vertical z axis illustrated in Figure 43.

Figure 43: Definition of the Tow Angle and the Rotation rz [27]


- 45 -

The orientation rz of the wheel around this axis is compounded of three independent

components: a kinematics component which included the toe angle and the movements

due to the suspension and the steering system, a compliance component, and an external

component which can be used for the user to influence the orientation of the wheels.

This external component is zero as a default value. The steering of the rear wheels was

implemented in the CarMaker model by overwriting this external component as shown

in Figure 44.

Figure 44: RWS Implementation in the CarMaker Model

The RWS yaw moment controller layout is given in Figure 45. Note that as the toe

angle is included in the kinematics component, an average of the front left –

Car.CFL.rz_kin – and front right – Car.CFL.rz_kin – wheel orientation was used to

estimate the front steer angle. The vehicle yaw rate Car.YawRate and the forward speed

Car.vx were also measured. A “Switch” block was used to able the active system to

operate only above 15 m/s.

Figure 45: CarMaker Yaw Moment Controller Layout for RWS


- 46 -


6.2.2.1 First Attempt

In a first approach, as shown in Figure 46, it has been considered to integrate the AFS

control system between the driver and the steering subsystems.

Figure 46: AFS Controller at the Steering Column

With such a configuration, the measured forward speed – Car.vx – and the steer angle

produced by the driver – DrivMan Steering Ang – would have been used do determine

the reference yaw rate which would have been compared with the vehicle yaw rate –

Car.YawRate. The error between the two states, corrected by the controller to produce

an active steer angle, would have been added to the driver steer demand and injected in

the steering subsystem. The layout of such a controller is illustrated in Figure 47.

Figure 47: AFS at the Steering Column - Controller Layout

This is quite a realistic representation of the real system which acts on the steer pinion.

However, it has been found that the relation between the steering wheel angle and the

steer angle at the front wheels is not linear and cannot be precisely evaluated with

accessible variables – only the ratio between the steering wheel angle and the rack


- 47 -

translation at the mid point is accessible. Moreover, with the planned comparison of

AFS and RWS, it has been preferred to develop the same approach used for RWS.

6.2.2.2 Final Design

The final implementation of AFS yaw moment feedback control is therefore very

similar of the RWS one. The layout in CarMaker is given in Figure 48. Only the

overwritten variables were changed. For AFS, these variables are Car.CFL.rz_ext for

the front left wheel and Car.CFR.rz_ext for the front right.

Figure 48: CarMaker Yaw Moment Controller Layout for AFS

6.3 Controller Tuning

The tuning of the controller was carried out with a succession of simulations using a

simple step steer input of 40º at 140 km/h without driver and without actuator. The

controller’s parameters P and Ti for both AFS and RWS were tuned to get the better

response: compromise between settling time and overshoot.

For that, in a first time, only a proportional term was used. Starting with a very small

value, the parameter was gradually increased until achievement of the lower overshoot

for the lower settling time. Then, the integral term has been added by starting with a

large value, progressively decreased until the suppression of the static error without too

much oscillation. Finally, the proportional term was adjusted to get the best settling time

while minimizing the overshoot. All the parameters of the controller are summed-up in

Table 2.


- 48 -

Table 2: P+I Controllers’ Parameters - Yaw Rate Feedback Control

AFS RWS

Proportional gain – P 0.6 0.3

Integral Time Constant – Ti 1 0.8

The controllers have been tuned before the introduction of the actuator since the system

has to be well controlled to investigate the effects of actuator. Nevertheless, the

parameters will have to be adjusted when the actuator will be added in order to optimize

the control.

6.4 Integration of the Actuator

6.4.1 Actuator Model

The actuator for such an application must provide excellent response and fine accuracy

of the steer angle. Its action has to be effective in the whole frequency range relevant to

the vehicle lateral dynamics without significant phase lags.

The high level actuator model used for this study is a simple first order lag:

1( )

1H s

sτ=

+ (6)

As the action range of the actuator is limited in a real system, saturation was also

included. This saturation level was estimated regarding previous studies: He et al. [24]

used a +/-10º saturation level for AFS while Yamanaka [31] founded that +/-2º would

be sufficient for a RWS system. However, as the main objective is to carry out

comparisons between the two active systems, the maximal steering angle that the

actuator can generate was fixed to +/- 5º at the wheels. The final actuator model

implemented in Simulink for IPG CarMaker is illustrated in Figure 49.

Figure 49: Actuator Model Subsystem


- 49 -

6.4.2 Influence of the Bandwidth

The bandwidth of an actuator is very often the limiting parameter which could

considerably impair the performance of the system. Previous studies on RWS actuators

[31] have shown that an acceptable bandwidth should be between 2 and 6 Hz. The

influence of the actuator bandwidth on the systems responses were so analyzed in this

range of frequency for the system without and with driver.

6.4.2.1 Bandwidth Analysis Without Driver in the Loop

The system used for this study is AFS; the results would have been similar with RWS.

The parameters of the controller which have been optimized for the system without

actuator were kept constant. The test consisted of a step steering wheel input of 40º - i.e.

0.035 rad steer angle at the front wheels, at a constant forward velocity of 140 km/h.

The driver was not included in the system, it was a pure step applied at the steering

wheel. Figure 50 shows yaw rate and corrective steer angle time responses for the AFS

system without actuator, and with actuator for three different bandwidths. A zoom has

been applied to the graph for a better visualization, the step steer demand starts however

at t=0s. Note that the overall responses and performance of AFS and RWS will be

discussed and compared later with the passive vehicle.

(a)

(b)

Figure 50: Actuator Bandwidth Influence - Step Steer Input

The influence of the actuator bandwidth is noticeable: the overshoot in the yaw rate

response (a) for the system with a 2 Hz bandwidth actuator is 10.8% while it is 9.4% for

the response without actuator. That corresponds to an overshoot increasing of 17%. It


- 50 -

can also be noticed that the lower the bandwidth is, the more the response is oscillatory

and so the more the stability of the system is damaged. Moreover, low bandwidth is

synonymous with higher actuator work load – Figure 50 (b), and so a high energy

consumption. Therefore, the actuator does not have to have a too low bandwidth. It has

been also noticed that a high bandwidth – e.g. 15 Hz – would not give much better yaw

rate response than a 6 Hz bandwidth while a high frequency actuator would involve

high performance components and so high cost. Therefore, a bandwidth of 4 Hz was

chosen for the continuation of the study; it is a compromise between performance and

actuator feasibility.

6.4.2.2 Bandwidth Analysis With Driver in the Loop

The previous section has shown that the actuator bandwidth without the driver in the

loop could impair the vehicle response. In this section, the influence of the bandwidth is

investigated when the driver is part of the system.

6.4.2.2.1 Simple Driver Model

Firstly, a simple driver model which only follows a desired path was integrated. In this

sense, the driver does not consider any torque feedback form the steering system and

any feeling he could have – e.g. high lateral acceleration or sliding of the vehicle – to

adjust the steering wheel input. The path which had to be followed was simple and

matched the step steer demand analyzed in Section 6.4.2.1. It is a 400 m straight line

plus a 200 m radius bend. The vehicle accelerates in the straight line from 0 km/h to

reach a cruise speed of 140 km/h before entering in the curve. The actuator bandwidth

was set to 4 Hz, the controller’s parameters were the same as before. The reading of the

yaw rate time response – Figure 51 – shows that a basic driver model has no unwanted

influence on the system and does not interact unfavourably with the actuator.

6.4.2.2.2 Advanced Driver Model

Then, a more advanced and realistic driver model was integrated. This optimized model

considers for example the torque feedback given by the steering system, a maximal

lateral acceleration – 4 m/s2, or a limit sideslip angle – 11.028º. The model also includes

driver’s knowledge about the vehicle behaviour and an algorithm which allows the

driver to learn about the vehicle response. An example illustrating the difference


- 51 -

between the basic driver model and the advanced one is a situation of strongly

oversteering. The simple model will try to follow the path without considering any

oversteering while the advanced model will follow the path and detect the oversteering

situation to counter steer and reduce it. It is important to underline that the models

characteristics mentioned above have been deduced from accessible variables. Indeed,

the IPG driver models are not fully accessible data for the users. The developer gives

very few details about its models since they are comprised in a supplementary paying

pack – IPG Driver.

By testing the system with the same scenario as before, important oscillations were

observed with the advanced driver model – Figure 51.

Figure 51: Time Histories: Basic vs. Optimized Driver Model

These oscillations started as soon as the vehicle reached 15 m/s – i.e. as soon as AFS

started to operate – in spite of the vehicle was going on the straight line. The steering

wheel angle time history shows that this instability is not only due to the active loop of

the system; it is a combined action of the active system and the driver. As the driver

model cannot be clearly investigated, only assumptions can be suggested to explain this

unstable behaviour. The most probable explications are reactions coming form the

driver. Indeed, the active component of the steer angle changes the vehicle response and

generates a reaction torque in the steering system sensed by the driver. Moreover, as the


- 52 -

vehicle does not react as expected by the driver – the driver has knowledge on the

vehicle behaviour – this one tried to correct the steer angle input to obtain the desired

vehicle motion. As the reference yaw rate is computed from the steering wheel angle,

the error between the desired yaw rate and the measured one increases, resulting on the

amplification of active steer angle component and so an increase of the driver

correction. Note that this oscillatory behaviour appeared even in a straight line: the

vehicle yaw rate is slightly changed during a gear change for example involving a small

active correction felt by the driver. Another explication of this oscillatory behaviour

could be a step solver error as IPG CarMaker “auto sets” the solver step size in

Simulink – 1 ms.

6.4.2.2.3 Controller Parameters and Actuator Bandwidth Update

The advanced driver model is obviously more representative of a real driver. Therefore,

the oscillatory behaviour seen in Section 6.4.2.2.2 has to be considered and decimated.

For that, several tests have been done by changing the accessible parameters of the

driver model – maximal lateral acceleration, tolerated deviation, maximal steering

wheel angle, velocity and acceleration. However, these parameters had any influence on

the oscillations. Thus, it has been chosen to review the controller parameters as well as

the bandwidth of the actuator. The proportional gain of the controller, fixed to 0.6 in a

preliminary design, was reduced to damp the oscillations. However, a too low gain

reduced considerably the yaw rate correction. Thus, the gain was set to 0.25: a

compromise between oscillation damping and effectiveness of the controller. The

bandwidth of the actuator was also increased. A 13 Hz bandwidth appeared at the lower

frequency which reduced considerably the oscillation. The improvement generated by

the reduction of the controller proportional gain and the increasing of the actuator

bandwidth are shown in Figure 52. The deterioration of the vehicle response when the

system was oscillatory is also clearly noticeable in this figure.


- 53 -

Figure 52: Time Histories: Bandwidth and Controller Tuning

It is important to be aware that a 13 Hz bandwidth is high for such an actuator

particularly regarding the bandwidth used in other studies. However, most of the studies

carried out on AFS or RWS used a simple driver models to track a desired path. Thus,

the undesirable interaction between the driver and the actuator was probably not

visualized.

Finally, it has to be said that this study on the actuator was necessary before any

performance evaluation because, as it has been seen, the actuator and the driver

interaction would have spoiled considerably the performance.

6.4.2.2.4 Considerations for RWS

The previous study has been carried out for AFS, nevertheless, the approach is similar

for RWS. Oscillations were also observable with the advanced driver model, but these

oscillations were lower than for AFS. The most probable explication is that the torque

feedback at the steering wheel is much more less than for AFS since the steer angle

correction is applied at the rear wheels. However, the driver feeling remains and

generates oscillations. With the same approach as for AFS, the controller proportional

gain was reduced from 0.3 to 0.08 for RWS. An actuator bandwidth of 8 Hz would have


- 54 -

been sufficient, however to compare AFS and RWS, the RWS actuator bandwidth was

also set to 13 Hz.

As a short reminder, the updated controller parameters for AFS and RWS are given in

Table 3.

Table 3: P+I Controllers’ Parameters after Actuator Integration - Yaw Rate Feedback Control

AFS RWS


Integral Time Constant – Ti 1 0.8


- 55 -

6.5 Performance Analysis

In this section, the performance of AFS and RWS using the yaw rate feedback

controller are evaluated with the test scenarios described in Section 4.4 and in Appendix

C. Time histories of several state variables are displayed for each system and compared

with those of the passive vehicle. All the results come from CarMaker Simulations but

are post processed and presented with Matlab. The vehicle acceleration periods have

been deleted as they are not of interest for such a handling analysis. Moreover, most of

the tests are at constant forward velocity, the vehicle body sideslip angle β and the

lateral velocity Vy response are very similar since:

= −

x

y

V

V1tanβ (7)

Thus, only one of the two variables is presented. Note also that the vehicle called

“passive vehicle” during the simulations refers to the conventional 2WS vehicle without

any active steering system. Moreover, steady state cornering is not a test of interest here

since the controllers have been designed to provide the steady state yaw rate of the

passive vehicle. The matching of the steady state values is noticeable in all the results.

6.5.1 Test 1: Step Steer Input Without Driver Control

This first test consists on a simple step steer input of 40º at the steering wheel – see

Figure 53 – when the vehicle is moving at 140 km/h. The driver is not integrated in the

loop for a pure evaluation of performance. Note that in spite of a step is set in

CarMaker, the steering wheel angle is a ramp.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Figure 53: Step Steer Input - Test 1 - Yaw Rate Control


- 56 -

Time histories of yaw rate (a), vehicle body sideslip angle (b), lateral acceleration (c)

and active steer angle (d) are given in Figure 54 for the passive, AFS and RWS

vehicles. Both AFS and RWS improve the vehicle stability during the transient

response. Indeed, the overshoot percentage in the yaw rate response is reduced from

39.4% – passive vehicle – to 18% for AFS and to 29% for RWS. The yaw rate settling

time – initially 3.43 s for the passive vehicle – is also reduced: by 60% for AFS and

32% for RWS. It has also to be noticed that one target of the controller is achieved: the

steady state behaviour of the active vehicles is identical as the one of the passive

vehicle.

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

Reference Yaw Rate

0 1 2 3 4 5 6 7 8 9 10-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8 9 10

-10

-8

-6

-4

-2

0

2

4

6

x 10-3

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

Figure 54: Time Histories - Test 1 - Yaw Rate Control

Higher damping and lower settling time on the lateral acceleration as well as in the body

sideslip angle responses are also noticeable. Moreover, AFS and RWS subtended area

in sideslip phase plane - Figure 56 - are much more less than the passive vehicle. It

means that the two active vehicles produce less sideslip and more slowly, thus they are

more stable.

(c) (d)

(b) (a)


- 57 -

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Sideslip Angle [rad]

Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS

Figure 55: Sideslip Phase Plane - Test 1 - Yaw Rate Control

Concerning the active steer angle - Figure 54 (c), the AFS contribution is more

important than the RWS one in the transient period. However, the active front steer

angle tends to zero after a transient period contrarily to RWS. That means RWS is

working even in steady state behaviour. It can also be noticed that the saturation of the

actuator is not reached during this manoeuvre for both AFS and RWS: for AFS the

maximal active steer angle is only 0.01056 rad – i.e. 0.6º.

Dint an improved transient response of all the state variables, the trajectory of the

vehicle is also enhanced as it can be seen in Figure 56: the vehicle turns more for the

same steer demand. This behaviour is also illustrated in Figure 57 where the ghost

vehicle is the passive one, the other is the AFS vehicle.

Finally, it can be clearly seen that for a “step” steer demand AFS appears as the most

efficient system as it provides the most damped and quickest response of all the state

variables. RWS remains quite efficient too.

0 10 20 30 40 50 600

1

2

3

4

5

6

Longitudinal Displacement [m]

Late

ral D

ispl

acem

ent

[m]

Passive

AFS

RWS

Figure 56: Vehicle Trajectory - Test 1 - Yaw

Rate Control

Figure 57: AFS vs. Passive Vehicle in IPG Movie -

Test 1 - Yaw Rate Control


- 58 -

6.5.2 Test 2: Step Steer Input With Driver Control

This second test is a derivation of the first one where the advanced driver model is

included to maintain the vehicle in a controllable handling region and to follow a given

trajectory: a straight line and left turn of 200m radius which corresponds almost to a 40º

step steer demand – see Appendix C. The forward speed is maintained to 140 km/h.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45

50

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8 9 10-10

-8

-6

-4

-2

0

2

4

6x 10

-3

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8 9 10

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS


(a) (b)

(c) (d)

(e)


- 59 -

Figure 58 represents a history comparison between passive vehicle, AFS vehicle and the

RWS vehicle for the steering wheel (a) and active steer (b) angles, the yaw rate (c), the

vehicle body sideslip angle (d), and the lateral acceleration (e). It can be noticed that the

AFS vehicle provides the most oscillatory responses: the peak to peak amplitude is

0.063 rad/s for the passive vehicle, 0.57 for RWS and 0.074 for AFS. The AFS system

adds also a delay in the lateral acceleration response – maximal delay of 0.4 s. This

deterioration of the response is due to a reaction between the driver and the active

system. Indeed, after t=1.5 s, the active steer angle components becomes negative to

correct the yaw rate response and reduces the steer angle at the wheels. However,

feeling the understeering, the driver increases his demand to follow the path and so

works against the active system. That explains peaks in steering wheel and active steer

angles around t=2s.

In counterpart, RWS provides improvement of the vehicle stability. Indeed, the vehicle

body sideslip angle - Figure 58 (e) - is more damped than the passive vehicle.

Moreover, after 6 s the driver does not have to provide any steering action for RWS

while he has to steer until more than 10 s for the passive or AFS vehicles. This

translates a decreasing of the driver work load, in other words an increasing of the

driver comfort.

Finally, in comparison to the step steer input test without driver, this second test shows

the importance of the driver feeling and feedback. AFS was the most efficient system

without driver, but could generate undesirable effects if the driver works against the

active system.

6.5.3 Test 3: Accelerating and Turning

This third test is an acceleration of 1.7 m/s2 from 100 km/h while the driver has to

follow a curve of 200m radius. This test characterizes the controller performance close

to the handling limit. It could also represent a highway entrance where the driver has to

run-up in a turn.


- 60 -

Figure 59 shows results of this test. The three vehicles reach the limit of adhesion which

results on a “spin out”. The AFS vehicle shows a response very close to the passive

vehicle. At a speed lower than 140 km/h, the tyres are able to generate enough tyres

forces to compensate the lateral acceleration.

0 2 4 6 8 10 12 14 16

-250

-200

-150

-100

-50

0

50

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 2 4 6 8 10 12 14 160

50

100

150

Time [s]

For

war

d V

eloc

ity [

km/h

]Passive

AFS

RWS

0 2 4 6 8 10 12 14 16-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 2 4 6 8 10 12 14 16

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWSReference Yaw Rate AFS

Reference Yaw Rate RWS

0 2 4 6 8 10 12 14 16

-2

-1.5

-1

-0.5

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS


(a) (b)

(c) (d)

(e)


- 61 -

However, when the speed becomes more than 140 km/h, the three vehicles starts to

oversteer as it can be seen in the yaw rate response (d). Since the vehicle is rear wheel

drive, a part of the rear tyre performance is used longitudinally for the acceleration.

Thus, the rear tyres are more stirred up than the front ones and so become saturated

before, resulting on an oversteering situation. The driver starts then to counter steer -

negative steer angle - to correct this oversteering. The two active systems reduce

considerably the driver work (a) during this counter steer action – 77% less for AFS and

98% for RWS. However, the two active steering actuators (c) get saturated and cannot

support the driver anymore involving the loss of control – “drop” of the body sideslip

angle (e).

In spite of the three vehicles span out, RWS shows better abilities to maintain the

vehicle under control. Indeed, as shown in Figure 60, while the passive vehicle is totally

out of control, the RWS one is still stable despite an important oversteering behaviour.

This is also noticeable on all the time responses where, at high speed, the state variables

for RWS are much lower than the passive or the AFS vehicle. The sideslip angle rate is

also much lower when RWS is used – see Figure 61. This is explained by a better

management of the rear tyre forces: by turning the rear wheels, the rear tyre lateral

forces are decreased due to a lower body sideslip angle.

Figure 60: RWS vs. Passive Vehicle in IPG

Movie - Test 3 - Yaw Rate Control

-2.5 -2 -1.5 -1 -0.5 0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS

Figure 61: Sideslip Phase Plane - Test 3 - Yaw

Rate Control


- 62 -

6.5.4 Test 4: Braking and Turning

This common test is a hard braking manoeuvre combined to a severe turning aiming to

represent an emergency manoeuvre like collision avoidance. As shown in Figure 62, the

step steering wheel input is set to 50º (a), the hard braking involves a deceleration about

1.01g (b) from an initial speed of 140 km/h.

0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

40

45

50

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

Time [s]

For

war

d S

peed

[km

/h]

Figure 62: Steering Wheel Angle and Forward Velocity - Test 4 - Yaw Rate Control

Regarding the yaw rate (a), body sideslip angle (b) and lateral acceleration (c) responses

in Figure 63, it can be seen that the active systems increase the state variables

particularly when the vehicle passes under 100 km/h. For example at 60 km/h, the AFS

yaw rate is increased by almost 0.05 rad/s by comparing with the passive vehicle. This

is advantageous for such a manoeuvre where the lateral displacement is more important

than the driver comfort. It is also interesting to notice that AFS and RWS respond

quicker since the yaw rates and lateral accelerations are established slightly before the

passive vehicle – 0.09 s for AFS and 0.06 s for RWS. The active systems cannot

achieve the reference yaw rate since both tyres and actuators become saturated.

(a) (b)


- 63 -

0 1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

0.25

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

Reference Yaw Rate

0 1 2 3 4 5 6 7 8-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


The objective in such a manoeuvre is to achieve the largest lateral displacement from

straight ahead path with the shortest longitudinal distance. The trajectory for each

vehicle is shown in Figure 64.

0 20 40 60 80 100 120 140 1600

0.5

1

1.5

2

2.5

3


Late

ral D

ispl

acem

ent

[m]

Passive

AFS

RWS

Figure 64: Vehicle Trajectory - Test 4 - Yaw Rate

Control

Figure 65: AFS vs. Passive Vehicle in IPG Movie

- Test 4 - Yaw Rate Control

(a) (b)

(c) (d)


- 64 -

Both AFS and RWS were able to turn inside the passive vehicle. AFS gave the best

trajectory by increasing the lateral displacement of the passive vehicle by 1 m when the

vehicles clamped down – see Figure 65. The RWS vehicle had a lateral displacement of

2.4 m which is 0.25 m more than the passive vehicle. Therefore, the AFS vehicle may

be able to avoid hitting an obstacle, another vehicle, or a pedestrian when the

conventional or RWS vehicles could not.

6.5.5 Test 5: Split-µ Braking

The split-µ test, further described in Appendix C, consists of braking on two different

road friction coefficients – µ=1 and µ =0.4 – when the vehicle is initially moving at 140

km/h. The driver is included here to control the vehicle motion. Regarding the times

histories given in Figure 66, it can be seen that both AFS and RWS provide any

improvement at all: the vehicle is totally out of control. In spite of the driver counter

steer - Figure 66 (a), supported by the active system (b), the vehicles span out.

0 0.5 1 1.5 2 2.5 3 3.5-300

-250

-200

-150

-100

-50

0

50

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

0 0.5 1 1.5 2 2.5 3 3.5-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

Reference Yaw Rate

0 0.5 1 1.5 2 2.5 3 3.5-1

0

1

2

3

4

5

6

7

8

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS


(a) (b)

(c) (d)


- 65 -

The total failing of the active systems is easily interpretable. The tyres in the low

friction side generate much lower lateral and longitudinal forces than the high adhesion

side and so an important yaw moment is created. The yaw rate controller acts by turning

the front or the rear wheels to correct this yaw moment, however one side cannot

generate the amount of forces needed; only half of the controller demand can be

generated. This engenders the controller to ask more and so saturates the actuators as

well as the tyres in the high µ side. Note that in such a situation, the loss of control is

mainly due to the longitudinal tyre saturation which could be hardly managed by

working on the lateral forces in opposition to ABS which aims to manage the

longitudinal forces.

6.5.6 Double Lane Change

Double lane change is a transient manoeuvres that drivers experience regularly. It is a

challenging manoeuvre both from vehicle dynamics and driver’s point of view as the

vehicle changes suddenly from understeer to a limit oversteering condition. Two double

lane change test were carried out, the first one is an ISO test at 100 km/h, and the

second is done at 140 km/h. Details about the tests’ configurations are enclosed in

Appendix C.

6.5.6.1 Test 6: ISO Double Lane Change

Results of the ISO test – Figure 67 – show that both AFS and RWS improve the vehicle

response. The state variables are reduced all along the manoeuvre. The improvement

due to the active systems appears particularly in the second part of the manoeuvre when

the vehicle is coming back in the initial lane and changing suddenly from understeering

to oversteering. The vehicle yaw rate (b), body sideslip angle (c) and lateral acceleration

(d) are much more damped with the active devices involving an enhancement of the

vehicle stability. From a driver point of view, AFS reduces considerably the driver work

(a) particularly during the second part of the manoeuvre where the steering wheel angle

is reduced from 78º – conventional vehicle – to 36º for AFS.


- 66 -

0 1 2 3 4 5 6-60

-40

-20

0

20

40

60

80

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 1 2 3 4 5 6

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS



0 1 2 3 4 5 6-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 1 2 3 4 5 6-8

-6

-4

-2

0

2

4

6

8

10

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS


The vehicle sideslip phase plane given in Figure 68 shows the important improvement

of stability for both AFS and RWS. Indeed, the area covered by the passive vehicle in

the plane is much more important than the ones covered by AFS or RWS.

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS


(a) (b)

(c) (d)


- 67 -

The vehicle trajectory – Figure 69 – is also improved: the lateral displacement when the

vehicle is coming back to the initial lane is reduced by almost 1.5 m for AFS - lower

oversteering. As shown in Figure 70, while the passive vehicle – ghost vehicle – is out

of the track, the AFS one remains between the traffic cones. The decreasing in driver

work load is also noticeable in this figure.

0 20 40 60 80 100 120 140 160 180-2

-1

0

1

2

3

4


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS


Rate Control



6.5.6.2 Test 7: High Speed Double Lane Change

Time histories recorded during the high speed double lane change test are shown in

Figure 71. The benefit of AFS and RWS are much less important than for the ISO test.

The AFS yaw rate (b) is slightly more damped than the passive vehicle. But, as it has

been noticed in the second test – Section 6.5.2 – AFS involves a short delay in the body

sideslip angle (c) and lateral acceleration (d) responses which highlights a loss of

responsiveness. On the other hand, RWS improves the responsiveness and damped

lightly the state variables. Regarding the driver work (a), no relevant changes are

noticed when active steering devices are used, except a lower oscillatory driver action

with AFS.


- 68 -

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-50

-40

-30

-20

-10

0

10

20

30

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.2

-0.1

0

0.1

0.2

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS



0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.04

-0.02

0

0.02

0.04

0.06

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-8

-6

-4

-2

0

2

4

6

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

1

1.5

2

2.5

3

3.5


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS


Considering the body sideslip phase plane shown in Figure 72, it can be noticed that

both AFS and RWS enhance slightly the stability as their curves are surrounded by the

passive vehicle curve.

(a) (b)

(e) (f)

(c) (d)


- 69 -

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS


This second lane change test shows well that AFS and RWS appear to be less efficient

at high speed. However, this is very relative: this test is less demanding than the ISO

one from a handling point of view since all the state variables are lower.

6.5.7 Side Wind

The ability to reject external disturbances is an important criterion during the evaluation

of a controlled system. Two tests with side wind disturbances were carried out in order

to evaluate the performance of AFS and RWS in the rejection of disturbances.

6.5.7.1 Test 8: Side Wind Without Driver Control

This test consists of applying a side wind of 40 km/h over 50 m – see Figure 73 (a) and

Appendix C. The simulation was carried out without driver – steering wheel angle

maintained to 0º – in order to evaluate the proper performance of the controllers when

the vehicle is moving at 140 km/h. With test results shown in Figure 73, it is noticeable

that the yaw rate amplitude (b) is reduced from 0.49 rad/s to 0.019 rad/s when AFS is

used and to 0.027 rad/s with RWS. However, the first peak in the vehicle body sideslip

angle response (c) is 24% more for AFS and 50% for RWS than for the conventional

vehicle. This is due to the active steer angle which makes the vehicle turning “against”

the disturbances and so increasing its lateral velocity.


- 70 -

0 2 4 6 8 10 12 14

-40

-35

-30

-25

-20

-15

-10

-5

0

Time [s]

Win

d S

peed

[K

m/h

]

0 2 4 6 8 10 12 14-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 2 4 6 8 10 12 14

-8

-6

-4

-2

0

2

4x 10

-3

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 2 4 6 8 10 12 14-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFSRWS

0 2 4 6 8 10 12 14

-3

-2

-1

0

1

2

3

4

x 10-3

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 100 200 300 400 500

-20

-15

-10

-5

0


Late

ral D

ispl

acem

ent

[m]

Passive

AFS

RWS


Regarding the active steer angle time history, it can be seen that the reaction time of the

active system is almost instantaneous which is important to reject disturbances. The

lateral deviation, from straight a head path, is considerably reduced as it can be seen in

Figure 73 (f). However, a perfect rejection of the disturbance would generate no lateral

displacement which is very difficult to achieve without any trajectory control.

(a) (b)

(c) (d)

(e) (f)


- 71 -

6.5.7.2 Test 9: Side Wind With Driver Control

This second test evaluates the controller

abilities to reject external disturbances when

the driver interacts. Different speeds of

wind – see Figure 74 – were applied on the

vehicle moving at 140 km/h.

Results in Figure 75 show that the stability

is improved for the AFS vehicle while it is

slightly impaired with RWS. RWS provides

higher yaw rate peak value – 17% more, and

higher body sideslip angle – 24% more than

0 5 10 15 20-50

-40

-30

-20

-10

0

10

20

30

40

50

Time [s]

Win

d S

peed

[K

m/h

]

Figure 74: Wind Disturbances - Test 9

the passive vehicle. However, a decrease of the driver’s steering correction (a) when the

side wind is acting is noticeable for AFS and RWS. This is due to the fast intervention

of the controllers despite small oscillations in the active front steer angle (d).

0 5 10 15 20

-10

-5

0

5

10

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 5 10 15 20

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFSRWS

0 5 10 15 20-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 5 10 15 20

-6

-4

-2

0

2

4

6

x 10-3

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


(d)

(a) (b)

(c)


- 72 -

Regarding Figure 76, the lateral displacement is more important for RWS than for the

passive vehicle contrarily to the test without driver where it was reduced. Nevertheless,

AFS still reduces the gap with the centre line. Figure 77 illustrates the reducing of the

driver work load – the steering angle is higher for the passive/ghost vehicle than for the

AFS vehicle. It also points the reduction in lateral deviation by using AFS.

0 100 200 300 400 500 600 700 800

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Longitudinal Displacement [m]]

Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS


Rate Control




The design, implementation and test of the yaw rate feedback controller using a lookup

table has shown interesting results which have been largely discussed. During the

design, it has been seen that the implementation in CarMaker involves some restrictions

since not the entire vehicle model is accessible for the user. The investigation about the

influence of the actuator and its bandwidth has pointed an important problem: the driver

interacts with the control system and creates undesirable oscillations. To remove these

oscillations, it was necessary to increase the actuator bandwidth as well as decrease the

controller gain without spoiling the controller performance. It has so been highlighted

that a high performance actuator would be necessary.

Finally, the nine tests carried out to evaluate the performance of AFS and RWS in

comparison to a conventional passive vehicle have provided relevant results. Both AFS

and RWS have demonstrated the potential to improve consequently the vehicle stability

in case of a step steer input. The transient response of all the state variables was greatly


- 73 -

improved: more damped and lower settling time. When the driver was used to steer the

vehicle, it has been shown that its effort was considerably reduced. However, the

interaction between the driver and the active steering systems could sometimes be

detrimental particularly with AFS. In situation of accelerating and turning – implying a

strong oversteering – RWS has been proved as the most efficient: the steer of the rear

wheels allowed a better management of the tyre forces. Both AFS and RWS exhibited

also significant improvements in collision avoidance manoeuvres – hard braking and

turning or double lane change. The feedback contribution has been validated since AFS

appeared also as efficient to reject internal disturbances both with and without driver

action while RWS impaired the vehicle stability when the driver corrected the motion.


- 74 -

7 DERIVATIVE OF THE LATERAL VELOCITY CONTROL

FOR STABILITY IMPROVEMENTS

The design of the yaw rate feedback controllers for AFS and RWS, and the evaluation

of their performance have been achieved in the previous chapter. In this chapter a new

control strategy to improve the transient response and keep the steady state value as

closer as possible to the passive vehicle is developed and analysed. It consists of

maintaining the derivative of the lateral velocity close to zero.

7.1 Design Structure

First of all, to understand the choice of this uncommon control strategy, it is important

to remind some characteristics of vehicle dynamics. The lateral acceleration, which is

not only the derivative of the lateral velocity, is expressed as:

rVVa xyy += & (8)

The lateral acceleration constitutes one of the most important state variables since it is

what the driver feels. The two active steering systems previously implemented

controlled the yaw rate: the second term of the lateral acceleration. In a logical way, it

appeared interesting to develop a controller acting on the first term of the lateral

acceleration.

When the forward speed is increased, the delay in the lateral acceleration becomes more

important than the yaw rate one: this extra delay is due to the lateral velocity. Moreover,

the derivative of the lateral velocity is equal to zero in a steady state condition - constant

lateral velocity. Therefore, in order to reduce this delay, it is so interesting to maintain

the derivative of the lateral velocity as closer as possible to zero to reach sooner a steady

state behaviour. However, the control law has to be designed with caution since a

derivative of the lateral speed always equals to zero would not able the vehicle to turn.

Moreover, the yaw rate controller implemented with a look-up table showed some

limitations, particularly with vehicle parameters or road friction coefficient changes.


- 75 -

This second strategy is totally independent of such changes and is efficient for every

vehicle.

It is important to be aware that the lateral velocity is difficult to measure in a real world.

However, the measure of its derivative is easier: the yaw rate and the lateral acceleration

as well as the forward speed are “easily” measurable or estimable. Therefore, the

derivative of the lateral speed can be obtained with the relation (8).

It has to be noticed that it would have been better to control the vehicle body sideslip

angle and set it to zero for RWS – Zero Side Slip strategy introduced in Section 2.1.2.2.

However, this objective is not conceivable for an AFS system since a sideslip angle is

needed to turn as explained in 2.1.1. Therefore, for a purpose of comparison, the RWS

controller has been limited to the derivative of the lateral velocity.


In order to keep the derivative of the lateral velocity as closer as possible to zero, the

error between this derivative – get from Relation (8) – and zero constitute the input of

the controller as illustrated in Figure 78.

Figure 78: Derivative of the Lateral Velocity Controller Structure for RWS

The controller is still a P+I controller to provide relevant comparisons with the yaw rate

feedback controllers. For reminder, the controller transfer function is:

⋅

⋅+⋅=

sTi

sTiPsG

1)( (9)


- 76 -


For AFS, the layout shown in Figure 79 is very similar to the RWS one. But, instead of

steering the rear wheels, the active component is added to the steer angle created by the

driver and used to steer the front wheels.

Figure 79: Derivative of the Lateral Velocity Controller Structure for AFS

7.2 System Adaptation for CarMaker

The method used to implement the yV& controller in CarMaker is similar to the one

presented in Section 6.2.1 for the RWS yaw rate controller. The actuation of the wheels

is still done by overwriting the orientation angle of the wheels. Thus, only the controller

block is presented here, it can be referred to Section 6.2.1 for a detailed explanation of

the system integration in the vehicle model.

Figure 80: CarMaker Derivative of the Lateral Velocity Controller Layout for RWS

As shown in Figure 80 for RWS, the lateral acceleration Car.ay, the yaw rate

Car.YawRate and the forward velocity Car.vx are read from the CarMaker dictionary

and used to calculate – Relation (8) – the derivative of the lateral velocity which is


- 77 -

compared with a constant sets to zero. The controller and actuator subsystems are the

same as for the yaw rate feedback controllers. The vehicle forward velocity Car.vx is

also used to provide a switch-off of the active device when the speed is less than 15 m/s.

The driver steer angle Delta_f is only calculated for presentation of the results; it does

not have any influence or interaction with the controller.

7.3 Integration of the Actuator

With the aim to compare this new control strategy with the yaw rate feedback

controller, the actuator model has to be the same. Therefore, the bandwidth of the

actuator is set to 13 Hz. Note that the interaction actuator/driver involved also

oscillations for this control strategy for low bandwidth.

7.4 Controller Tuning

The two controllers have been tuned by following the same method introduced in

Section 6.3. A summarization of the parameters is given in Table 4 – actuator

integrated.

Table 4: P+I Controllers’ Parameters - Derivative of the Lateral Velocity Control

AFS RWS


Integral Time Constant – Ti 10 10

7.5 Performance Analysis

All the tests performed in this section aim to evaluate the performance of this second

controller. Theses tests are the same as those used for the yaw rate feedback controller

analysis. Therefore, the test boundaries are not discussed again. For each test, AFS and

RWS vehicles responses are compared with the passive FWS vehicle.


- 78 -

7.5.1 Test 1: Step Steer Input Without Driver Control

Figure 81 compares results of this first test for the conventional vehicle with the AFS

and RWS vehicles.

0 1 2 3 4 5 6 7 8

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time [s]

Der

ivat

ive

of t

he L

ater

al V

eloc

ity [

m/s2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2

0.25

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

9

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8

-0.015

-0.01

-0.005

0

0.005

0.01

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

Passive

AFS

Figure 81: Time Histories - Test 1 - Derivative of the Lateral Velocity Control

(a) (b)

(c) (d)

(e)


- 79 -

Both AFS and RWS damp significantly the derivative of the lateral velocity (a) in spite

of RWS shows some oscillations visible in the active steer angle time response (e).

Resulting from a great damping of the derivative of the lateral velocity response, all the

other state variables are also well damped. The first overshoot in the yaw rate response

(b) is reduced by 94% with AFS and by 78% with RWS. Moreover, the settling time is

improved by 1.76 s when AFS is used, and by 1.2 s with RWS. However, by analysing

the lateral acceleration response (d), a delay maximum of 0.5 s for AFS, 0.3 s for RWS,

can be noticed. It has also to be mentioned that, as for the yaw rate feedback controllers,

the steady state behaviour of the active steering vehicles is similar to the passive one

fulfilling an objective of the controller.

Vehicle lateral stability is also greatly improved in terms of sideslip angle – Figure 81

(c) – which is strongly damped with both AFS and RWS. The vehicle sideslip phase

plane – Figure 82 – illustrated also this improvement in sideslip response. The active

steering devices produce much less sideslip angle and much more slowly involving an

improvement in vehicle stability.

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS

Figure 82: Sideslip Phase Plane - Test 1 -

Derivative of the Lateral Velocity Control

0 50 100 150 2000

50

100

150

200

250


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS

Figure 83: Vehicle Trajectory - Test 1 - Derivative

of the Lateral Velocity Control

However, by damping the responses, the AFS and RWS controllers reduce the vehicle

radius of turn as shown in Figure 83. That could be undesirable in some situations as

collision avoidance – see Section 7.5.4.


- 80 -

7.5.2 Test 2: Step Steer Input With Driver Control

This second test – 40 º step steer input at 140 km/h with driver trajectory control –

points a negative interaction between the driver and the AFS controller when yV& control

is used. Test results in Figure 84 show that the vehicle stability is made worse with AFS

but improved with RWS. The peak to peak amplitude in the yaw rate response (c) is

increased by 40% with AFS while it is decreased by 17% with RWS. The derivative of

the lateral velocity (b) is higher for AFS than the passive vehicle showing a failing

control. This is due to the driver reaction: he increases considerably its work load (a) to

counteract the active correction. In spite of the driver actions is also increased with

RWS, the vehicle stability and responsiveness is improved when the rear wheels are

steered: the lateral acceleration peak to peak amplitude is decreased by 0.1 m/s2.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Time [s]

Der

ivat

ive

of t

he L

ater

al V

eloc

ity [

m/s2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

0.25

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS


(c)

(a) (b)

(d)


- 81 -

Moreover, the vehicle sideslip phase plane given in Figure 85 shows that the RWS

subtended area is less than the passive vehicle resulting in lower sideslip angle and

sideslip rate. This confirms improvements of the vehicle stability.

-0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01-0.08

-0.06

-0.04

-0.02

0

0.02

0.04


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS

Figure 85: Sideslip Phase Plane - Test 2 - Derivative of the

Lateral Velocity Control

7.5.3 Test 3: Accelerating and Turning

Time histories in Figure 86 correspond to a 1.7 m/s2 acceleration from 100 km/h when

the driver follows a 200 m radius turn. Whatever the vehicle – passive, AFS or RWS –

the loss of control happens approximately at 150 km/h. As mentioned for the yaw rate

feedback control strategy, the rear tyres are closed to saturation – rear wheel drive

vehicle – which causes oversteering. When the vehicle is still controllable – speed

inferior to 148 km/h, the driver action (a) is slightly increased when active steering

systems are used – 15º more for AFS, 9º for RWS. However, when the vehicle is

strongly oversteering, the driver work load to counter steer is reduced by 116º for AFS

and 222º for RWS. Moreover, RWS provides the better response: both yaw rate (c) and

side slip angle (d) are kept lower during the skid.


- 82 -

0 2 4 6 8 10 12 14 16-300

-250

-200

-150

-100

-50

0

50

100

150

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 2 4 6 8 10 12 14 16-8

-6

-4

-2

0

2

4

6

8

10

12

Time [s]

Der

ivat

ive

of t

he L

ater

al V

eloc

ity [

m/s2 ]

Passive

AFSRWS

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFSRWS

0 2 4 6 8 10 12 14 16

-2

-1.5

-1

-0.5

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 2 4 6 8 10 12 14 160

50

100

150

Time [s]

For

war

d V

eloc

ity [

km/h

]

Passive

AFS

RWS

0 2 4 6 8 10 12 14 16

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


The active steer angle time history – Figure 86 (f) – shows that the controller correction

is very small until the loss of control due to small variations in lateral velocity are small.

When the vehicles start to skid, the lateral velocity rate changes suddenly and involves

an important controller correction.

(a) (b)

(c) (d)

(e) (f)


- 83 -

7.5.4 Test 4: Braking and Turning

As a quick remind, this test is a combination of a step steer input of 50º and a hard

braking generating a 1.01g deceleration. Yaw rate (a), body sideslip angle (b) and lateral

acceleration (c) time histories as well as the vehicle trajectories are represented in

Figure 87. It can be noticed that the state variables are reduced by the active systems

resulting in a lower lateral displacement (d). This is due to the structure of the

controller: it aims to minimize sudden lateral velocity variations and so damp sudden

variations in all state variables. The lateral displacement of the AFS vehicle is 1.37 m

whereas it is 2.14 m for the passive vehicle and 2.02 m for RWS.

0 1 2 3 4 5 6 7 8

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFSRWS

0 1 2 3 4 5 6 7 8

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 20 40 60 80 100 120 140 1600

0.5

1

1.5

2


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS


The vehicle body sideslip phase plane – Figure 88 – demonstrates that the vehicle

stability is nevertheless improved for both AFS and RWS since the sideslip angle is

reduced by 37% for AFS and by 32% for RWS. The vehicle sideslip rate is also

reduced: 39% less for AFS and 33% for RWS.

(a) (b)

(c) (d)


- 84 -

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2


Sid

eslip

Rat

e [r

ad/s

]

Passive

AFSRWS

Figure 88: Sideslip Phase Plane - Test 4 - Derivative of the Lateral Velocity Control

7.5.5 Test 5: Split-µ Braking

As for the yaw rate feedback controllers, the vehicle lateral behaviour in split-µ braking

condition is not improved at all by the active steering systems. Such an impotence of the

active controllers has been largely discussed in Section 6.5.5 and is not addressed again.

7.5.6 Double Lane Change

7.5.6.1 Test 6: ISO Double Lane Change

With time histories given in Figure 90,

improvements in the vehicle stability and in

responsiveness during sudden lane change

manoeuvres at 100 km/h can be noticed when

RWS is used. In particular, when the vehicle

comes back to the initial lane, RWS yaw rate

(c) and lateral acceleration (e) establishment

are 2 s in advance to the passive vehicle

involving a premature lateral displacement as

Figure 89: RWS vs. Passive Vehicle in IPG

Movie - Test 6 - Derivative of the Lateral

Velocity Control

shown in Figure 89 – the ghost vehicle is the passive FWS vehicle.

The maximal lateral acceleration during this phase is reduced by 32%. The fluctuations

in body sideslip angle (d) are also greatly reduced with RWS – peak to peak amplitude

reduced by 53%.


- 85 -

0 1 2 3 4 5 6

-100

-50

0

50

100

150

200

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 1 2 3 4 5 6-6

-4

-2

0

2

4

6

8

Time [s]

Der

ivat

ive

of t

he L

ater

al V

eloc

ity [

m/s2 ]

Passive

AFSRWS

0 1 2 3 4 5 6-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 1 2 3 4 5 6-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 1 2 3 4 5 6-10

-8

-6

-4

-2

0

2

4

6

8

10

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 1 2 3 4 5 6-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


On the other hand, AFS spoils considerably the vehicle motion. During the first lane

change, AFS shows a high understeering behaviour due to a higher driver steering input

increased by the active steer angle. This understeering reduces the radius of turn and

drives the vehicle out of the cones as shown in Figure 91 and Figure 92.

(a) (b)

(c) (d)

(e) (f)


- 86 -

0 20 40 60 80 100 120 140 160 180-6

-4

-2

0

2

4

6


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS

Figure 91: Vehicle Trajectory - Test 6 -



Test 6 - Derivative of the Lateral Velocity Control

The driver, trying to follow the path intensifies the understeering: negative peak in the

steer angle response around t=2.5 s in Figure 90, noticeable also in Figure 92. That

involves an increase of the vehicle yaw rate and lateral acceleration. Then, when the

driver tries to come back in the original lane, the load transfer and the swinging from

understeering to oversteering is much more severe and involves the loss of control. This

illustrates again the difficult interaction between the driver and the active system.

7.5.6.2 Test 7: High Speed Double Line Change

This second lane change test at higher speed gives quite similar results to the ISO test.

Indeed, as shown in the yaw rare time response in Figure 93 (a), the RWS vehicle is

more stable than the passive one while the AFS vehicle becomes out of control and goes

out of the track – see Figure 94. This is due to the strong understeering behaviour of the

AFS vehicle discussed in Section 7.5.6.1.


- 87 -

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFSRWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


Figure 94: AFS vs. RWS - Test 7 - Derivative of

the Lateral Velocity Control

-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2


Sid

eslip

Rat

e [r

ad/s

]Passive

AFSRWS

Figure 95: Sideslip Phase Plane - Test 7 -


The stability improvement mentioned for RWS is confirmed by the vehicle sideslip

phase plane given in Figure 95 as its curve is always surrounded by the one of the

passive vehicle. The loss of control for the AFS vehicle is also noticeable in this figure:

both sideslip angle and sideslip rate are hugely increased.

7.5.7 Side Wind

7.5.7.1 Test 8: Side Wind Without Driver Control

As said during the performance evaluation of the yaw rate feedback controllers, this test

aims to evaluate the controllers’ performance to reject external disturbances. Time

histories for this test are given in Figure 96. It can be seen that both AFS and RWS

reject the disturbance since the vehicle remains stable. However, the AFS correction (e)

is oscillatory which deteriorates the vehicle response. Indeed, the yaw rate (b) and

(a) (b)


- 88 -

lateral acceleration (d) peak values are much more important than for the passive

vehicle – yaw rate peak value multiplied by 7. Despite this distortion in yaw rate and

lateral acceleration, the vehicle body sideslip angle response (c) is well damped for AFS

since the peak to peak amplitude is reduced by 36%, thus improving the vehicle

stability.

0 2 4 6 8 10 12 14-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time [s]

Der

ivat

ive

of t

he L

ater

al V

eloc

ity [

m/s2 ]

Passive

AFS

RWS

0 2 4 6 8 10 12 14

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS

RWS

0 2 4 6 8 10 12 14

-4

-3

-2

-1

0

1

2

3

x 10-3

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 2 4 6 8 10 12 14

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 2 4 6 8 10 12 14-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

0 50 100 150 200 250 300 350-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS


(a) (b)

(c) (d)

(e) (f)


- 89 -

Concerning RWS, the stability is greatly enhanced since all the state variables are better

damped – no oscillation anymore. The overshoots in the yaw rate and lateral

acceleration responses are suppressed, and the peak to peak amplitude in body sideslip

angle is reduced by 44% in comparison with AFS and by 94% with the conventional

vehicle.

In spite of the vehicle stability is greatly improve with RWS and slightly with AFS, the

vehicle trajectory is not influenced by the active steering systems as shown in Figure 96

(f): the lateral deviation is changed by less than 10 cm.

7.5.7.2 Test 9: Side Wind With Driver Control

Results of this second side wind test – wind profile shows in Figure 97 (f) with driver

control – are shown in Figure 97. The two controllers reject the disturbance.

Nevertheless, all the state variables are increased. For example the yaw rate amplitude is

multiplied by 4.2, the vehicle body sideslip angle by 1.7 for AFS. That means the active

steering system impairs the vehicle stability when the driver controls the path,

highlighting one more time the detrimental interaction between the driver and the active

systems. In that results a growth of the necessary steering correction from the driver

when side wind is acting.

0 5 10 15 20-50

-40

-30

-20

-10

0

10

20

30

40

50

Time [s]

Win

d S

peed

[K

m/h

]

0 5 10 15 20-40

-30

-20

-10

0

10

20

30

40

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

(a) (b)


- 90 -

0 5 10 15 20

-0.1

-0.05

0

0.05

0.1

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFSRWS

0 5 10 15 20

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 5 10 15 20-6

-4

-2

0

2

4

6

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFSRWS

0 5 10 15 20-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS


As it can be seen in Figure 98, the lateral deviation form straight ahead path is increased

with RWS and AFS. AFS impairs particularly the lateral displacement since the

deviation is increased by 150% in comparison to the FWS conventional vehicle. Figure

99 is an illustration of this difference in lateral deviation – the ghost vehicle is the

passive one.

(c) (d)

(e) (f)


- 91 -

0 100 200 300 400 500 600 700 800

-1

-0.5

0

0.5

1


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS

Figure 98: Vehicle Trajectory - Test 9 -



Test 9 - Derivative of the Lateral Velocity Control


The development and integration of this second control strategy, which aims to make

the derivative of the lateral speed as closer as possible to zero, has been quite similar to

the one achieved for the yaw rate feedback control strategy. This new control strategy

involves also a great improvement of vehicle stability. Relative to the passive vehicle

response, AFS and RWS provide better damped responses with smaller overshoot and

shorter settling time when a step steer input is applied.

For most of the tests, it has been shown that RWS is more efficient than AFS. In an

accelerating and turning manoeuvre, the handling region is slightly extended and the

driver action to keep the vehicle under control is reduced. During a collision avoidance

manoeuvre, RWS appeared more stable than the passive vehicle while the lateral

displacement is not too much influenced. In double lane change manoeuvres, RWS was

the most powerful system enhancing considerably the vehicle stability as well as the

trajectory. Concerning the rejection of disturbances, RWS has been shown efficient by

damping considerably all the state variables when the driver does not correct the path.

However, the vehicle behaviour was impaired when the driver was added to correct the

motion.

In the other hand, it has been found that AFS impaired the vehicle stability and

trajectory except during a step steer input which is not a very common situation in a real

world.


- 92 -

8 COMPARISON OF THE TWO CONTROL STRATEGIES

In this chapter, the two control strategies developed before – yaw rate feedback control

and derivative of the lateral velocity control – are compared and discussed. This

comparison is carried out by analysing the change percentages in Root Mean Square

(RMS) value with the passive vehicle. RMS value gives relevant information about the

performance of the systems during the transient responses: it has been seen in Sections

6.5.1 and 7.5.1 that the steady state behaviour of the active vehicles are the same as the

passive vehicle. Nevertheless, RMS values have to be considered with caution: it is not

because RMS values are reduced that the vehicle stability is enhanced: all the graphical

results presented in Sections 6.5 and 7.5 have to be kept in mind.

In all the tables, vehicle body sideslip angle β and roll angle φ are expressed in [rad],

steering wheel angle δsw and active steer angle at the wheels δfact or δr in [deg], yaw rate

r and roll velocity φ& in [rad/s], lateral acceleration ay in [m/s2], and lateral deviation η in

[m].

Note that the test 5 – Split-µ Braking – is not part of this comparison since it has been

found in Sections 6.5.5 and 7.5.5 that, whatever the controller, the two active systems

do not improve the vehicle stability at all.


- 93 -

8.1 Test 1: Step Steer Input Without Driver Control

For the test 1 – steering wheel step input of 40º at 140 km/h – it can be seen in Table 5

that all states variables are reduced except the roll velocity when a yaw rate control is

used with RWS.

Table 5 : RMS Value Comparison - Test 1

AFS – Change % RWS – Change % Parameter Passive

Vehicle Yaw Control yV& Control Yaw Control yV& Control

β 5.48*10-2 - 2.92 - 7.70 - 6.52 - 8.54

r 2.01*10-1 - 1.06 - 4.39 - 1.59 - 2.50

φ& 4.22*10-2 - 6.42 - 29.49 + 17.23 - 15.31

φ 9.89*10-2 - 0.37 - 3.15 - 0.60 - 1.63

ay 7.44 - 0.67 - 3.79 - 0.99 - 2.12

δfact or δr / 0.144 º 0.299 º 0.110 º 0.182 º

Generally, yV& control is more efficient than yaw control since the change percentages

are higher. The yV& controller “uses” also more the potential of the active devices as the

active steer angles are higher. It could appear strange that for AFS the roll angle and roll

velocity are reduced despite a higher steer angle which should increase these variables.

But, this is explained by better damping of all the state variables and so a better

management of the load transfer.

8.2 Test 2: Step Steer Input With Driver Control

When the driver is included into the loop to control the vehicle and follow a path,

improvements provided by the active systems are less important and the driver work

load is increased – Table 6. An obvious observation has to be highlighted: when the

yaw rate is controlled its RMS value is reduced, and when yV& control is performed, the

vehicle body sideslip angle is reduced – better damping of the lateral velocity.


- 94 -




β 4.69*10-2 + 0.26 + 1.78 - 2.43 - 4.11

r 1.83*10-1 - 0.05 + 0.47 - 0.89 + 1.41

φ& 3.75*10-2 -4.5 + 1.33 + 14.84 + 3.94

φ 9.17*10-2 - 0.07 - 0.02 + 0.09 + 0.05

ay 6.80 - 0.04 + 0.12 + 0.03 - 0.03

δsw 31.68 + 4.29 + 16.52 + 2.39 + 6.67

δfact or δr 0.15 º 0.44 º 0.07º 0.19 º

Moreover, when yaw rate control is used for RWS, the roll velocity is increased a lot

resulting in comfort degradation for the occupants. For this second test, RWS with yaw

rate control is identified as the most efficient controller which is confirmed by the time

histories discussed in Sections 6.5.2 and 7.5.2. RWS with yV& control would have

improved the vehicle stability by reducing the body sideslip angle, but the yaw rate

response would have been made worse. The overall vehicle stability and driver feeling

is therefore a compromise between yaw rate and body sideslip angle responses when

both cannot be improved together.

8.3 Test 3: Accelerating and Turning

RMS value and change percentages given in Table 7 for the test 3 show that the vehicle

stability is greatly improved when the yaw rate control strategy is used for RWS since

most of the state variables are reduced. Only the roll angle is slightly increased but this

is totally justifiable. Indeed, as seen in 6.5.3, the RWS vehicle stays controllable longer

despite a strong oversteering. The load transfer is so maintained longer – involving a

higher roll angle – in comparison to the other vehicles which are sliding and so reducing

their roll angles as it can be seen in the Figure 100.


- 95 -

0 5 10 150

0.02

0.04

0.06

0.08

0.1

0.12

Time [s]

Rol

l Ang

le [

rad]

Passive

AFS Yaw Control

RWS Yaw ControlAFS Vy-dot Control

RWS Vy-dot Control

Figure 100: Roll Angle Time Response - Test 3 - Controller Comparison

The steering effort extended by the driver has been largely decreased with the active

systems whatever the control strategy. As seen in Sections 6.5.3 and 7.5.3, this

improvement is particularly done during the counter steer manoeuvre when the vehicle

is oversteering.

Moreover, for both yaw and yV& control implemented for RWS, the vehicle body

sideslip angle is greatly reduced involving an extension of the handling region and an

improvement of the driver feeling. All these values have however to be considered with

caution as the three vehicles span out.




β 6.11*10-1 + 12.97 + 7.07 - 59.01 - 14.57

r 2.79*10-1 + 8.65 + 3.61 - 19.23 + 2.19

φ& 2.78*10-2 - 35.23 - 23.14 - 33.55 - 29.01

φ 7.9*10-2 + 1.06 + 0.96 + 1.33 + 0.02

ay 6.35 - 0.32 - 0.01 - 1.26 + 0.21

δsw 124.41 - 81.2 - 51.39 - 84.15 - 79.06

δfact or δr / 2.17 º 1.64 º 2.49 º 0.92 º

Results show thereby RWS control by yaw rate feedback gives the greater stability

improvement since both yaw rate and body sideslip angle are considerably reduced as

well as the lateral acceleration and the driver steering action.


- 96 -

8.4 Test 4: Braking and Turning

For braking and turning manoeuvre, it can be seen in Table 8 that all the state variables

are considerably reduced when the derivative of the lateral velocity is controlled which

highlights a great stability improvement. However, the lateral deviation η is reduced

which is obviously undesirable in a collision avoidance manoeuvre. Indeed, in such a

situation, the most important is to deport the vehicle as much as possible from the centre

lane. The driver comfort or even the vehicle stability are secondary as long as the crash

is avoided. Therefore, yaw rate control is more suitable for collision avoidance

manoeuvres especially for AFS – yaw control with AFS provides the highest lateral

deviation but reduces the vehicle stability and the driver comfort.




β 1.77*10-1 + 24.03 - 40.82 + 12.56 - 36.13

r 7.14*10-2 + 26.06 - 40.14 +12.48 - 32.48

φ& 1.05*10-1 +30.76 - 38.56 +21.05 - 5.71

φ 2.83*10-2 +25.02 - 39.71 +13.79 - 27.67

η 1.48 + 48.29 -35.75 + 13.09 - 4.18

ay 1.71 + 24.86 - 39.48 +12.41 - 32.48

δfact or δr / 2.23 º 0.41 º 1.06 º 0.27 º

8.5 Test 6: ISO Double Lane Change

For the double lane change carried out at 100 km/h, only AFS with a yV& controller does

not improve the vehicle stability – see Table 9. The handling performances are very

impaired since all the state variables are increased by more than 16%. The driver work

is also hugely increased while the active compensation is tripled in comparison to the

other active systems. This inefficiency to improve the vehicle stability, and at the

contrary to impair the vehicle response, has already been noticed in Section 7.5.6.1.


- 97 -




β 3.77*10-2 - 44.26 + 46.67 - 30.11 - 47.27

r 2.16*10-1 - 30.77 + 25.72 -18.81 - 22.86

φ& 2.47*10-1 -28.41 + 16.13 -6.64 - 31.04

φ 7.56*10-2 - 24.19 + 18.86 - 9.92 - 19.18

ay 5.057 - 26.35 + 24.28 - 11.21 - 20.56

δsw 34.79 - 34.37 + 177.03 - 26.01 - 4.82

δfact or δr / 0.53º 1.54 º 0.39 º 0.45 º

On the other hand, the three other systems improve significantly the lateral stability as it

can be noticed in Table 9. AFS with yaw rate feedback control gives the higher

improvements in terms of yaw rate, roll angle, lateral acceleration and driver work load.

The body sideslip angle is also greatly reduced – almost by 50%.

8.6 Test 7: High Speed Double Lane Change

For this second double lane change test at high speed – 140 km/h – results given in

Table 10 are quite similar to the previous test. The yV& control strategy applied to AFS

still impairs considerably the lateral responses and makes this controller not suitable at

all for AFS. The body sideslip angle is multiplied by 3.4, the yaw rate by 2 and the

driver steering input by 5.5.




β 2.71*10-1 - 4.20 + 238.65 - 5.04 - 37.68

r 1.30*10-1 - 3.34 + 102.62 - 4.34 - 14.24

φ& 1.71*10-1 - 3.51 + 78.15 + 11.11 - 22.14

φ 6.01*10-2 -1.02 + 47.64 + 1.98 - 14.34

ay 3.97 - 1.73 + 55.27 + 1.58 - 15.66

δsw 16.56 + 5.23 + 452.22 - 3.97 + 31.58

δfact or δr / 0.37 º 2.21 º 0.24 º 0.45 º


- 98 -

However, the three other systems show interesting improvement of the vehicle stability

and driver comfort. The three appear as almost equivalent and involve compromises:

the driver action increases in the same rate that the state variables are reduced.

Moreover, when the driver action is reduced – improving its comfort, lateral

acceleration, roll angle and roll velocity are spoiled – reducing the vehicle stability.

Note that the delay in the body sideslip angle for AFS with yaw rate control –

mentioned in Section 6.5.6.2 – is not visible here with RMS value.

8.7 Test 8: Side Wind Without Driver Control

As for the double lane change tests, all the state variables have to be minimized to

improve the vehicle stability. In Table 11, it is noticeable that a yaw rate control

strategy increases hugely the body sideslip angle reducing the lateral deviation despite

the yaw rate RMS values are reduced. In opposition, when the derivative of the lateral

velocity is controlled, the yaw rate is slightly impaired; the sideslip angle reduced

involving an augmentation of the lateral deviation. Therefore, it can be seen that there is

not a unique best controller reducing all the variables.




β 8.94*10-4 + 100.12 - 40.67 + 156.97 - 44.33

r 1.31*10-2 - 63.55 + 3.86 - 49.21 + 0.74

φ& 1.39*10-2 + 16.29 - 13.97 - 18.65 - 65.16

φ 2.01*10-3 + 140.84 - 43.2 + 84.30 - 69.88

η 10.06 - 72.13 + 2.82 - 64.15 + 1.63

ay 4.86*10-1 - 45.03 + 10.13 - 26.74 + 3.53

δfact or δr / 0.064 º 0.099 º 0.051 º 0.029 º

Yaw rate controllers have potential to reduce consequently the lateral deviation as well

as the yaw rate but impair the body sideslip angle involving driver bewildering: the

vehicle head will point a direction and goes into another one as illustrated in Figure 101.


- 99 -

Figure 101: Vehicle Body Sideslip Angle, Vehicle Heading and Direction of Motion

yV& controllers can reduce greatly the body sideslip angle, but increase the yaw rate and

the lateral displacement. Higher lateral displacement could involve a collision with

another vehicle for example. Nevertheless this discussion has to be considered carefully

as it is a side wind disturbance without any driver correction. This is theoretically very

uncommon: a driver must always keep his hands on the steering wheel!

8.8 Test 9: Side Wind With Driver Control

In this last test, the driver is now part of the loop and corrects the vehicle motion when

side winds are acting. It can be seen in Table 12 that only one configuration gives

relevant improvements: AFS with yaw rate feedback control. It combines lower sideslip

angle, lower yaw rate, lower lateral deviation and lower driver work. The performances

of AFS with derivative of the lateral velocity control are particularly bad: all the state

variables are increased – four over seven variables are at least multiplied by two. RWS

does not appear as efficient to reject external disturbances. Moreover, the lateral

deviation from straight ahead path and the yaw rate are hugely increased with a

derivative of lateral velocity control strategy.

Vehicle heading


- 100 -




β 6.2*10-3 - 0.92 + 45.89 + 28.29 - 6.30

r 9.8*10-3 - 10.59 + 281.01 + 16.88 + 98.28

φ& 4.24*10-2 + 0.14 + 33.59 + 10.19 - 20.91

φ 1.76*10-2 - 1.58 + 44.16 + 3.66 + 4.77

η 1.43*10-1 - 11.86 + 189.27 + 11.42 + 76.94

ay 5.65*10-1 - 8.24 + 158.28 + 13.13 + 36.64

δsw 4.03 - 52.11 + 188.03 - 31.68 + 51.10

δfact or δr / 0.12 º 0.39 º 0.10 º 0.11 º


This analysis of RMS value and change percentages has pointed aspects which were not

easily noticeable with time responses analyses. The two approaches are complementary

and provide relevant support to compare and evaluate the potential of AFS and RWS to

improve the vehicle stability.

Several results discussed in this chapter have shown that there is not one best controller

which improves the vehicle stability in all the situations. Compromises between lateral

deviation, driver work, comfort or safety, and vehicle stability are necessary.

Nevertheless, it has been noticed that AFS controlled with a derivative of the lateral

speed strategy was not suitable to improve the vehicle stability. This system appeared

efficient only for a step steer input but made worse the vehicle stability in all the other

tests.


- 101 -

9 YAW MOMENT CONTROL FOR HANDLING

IMPROVEMENTS

In the three previous chapters, the controllers aimed to improve the vehicle stability

during the transient response while keeping the steady state behaviour as closer as

possible to the passive vehicle. In Section 4.3, it has been mentioned that active steering

could also be used to improve the vehicle handling by achieving a desired steering

response. The objective of this chapter is so to investigate the potential of AFS and

RWS to achieve the performance of a 2-DOF linear model, or those of neutral steering.

In this section, performances of the active steering systems are also compared with

Torque Vectoring Differential (TVD). This study on TVD has been carried out by I.

Olazarri [32] in parallel to this project. However, TVD has not been implemented in

CarMaker. Therefore, the comparison is done in Matlab/Simulink by using the 3-DOF

vehicle model presented in Section 5.1. Several simulations are still done in CarMaker.

The yaw rate feedback controllers introduced in Section 6.1.1 for RWS and Section

6.1.2 for AFS are used – refer to Figure 38 and Figure 39 for the controller layouts.

Only the reference yaw rate subsystem has to be changed.

9.1 Two Degree of Freedom Linear Model Objective

9.1.1 Reference Model

9.1.1.1 Concept

It has been seen in Section 5.1.2 that the lateral vehicle behaviour is mainly damaged by

the non-linearity of the tyres. Therefore, it appears sensible to use a 2-DOF linear

bicycle reference model which can improve this non-linearity. Wheals et al [33] derived


- 102 -

a speed dependent function providing the yaw rate as a function of the steer angle input

for a 2-DOF linear model. This function is:

)(22

frxrf

rfx

f

ref

aCbCmVCCl

ClCVr

−+=

δ (10)

The tyre stiffness’s coefficient Cf and Cr are calculated from the product “BCD”

included in the Pacejka’s non-linear tyre model derived for the 3-DOF handling – see

Appendix B.

It has to be noticed that the use of a 2-DOF reference model involves some limits for the

system: linear tyre stiffness coefficient, steady state limitation, and derivation assumed

for small slip angle. Therefore, the reference model has to be tuned to consider these

limitations.

9.1.1.2 Pure Time Delay

Relation (10) accounts only for steady state yaw rates. In a real vehicle, a delay exists

between the steer input and the generation of the yaw rate. Therefore, a pure time delay

Td of 20 ms is added in the reference model: it delays the yaw rate output generated by

the reference model. This delay is implemented in Simulink with the function:

sTdesD−=)( (11)

9.1.1.3 Saturation

A 2-DOF linear model ignores that tyre forces have a finite limit. Therefore, when the

vehicle is in strong non-linearity conditions and the tyres are close to saturation, the

reference yaw rate is too ambitious involving the loss of control. Saturation is so

included by limiting the steering input when the maximum attainable steady state yaw is

reached. As suggest by Hancock [34], this maximum yaw rate can be calculated from:

x

y

V

ar

lim

lim = (12)

aylim is the theoretical limit lateral acceleration that the vehicle can achieve. As

highlighted by Hancock, some vehicles are able to generate a lateral acceleration higher

than 1g, thus a road friction coefficient of 1 could saturate the yaw rate too early. He


- 103 -

proposed to define the limit lateral acceleration with a tuneable parameter µHi – sets to

1.03 here:

Hiy ga µ⋅=lim (13)

Finally, the limit steer input can be obtained with:

xV

lr ⋅= lim

limδ (14)

The saturation is added to the “Reference Model” subsystem as illustrated in Figure

102. Note that in this figure, “f(u)” is the function (10).

Figure 102: Two Degree of Freedom Reference Model with Saturation

The tuning of the P+I controller is not presented here. It has been optimized to reduce

the time response without too much overshoot. The final parameters are given in Table

13.

Table 13: P+I Controllers’ Parameters - 2-DOF Reference Model

AFS RWS


Integral Time Constant – Ti 0.5 0.4

9.1.2 Performance Analysis

Different tests were carried out to evaluate the performance of this yaw rate feedback

controller using a 2-DOF reference model.


- 104 -

9.1.2.1 Cornering Performance at Constant Speed

This first test aimed to characterize the steering response when the vehicle was moving

at constant speed – 140 km/h. The steering angle input was increased by 0.001 rad/s.

This test has been carried out in Simulink with the 3-DOF handling model to compare

AFS and RWS with TVD. The resulting Understeer Diagram is given in Figure 103.

0 1 2 3 4 5 6 7 8 90

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Lateral Acceleration [m/s2]

Ste

erin

g A

ngle

[ra

d]

Passive

AFSRWS

TVD

Figure 103: Understeer Diagram with the 3-DOF Model - 2-DOF Reference Model

It can be seen that when the lateral acceleration exceeds approximately 5 m/s2, the

steering characteristics of the passive vehicle starts to be non-linear. AFS, RWS as well

as TVD extend the linear region of handling to 7.5 m/s2 which is approximately 50%

more than the passive vehicle. Therefore, the active vehicles exhibit less pronounced

non-linear steering characteristics in the high lateral acceleration range leading to a

vehicle that will handle in a more predictable manner in higher lateral accelerations.

However, the maximal lateral acceleration that the vehicle can generate is reduced by

0.32 m/s2 with RWS and TVD – by 0.53 m/s

2 with AFS – which could be undesirable

for a sport vehicle and frustrating for drivers looking for sensations.

9.1.2.2 Step Steer Inputs

The vehicles responses to step steer inputs are investigated in this section. In a first time

the step input is set to 0.03 rad when the vehicle is moving at 140 km/h. Figure 104

compares the yaw rate time histories of the passive vehicle, with AFS, RWS and TVD;

the reference yaw rate is also included. Note that these results are generated in Simulink

with the 3-DOF vehicle model.


- 105 -

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]Steer Input = 0.03rad

Reference

Passive

AFSRWS

TVD

Figure 104: Yaw Rate Time Response with 3-

DOF Vehicle Model - 0.03rad Step Steer Input -

2-DOF Reference Model

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]

Reference

Passive

AFS

RWS

Figure 105: Yaw Rate Response with CarMaker

Vehicle Model - 0.03rad Step Steer Input - 2-DOF

Reference Model

It can be seen that the yaw rate response is greatly improved with AFS and RWS. In

spite of the first overshoot is increased by 10%, the settling time is reduced from 1.53 s

to 0.24 s with RWS and to 0.21 s with AFS. The vehicle responsiveness is so improved

and the active steering vehicles are less understeering: the steady state yaw rates are

increased by almost 20%. Concerning TVD, the handling behaviour is also enhanced

since the steady state yaw rate is increased. However, TVD makes the yaw rate response

more oscillatory and so damages the vehicle stability.

This step steer test has also been carried out with the vehicle model in CarMaker for

AFS and RWS. The yaw rate responses are shown in Figure 105. Responses are quite

similar to those obtained with the 3-DOF vehicle model. However they are more

oscillatory, even for the passive vehicle. This is due to the better accuracy of the vehicle

model which includes for example the suspension kinematics and a more relevant

representation of the weight transfer. It has also to be noticed that the reference yaw rate

is slightly lower when the simulation is done in CarMaker than with the 3-DOF model.

This is due to the speed diminution when the vehicle turns – not considered by the 3-

DOF model.

The two previous simulations have been done with a pure step steer input which is not

conceivable in reality. Therefore, a ramp steer input – duration 1 s, amplitude 0.03 rad –

is used to generate time histories given in Figure 106. It can be noticed that by making


- 106 -

the steering demand more realistic the first overshoot in the yaw rate response (a) is

greatly reduced improving the vehicle stability during the transient response. It reduces

also the oscillation generated by the RWS vehicle.

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

Time [s]

Yaw

Rat

e [r

ad/s

]

Reference

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8 9 10-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFSRWS

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Late

ral D

ispl

acem

ent

[m]

Passive

AFS

RWS

0 1 2 3 4 5 6 7 8 9 10-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

Figure 106: Time Histories - 0.03rad Step Steer - 2-DOF Reference Model

(a) (b)

(c) (d)

(e)


- 107 -

By analysing the times histories, it has first to be noticed that the active vehicles follow

well the reference yaw rate (a) – demonstrating a relevant controller tuning. Moreover,

as mentioned before, the steady state vehicle behaviour is changed: the active vehicles

are less understeering improving so the handling behaviour. However, the steady state

lateral acceleration (c) is increased by 0.51 m/s2, i.e. 7% more than the passive vehicle.

The body sideslip angle (d) is also increased by 19% for AFS and by 44% for RWS.

These increases are obvious insofar as the vehicles are made less understeering and so

more solicited. Nevertheless, the driver could be confused since his feeling is changed:

the vehicle is pointing in another direction to where he is used and he feels higher lateral

constraints even in a steady state cornering. Apart of this consideration, the lateral

displacement – Figure 106 (c) – is increased when an active steering system is used.

The AFS vehicle swerves before the RWS. But after 6 s the two vehicles generate

almost the same trajectory.

The step steer input has been increased to 0.08 rad in order to evaluate the performance

of the active systems close to the handling limit. Figure 107 shows the yaw rate

responses of the passive vehicle, AFS and RWS vehicles as well as TVD vehicle.

0 0.5 1 1.5 2 2.5 3 3.5 4-1.5

-1

-0.5

0

0.5

1

Time [s]

Yaw

Rat

e [r

ad/s

]

Steer Input = 0.08rad

ReferencePassive

AFSRWS

TVD

Figure 107: Yaw Rate Response with 3-DOF Vehicle Model - 0.08rad

Step Steer - 2-DOF Reference Model

It has to be noticed that the passive vehicle is totally unstable and out of control while

the three active vehicles remain stable. The TVD vehicle shows some oscillations which


- 108 -

are damped and enters in the settling time band around 2.5 s. This test demonstrates the

potential of AFS, RWS and TVD to extend the handling region.

9.1.2.3 Double Step Steer

With the aim to represent in a simple manner a double lane change, a double step steer

input of 0.03 rad is applied– 3-DOF vehicle model. In Figure 108 are represented the

yaw rate time responses obtained with such an input when the vehicles are moving at

140 km/h for the passive, AFS, RWS and TVD vehicles.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]

Reference

Passive

AFSRWS

TVD

Figure 108: Yaw Rate Response with 3-DOF Vehicle Model -

Double Step Steer Input - 2-DOF Reference Model

It can be noticed that the responsiveness is considerably improved when AFS and RWS

are used. The two active steering controllers are able to track the reference yaw rate

without major oscillations and so enhance the vehicle handling – less understeering.

However, the overshoot during the second step is increased by 14% for AFS and by

35% for RWS. Overshoots are also created when the steer input is set to zero at the end

of the test. Regarding TVD, the stability is slightly impaired due to a more oscillatory

response. Nevertheless, the yaw rate with TVD is higher than the passive vehicle

involving a vehicle less understeering.

9.1.2.4 High Speed Double Lane Change – Test 7

In order to evaluate the performance of AFS and RWS in a more realistic double lane

change manoeuvre when a 2-DOF reference model is used, the high speed double lane

change test used in Sections 6.5.6.2 and 7.5.6.2 is used. Time histories of steering wheel


- 109 -

angle (a), yaw rate (b), body sideslip angle (c), and active steer angle (e) are given in

Figure 109.

As for the yaw rate controller with lookup table, the improvements in vehicle response

are small but existing. First, the driver work load (a) is reduced by using AFS: from 72º

peak to peak amplitude for the passive vehicle, it drops to 61º with AFS. It is

nevertheless increased by 2º when RWS is used. It can also be noticed that the reference

yaw rates (b) get saturated when the vehicles arrive in the second line – around t=2.2 s

but this does not influence the vehicle response.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-50

-40

-30

-20

-10

0

10

20

30

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.2

-0.1

0

0.1

0.2

0.3

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS



0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.04

-0.02

0

0.02

0.04

0.06

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

Figure 109: Time Histories - Test 7 - 2-DOF Reference Model

The body sideslip angle response (c) shows that RWS generates higher sideslip angle

than AFS and the passive vehicle involving higher lateral displacement as noticeable in

Figure 110 where the vehicle trajectories of the three vehicles are represented. RWS

swerves less than the passive vehicle – ghost vehicle – at the beginning of the lane

(a) (b)

(c) (d)


- 110 -

change which might be depreciable in case of collision avoidance. Moreover, when the

vehicle reaches the other lane, RWS shows a higher lateral deviation: the vehicle could

be out of the road.

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS

Figure 110: Vehicle Trajectory - Test 7 - 2-DOF Reference Model

It has been seen in Section 6.5.6 that improvements are much more important and

noticeable when the lane change test is carried out at 100 km/h – ISO lane change.

Therefore, the ISO test has been carried out to visualise the improvements. Yaw rate

time responses (a) as well as vehicle trajectories (b) are given in Figure 111.

0 1 2 3 4 5 6

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS



0 20 40 60 80 100 120 140 160 180-2

-1

0

1

2

3

4


Late

ral D

ispl

acem

ent

[m]

Passive

AFSRWS

Figure 111: Yaw Rate and Vehicle Trajectory - Test 6 - 2-DOF Reference Model

The yaw rate responses of AFS and RWS are greatly improved when the vehicle comes

back to the initial lane at the end of the manoeuvre. By using a 2-DOF reference model,

the sudden change from understeering to strong oversteering is managed better. Indeed,

(a) (b)


- 111 -

the reduction of understeering in the first part of the manoeuvre – lower yaw rate –

reduces the curt load transfer when the vehicle returns to the initial lane.

9.1.2.5 Accelerating and Turning – Test 3

This test has been introduced in Sections 6.5.3 and 7.5.3. It consists of accelerating the

vehicle from 100 km/h with an acceleration of 1.7 m/s2 – see Figure 112 (a) – until the

loss of control. Time histories are shown in Figure 112 for the passive vehicle as well as

for the AFS and RWS vehicles.

0 2 4 6 8 10 12 14 160

50

100

150

Time [s]

For

war

d V

eloc

ity [

km/h

]

Passive

AFS

RWS

0 2 4 6 8 10 12 14 16

-250

-200

-150

-100

-50

0

50

Time [s]

Ste

erin

g W

heel

Ang

le [

deg]

Passive

AFSRWS

0 2 4 6 8 10 12 14 16

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time [s]

Yaw

Rat

e [r

ad/s

]

Passive

AFS



0 2 4 6 8 10 12 14 16

-2

-1.5

-1

-0.5

0

Time [s]

Veh

icle

Bod

y S

ides

lip A

ngle

[ra

d]

Passive

AFS

RWS

(a) (b)

(c) (d)


- 112 -

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

9

10

Time [s]

Late

ral A

ccel

erat

ion

[m/s

2 ]

Passive

AFS

RWS

0 2 4 6 8 10 12 14 16-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time [s]

Act

ive

Ste

er A

ngle

[ra

d]

AFS

RWS

Figure 112: Time Histories - Test 3 - 2-DOF Reference Model

It has to be noticed that the reference yaw rate saturates and drops as soon as the vehicle

spins out due to a counter action steer from the driver. This implies the saturation of the

active actuators. AFS demonstrates a behaviour close to the passive vehicle in spite of

the driver work load is considerably reduced during the counter steering. RWS

improves consequently the vehicle handing: yaw rate, body sideslip angle and lateral

acceleration remain at acceptable level during the entire manoeuvre: the handling limit

is extended with RWS.

9.2 Neutral Steering Objective

9.2.1 Reference Model

The active systems developed in the previous section have shown the potential of AFS

and RWS to follow a 2-DOF handling model. The capabilities of active steering to

make the vehicle neutral steering are now investigated. The yaw rate function given in

Section 9.1.1.1 is replaced by a neutral steering yaw rate function:

ba

Vrx

f

ref

+=

δ (15)

The saturation and the pure time delay remain unchanged. The controller’s parameters

obtained for the 2-DOF reference model yaw rate controllers appeared as the most

efficient for neutral steering reference model too.

(f) (e)


- 113 -

9.2.2 Performance Analysis

It has been chosen to characterise the potential of AFS and RWS to make a vehicle

neutral steering with a simple test: the vehicle is moving at constant speed and the steer

input is progressively increased – 0.01 rad/s – until the loss of control. Two tests have

been carried out: one is at moderate speed – 70 km/h, the other is at high speed – 140

km/h. For each test, the yaw rate is drawn versus the steer angle input. Figure 113 is the

resulting graph for the moderate speed test; Figure 114 is for the high speed test.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.1

0.2

0.3

0.4

0.5

0.6

Steer Angle [rad]

Yaw

Rat

e [r

ad/s

]

Neutral Steering

Passive

AFSRWS

TVD

Figure 113: Yaw Rate vs. Steer Angle -

Vx=70km/h - Neutral Steering Target

0 0.01 0.02 0.03 0.04 0.05 0.060

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Steer Angle [rad]

Yaw

Rat

e [r

ad/s

]

Neutral Steering

PassiveAFS

RWS

Figure 114: Yaw Rate vs. Steer Angle -

Vx=140km/h - Neutral Steering Target

For both tests, the understeering behaviour of the passive vehicle is noticeable: as long

as the steer angle increases, the yaw rate generated by the passive vehicle becomes

lower than the reference neutral steering. This is much more manifest at high speed

where the tyres get sooner in the non-linear region due to higher lateral accelerations.

The two active steering devices are capable of suppressing the understeer characteristic

and achieve a neutral steering response until a certain range of steer angle. The

efficiency limit is slightly higher for and RWS than AFS: at 70 km/h AFS cannot

provide the neutral steering behaviour for a steer angle more than 0.074 rad while the

limit for RWS is 0.08 rad. However, at high speed, the limit is almost the same for the

two active vehicles. When the active steering vehicles are not able to afford neutral

steering anymore, the vehicle behaviour is made worse: the yaw rate fluctuations are

quite important for a small change of steer angle input.


- 114 -

Regarding the capabilities of TVD – Figure 113, it can be notice that TVD provides the

same performance as AFS and RWS. However, while AFS and RWS make the vehicle

understeering when they cannot achieve the neutral steering anymore, TVD gives

oversteering behaviour to the vehicle – yaw rate superior to the neutral steering

reference.

These two simple tests have illustrated the capabilities of the AFS, RWS and TVD to

achieve neutral steering responses in a certain range of steer angle and forward velocity.

They have also shown that when the stability control systems are not able to achieve the

targeted neutral steering, the vehicle handling could be damaged.


It is clear that both AFS and RWS have the potential to influence the steady state

vehicle behaviour by making the vehicle less understeering or even neutral steering.

TVD has also proved its abilities for such improvements. A very ambitious handling

behaviour target – e.g. neutral steering – has to be considered with caution since when

the active system is not efficient anymore; the vehicle stability could be impaired.


- 115 -

10 CONCLUSIONS

Most of the objectives defined at the beginning of the project have been achieved. The

three control strategies investigated in this report – yaw rate feedback control, derivative

of the lateral velocity and reference model tracking – have clearly shown the potential

of Active Front Steering (AFS) and Rear Wheel Steering (RWS) to improve the vehicle

stability as well as the handling behaviour. The influence of the actuator and the driver

interaction constitutes also an interesting founding.

10.1 Influence of the Actuator, Interaction with the Driver

It has been shown that a low bandwidth actuator could generate an oscillatory behaviour

even in a straight line when steer actions are minor. The investigation has demonstrated

that is due to a counter reaction of the driver who feels the correction generated by the

active system – the oscillations were not noticeable with a simple driver model which

did not consider any feedback from the vehicle. It has so been proposed that a

bandwidth around 13 Hz would be appropriate knowing it involves quite a high

performance actuator. This investigation on the actuator and the interaction with the

driver has finally shown that it is important to consider and integrate an advanced driver

model to carry out relevant analyses about active steering. Moreover, it has often been

noticed that the driver action works against the active devices making worse the vehicle

response, particularly with AFS.

10.2 Stability Improvement

In this study, the focus has been on the capabilities of AFS and RWS to improve the

vehicle stability by investigating two different control strategies: yaw rate feedback

control with a look-up table and minimization of the derivative of the lateral velocity

control. Both improve the vehicle stability while the steady state behaviour is kept as

closer as possible to the passive vehicle to not impair the driver enjoyment. It has been

found that the two active systems demonstrate great potential. The nine typical tests


- 116 -

which have been carried out have allowed a relevant evaluation of the performance of

each systems as well as comparison with the passive front wheel steering vehicle.

Results have been consolidated by Root Mean Square value comparisons. However, it

has been discussed that there is not only one best control strategy: when one is efficient,

the other could impair the vehicle stability. The final choice of a controller strategy

depends considerably on the design objectives fixed for the vehicle. Nevertheless,

practical considerations are important: the yaw rate feedback control strategy is based

on a look-up table which limit the range of utilisation since the controller has to be

improved to consider vehicle parameter changes or variations in the road friction

coefficient. In opposition, the derivative of the lateral speed strategy is applicable for

all vehicles and is not influence by vehicle parameters or road friction coefficient

changes. This strategy uses variables “easily” measurable. Finally, some general

characteristics implied by active steering can be summed-up as follow:

- Better damped response and lower settling time.

- Reduction of the driver work in most of the situations.

- Rejection of external disturbances as side wind excitations and reduction of the

lateral deviation from straight ahead path.

- Increase of the lateral deviation in case of collision avoidance manoeuvres.

10.3 Handling Behaviour Improvement

The capabilities of AFS and RWS to improve the handling behaviour by making the

vehicle less understeering or even neutral steering are important. The linear handling

region can be extending with both AFS and RWS. However, non-linearity has to be

considered in the reference model to avoid a premature saturation of the tyre and so

avoid degradation of the handling behaviour close to the handling limit.

Moreover, is spite of active steering systems are able to improve the lateral behaviour,

they are not able to push back the handling limit when a two degree of freedom or

neutral steering references models are used.

Finally, this objective – improve the vehicle handling behaviour – may appear as not so

relevant since it could impair the driver enjoyment by suppressing all understeering or


- 117 -

oversteering conditions. Obviously, such a strategy could be interesting for a certain

range of luxury vehicle where comfort and safety are the most important criterion.

10.4 Recommendations: “AFS or RWS?”

It is difficult to recommend a system more than the other since both demonstrate

important improvements in the vehicle stability. Each system shows advantages and/or

weaknesses. AFS is very efficient to reject external disturbances while it does not

provide any improvements in a situation of accelerating and turning. On the other hand,

RWS helps considerably the driver in a turn at high speed in spite of it fails to reject

disturbances. Moreover, it has to be highlighted that a derivative of the lateral speed

control strategy is not suitable at all for AFS since this system has shown significant

degradations in the vehicle stability and handing behaviour. AFS and the driver have

often shown undesirable interaction making worse the vehicle stability too.

Nevertheless, to conclude, both Active Front Steering and Rear Wheel Steering appear

as suitable for a new control stability device in a future sedan vehicle. The choice

depends mainly on the objective fixed for the overall vehicle design.

10.5 Future Work

Some further investigations could be interesting in order to analyse some aspects which

have not been considered in this study. These recommended works are list below:

- Integrate an adaptive control in the yaw rate feedback controller with look-up table to

consider changes in vehicle parameters and road friction coefficient. This would also

involve the development of a system aiming to evaluate the road friction coefficient.

- P+I controllers give more than acceptable results, however the development of a

more advanced controller using LQR or H-∞ Theory should be pertinent to increase

the controller robustness and optimise its action.

- IPG CarMaker provides a toolbox to integrate sensors in order to measure state

variables. Thus, the implementations of the controllers could be improved and made

closer to the reality by adding sensors in the model to measure all the state variables

needed, instead of using CarMaker’s accessible variables.


- 118 -

- Investigate the potential of a Dual Steering Scheme to improve the vehicle stability.

By controlling two state variables – e.g. yaw rate and derivative of the lateral

velocity – it could be possible to combine the benefits of both Active Front Steering

and Rear Wheel Steering in the same vehicle.

- As the front and/or rear steering system is a crucial component for the vehicle safety,

the fail safe of the system – mechanical and electronic – should be considered in a

deeper analysis. That could be start by investigating alternative or error flows in the

Use Case.

- The undesirable interactions between the driver and the active steering systems have

been pointed often in this study and some assumptions have been proposed to

understand the results. Test in a real vehicle with a real driver could confirm the

interaction but also give a better understanding of the driver reaction.

- Finally, it could be interesting to investigate the combination of active steering with

other stability control devices as Roll Moment Distribution to provide a better

management of the load transfer which influence the lateral tyres forces.


- 119 -

REFERENCES

[1] Sano, S., Furukawa, Y., and Shiraishi, S., “Four Wheel Steering System with Rear

Wheel Steer Angle Controlled as a Function of Steering Wheel Angle”. SAE paper

86-0625, 1986.

[2] Nikzad, S., V., and Naraghi, M., “Model Reference Tracking Control of a 4WS

Vehicle Using Single and Dual Steering Strategies”. SAE paper 2002-01-1590,

2002.

[3] Furukawa, Y., Yuhara, N., Sano, S., Takeda, H., and Matsushita, Y., “A Review

of Four-Wheel-Steering Studies from the Viewpoint of Vehicle Dynamics Control”.

Vehicle System Dynamics, Vol. 18, No.1-3, 1989, p151-186.

[4] Pascali, L., Gabrielli, P., and Caviasso, G, “Improving Vehicle Handling and

Comfort Performance Using 4WS”. SAE paper 2003-01-0961, 2003.

[5] Nalecz, A., G., and Bindemann, A., C., “Handling Properties of Four Wheel

Steering Vehicles”. SAE paper 89-0080, 1989.

[6] Morgando, A., Velardocchia, M., Danesin, D., and Rossi, E., “An Innovative

Control Logic for a Four-Wheel-Steer Vehicle. Part 1: Analysis and Design”. SAE

paper 2005-01-1267, 2005.

[7] Akita, T., Satoh, K., and Gaunt, M. C., ”Development of 4WS Control Algorithm

for a SUV”. SAE paper 2002-01-1216, 2002.

[8] Whitehead, J. C., “Four Wheel Steering: Manoeuvrability and High Speed

Stabilization”. SAE paper 88-0642, 1988.

[9] Xia, X., and Law, E. H., “Nonlinear Dynamic Response of Four Wheel Steering

Automobiles to Combined Braking and Steering Commands on Collision Avoidance

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- 120 -

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Integrated System of 4WS and 4WD by H-∞ Control”. SAE paper 93-0267, 1993.

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Singapore, 2003, p73-74, 517-518.


- 123 -

APPENDIX A: VEHICLE DATA

The data detailed is representative of a saloon prototype vehicle.

Masses and Inertias

Sprung mass (kg) 1665.9

Unsprung mass per wheel (kg) 47.98

Weight distribution 53.2/46.8

Centre of gravity height (m) 0.554

Roll inertia (kgm2) 655.2

Pitch inertia (kgm2) 3319

Yaw inertia (kgm2) 3515

Product of inertia about the roll and yaw axes (kgm2) 21.7

Dimensions

Wheelbase (m) 2.906

Track (m) 1.536

Distance from the sprung mass CG to the front axle (m) 1.349

Distance from the sprung mass CG to the rear axle (m) 1.557

Height of front unsprung mass CG (m) 0.308

Height of rear unsprung mass CG (m) 0.311

Suspension

Front wheel rate (N/m) 26290

Rear wheel rate (N/m) 25830

Front single wheel bump rate (N/m) 75370

Rear single wheel bump rate (N/m) 32439

Front roll centre height (m) 0.0914

Rear roll centre height (m) 0.141

Front damper rate (Ns/m) 1000

Rear damper rate (Ns/m) 1130

Front static camber (deg) -0.620

Rear static camber (deg) -0.939

Steering

On centre rack ratio 17.58

Front static toe-in (rad) -0.00360

Rear static toe-in (rad) -0.00180

Front toe change per unit bump (rad/m) -0.1196


- 124 -

Rear toe change per unit bump (rad/m) -0.0078

Brakes

Braking distribution (fixed) 70/30

Tyres

Rolling radius (m) 0.329

Lateral tyre relaxation length (m) 0.5

Front caster trail (m) 0.0376

Rear caster trail (m) 0

Wheel Inertia (kgm2) 1

Tyre designation P6000 225/55 ZR17

Pressure (Psi) 31

Aerodynamics

Frontal area (m) 2.2

Drag coefficient 0.305


- 125 -

APPENDIX B: 3 DEGREE OF FREEDOM HANDLING MODEL

This Appendix describes the derivation of the non-linear model which has been

developed in Matlab/Simulink. The 2WS model consists on 3 degrees of freedom which

includes longitudinal, yaw, and roll motions. For the purpose of the study, longitudinal

and pitch motions are disregarded as well as driveline dynamics and aerodynamics

effects. The model is derived by using an 8-DOF model derived by He et al [24] as a

reference.

Figure 115 is an illustration of the general structure for the model.

Figure 115: Structure of the 3-DOF Model - 2WS

Notations used for this model, degrees of freedom and external forces are illustrated in a

free body diagram - Figure 116. Note that:

- The coordinate system used here is the SAE one where (Y) is pointing to the

right; different to the one used in CarMaker – ISO – where (Y) is pointing left.

- The model is a four wheel model in order to include the load transfer during

cornering.


- 126 -

Figure 116: 3-DOF Vehicle Model

All the parameters used are from a prototype car developed by Jaguar Land Rover and

are enclosed in Appendix A.

B.1. Equations of Motion Subsystem

The three equations of motion are:

( ) ∑=++ ysxy FhmrVVm φ&&& (B-1)

∑=−++ xxzxysxx MrIrVVhmI &&&& )(φ (B-2)

∑=− zxzzz MIrI φ&&& (B-3)

Where:

4321 yyyyy FFFFF +++=∑ (B-4)

( )[ ] ( )φφ φφφφ&

rfrfsx CCKKghmM +−+−=∑ (B-5)

( ) ( )∑ +−+= 4321 yyyy FFbFFaMz (B-6)

s fu urm m m m= + + (B-7)

B.2. Slip Angles Subsystem

The sideslip angle is derived for each wheel with the relations given below. Note that in

order to include the rear wheel steering in the model, only the steer angle at the rear

wheels has to be added in the expression.

a

b

Fy1

Roll centre

φφφφ

msay h

Fy3 Fy4

Fy2

Fzl Fzr

Vx

Vy

x

y

y

z r

δf δf

msg

t

1 2

3 4


- 127 -

1

1 tan( / 2)

y

f

x

V ar

V r tα δ−

+ = −

+

&

& (B-8)

1

2 tan( / 2)

y

f

x

V ar

V r tα δ−

+ = −

−

&

& (B-9)

1

3 tan( / 2)

y

x

V br

V r tα −

− =

+

&

& (

rδ− ) only for 4WS vehicle model (B-10)

1

4 tan( / 2)

y

x

V br

V r tα −

− =

−

&

& (

rδ− ) only for 4WS vehicle model (B-11)

B.3 Non-linear Tyre Model Subsystem

B.3.1 Vertical Loads

The lateral load transfer is considered: vertical tyre load are derived from [24] as the

sum of the static tyre load and a load transfer due to the roll and lateral motions. The

equations are for each wheel:

( )1

1

2

y s rs f

z uf uf f f

a m l hmgbF m h K C

l t l tφ φφ φ

= + + + − −

& (B-12)

( )2

1

2

y s rs f

z uf uf f f

a m l hmgbF m h K C

l t l tφ φφ φ

= − + − − −

& (B-13)

( )3

1

2

y s fs r

z ur ur r r

a m l hmgaF m h K C

l t l tφ φφ φ

= + + + − −

& (B-14)

( )4

1

2

y s fs r

z ur ur r r

a m l hmgaF m h K C

l t l tφ φφ φ

= − + − − −

& (B-15)

B.3.1 Tyre Model

The non-linearity of the tyre must be taken into consideration since the lateral

acceleration could be important at high speed. An empirical tyre model developed by

Pacejka [35] is used. This model, commonly called “Magic Formula”, calculates the

lateral force as a function of the side slip angle and the vertical load on the tyre:

[ ]{ }( )sin arctan (1 )( ) arctan ( )y h h v

F D C B E S E B S Sα α= − + + + + (B-16)


- 128 -

Note that the self-aligning torque and the longitudinal forces are neglected. The

standard SAE definition is used for the wheel axis system.

The evaluation of the coefficients B, C, D and E, which are respectively stiffness factor,

shape factor, peak factor and curvature factor, is done with expressions derived by

Genta [36]:

0C a= (B-17)

1 2( )z z

D a F a F= + (B-18)

6 7zE a F a= + (B-19)

( )3 5

4

sin 2arctan 1zF

BCD a aa

γ

= −

(B-20)

The values used for the i

a parameters are also proposed by Genta for a front-wheel

drive saloon vehicle.

The camber angle γ is expressed using the static camber angle and the roll angle. For

right hand wheels, the camber angle is given by:

sγ γ φ= − − (B-21)

It is for the left side:

sγ γ φ= − + (B-22)

The offset Sh and Sv which come from plysteer and conicity are neglected.

Note: - Attention has to be paid on the units as Fz is in [kN], α and γ are in [deg], and

Fy in [N].

- The lateral forced obtained with the Magic Formula must be resolved in the

vehicle coordinate system – Figure 117 – by using the transformation:

Figure 117: Tyre Force in the Vehicle Coordinate

System

cosglobal tyrey y

F F δ= (B-23)


- 129 -

APPENDIX C: TEST SCENARIOS

This Appendix sums-up the characteristics of the nines test carried out in Sections 6.5,

7.5, and 8.

Table 14: Data Sheet Test 1

TEST 1: Step Steer Input Without Driver

Longitudinal Speed control: 140 km/h Friction Coefficient µ=1

Lateral Step steer input 0º (acceleration 20s) + Step steer input 40º (10s)


TEST 2: Step Steer Input With Driver Control


Lateral IPG Driver

TEST TRACK

Width: 30 m ; Angle: 180°

Radius 200 m

ACCELERATION TRACK Width: 6 m ; Length: 420 m

ACCELERATION AND TEST TRACK

Width: 1000 m ; Length: 1000 m


- 130 -


TEST 3: Accelerating and Turning

Longitudinal Speed control (1) Friction Coefficient µ=1

Lateral IPG Driver


TEST 4: Braking and Turning

Longitudinal Speed control (1) Friction Coefficient µ=1

Lateral Steer input 0º (acceleration 650m) + Step steer input 50º (10s)

ACCELERATION TRACK


TEST TRACK


(1) 140 km/h then

hard braking

(1) 0 km/h

TEST TRACK Width: 30 m ; Angle: 180°

Radius 200 m

ACCELERATION TRACK Width: 6 m ; Length: 420m

(1) 100 km/h then acceleration gas value 0.8


- 131 -


TEST 5: Split-µµµµ Braking

Longitudinal Speed control (1) Friction Coefficient see below

Lateral IPG Driver


TEST 6: ISO Double Lane Change


Lateral IPG Driver

ACCELERATION TRACK


TEST TRACK


ACCELERATION TRACK (µµµµ=1)


TEST TRACK (µµµµ=1 AND 0.4)


(1) 140 km/h

then hard

braking

(1) 0 km/h


- 132 -


TEST 7: High Speed Double Lane Change


Lateral IPG Driver


TEST 8: Side Wind Without Driver Control


Lateral Steer input 0°

Side wind 40 km/h

over 50 m

ACCELERATION TRACK


TEST TRACK


ACCELERATION TRACK + TEST TRACK



- 133 -


TEST 9: Side Wind With Driver Control


Lateral IPG Driver

ACCELERATION TRACK + TEST TRACK


Side wind

25 km/h

over 100 m

Side wind

50 km/h

over 50 m

confidentiel jusqu’au septembre 2009 - insa...

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