PhD Thesis 640529

CRANFIELD UNIVERSITY

MUHAMMAD ADEEL AWAN

Compensation of Low Performance

Steering System Using Torque

Vectoring

DEPARTMENT OF ENGINEERING & APPLIED SCIENCES

Weapon And Vehicle Systems Group

PhD THESIS

Academic Year: 2012-13

Supervisors:

Dr. David Purdy

Dr. Amer Hameed

JULY 2012

CRANFIELD UNIVERSITY

DEPARTMENT OF ENGINEERING & APPLIED SCIENCES

Weapon And Vehicle Systems Group

PhD THESIS

Academic Year: 2012-13

Muhammad Adeel Awan

Compensation of Low Performance Steering System

Using Torque Vectoring

Supervisors:

Dr. David Purdy

Dr. Amer Hameed

JULY 2012

This thesis is submitted in partial fullment of the requirements

for the degree of Doctor of Philosophy

c Craneld University 2012. All rights reserved. No part of thispublication may be reproduced without the written permission of

the copyright owner.

Acknowledgements

Writing the acknowledgement section brings a big sigh of relief for a PhD

candidate. For me this moment would not have been possible without the

help of the Almighty, without whose blessing I am nothing.

After this my special gratitude goes to Dr. David Purdy, my supervi-

sor and mentor, who was always there with patience and persistence, whether

it was early morning discussions or emails from abroad. Many of the ideas in

this thesis were developed with his suggestions and guidance.

I was lucky enough to have two supervisors instead of one. I am very

grateful to Dr. Amer Hameed for initiating this project and for providing

me with valuable guidance, advice and support. Without his forthcoming

support the idea of steer-by-wire test vehicle would not have materialised.

I would also like to thank my advisory committee, Dr. Hugh Goyder

and Mr. Dave Simner, for taking the time to read and critique my work.

A special thanks go to Mr. John Crocker and Mr. James Harber for their

unconditional support in vehicle testing and laboratory work. Their role as

the test drivers is commendable, because without them the experimentation

phase would not have been completed. I am also thankful to NP Aerospace

for partially sponsoring my work.

Lastly I would like to thank all of my family members for their sup-

portive role. My mother's prayers were always there with me. A special

thanks go to my wife and children who allowed me to pursue my goal at the

cost of their time. Without their support I would have struggled all along.

ii

Abstract

In this work torque vectoring methods are used to compensate for a low per-

formance steer-by-wire system. Currently a number of vehicle manufacturers

are considering introducing steer-by-wire into their range of vehicles. Some of

the key concerns for the manufacturers are safety and cost. The safety can be

subdivided in the integrity of the steering system and the eect on handling.

The focus of this study is the use of low cost steering actuators on a vehicle

and identify its eects on the vehicle's handling response. The test vehicle

is dune buggy modied to accommodate the low performance steer-by-wire

system without a direct mechanical link between the steering wheel and the

wheels and equipped with various sensors to data recording.

In order to investigate the inuence of torque vectoring system on the

steer-by-wire, an eight degrees of freedom vehicle model in Matlab/Simulink

has been developed. The eight degrees of freedom are longitudinal and lat-

eral translations, yaw and roll motion and rotation of each wheel. The Mat-

lab/Simulink model also includes the dynamics of the actuators, which is

validated against the experimental data. The actuator was shown to have a

bandwidth of less than 0.3 Hz. The eight degrees of freedom model's response

was validated against experimental data for both steady state and transient

response up to 0.5 g. The tyre forces and moments are implemented by us-

ing the Dugo tyre model, which has been validated against experimentally

measured data.

The torque vectoring system uses the cascade approach based on a refer-

ence model, which uses a two degrees of freedom (bicycle model) to generate

the reference signal for control purposes. The upper level yaw controller is

based on the optimal control theory and uses the LQR (Linear-quadratic reg-

ulator) approach. The lower level wheel slip controller is based on a sliding-

mode structure and prevents tyre force saturation. The simulation results

show that the vehicle augmented with the torque vectoring system outper-

forms the low performance steer-by-wire vehicle and also the vehicle with

conventional steering arrangement.

Contents

1 Introduction 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature Review 7

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Steer-by-Wire System . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Vehicle Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Tyre Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Driver Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.6 Vehicle Control Systems for Handling . . . . . . . . . . . . . . 37

3 Vehicle, Tyre and Driver Modelling 47

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Vehicle Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1 Coordinate system . . . . . . . . . . . . . . . . . . . . 49

3.2.2 Two degrees of freedom model (Bicycle model) . . . . . 49

3.2.3 Non-linear vehicle model with seven DOF . . . . . . . 53

3.2.4 Non-linear vehicle model with eight DOF . . . . . . . . 56

3.2.5 In-wheel motor model . . . . . . . . . . . . . . . . . . 58

3.2.6 Wheel load transfer . . . . . . . . . . . . . . . . . . . . 58

3.3 Tyre Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3.1 Composition and construction . . . . . . . . . . . . . . 61

3.3.2 Tyre coordinate system . . . . . . . . . . . . . . . . . . 61

3.3.3 Forces and moments . . . . . . . . . . . . . . . . . . . 62

3.3.4 Combined slip . . . . . . . . . . . . . . . . . . . . . . . 68

3.3.5 Dugo tyre model . . . . . . . . . . . . . . . . . . . . . 69

3.4 Driver Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4 Testing and Model Validation 79

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.2 Tyre Test Rig Experiments . . . . . . . . . . . . . . . . . . . . 80

4.2.1 Tyre model validation . . . . . . . . . . . . . . . . . . 83

4.3 The Test Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 83

iv Contents

4.3.1 Vehicle mounted sensors . . . . . . . . . . . . . . . . . 86

4.3.2 Vehicle mass and centre of gravity calculations . . . . . 88

4.4 Actuator's Response . . . . . . . . . . . . . . . . . . . . . . . 90

4.4.1 Actuators' calibration . . . . . . . . . . . . . . . . . . 90

4.4.2 Potentiometer calibration . . . . . . . . . . . . . . . . 91

4.4.3 Square wave response . . . . . . . . . . . . . . . . . . . 93

4.4.4 Steering system model . . . . . . . . . . . . . . . . . . 95

4.4.5 Sine wave response . . . . . . . . . . . . . . . . . . . . 96

4.5 Vehicle Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.5.1 Steady-state circular testing . . . . . . . . . . . . . . . 98

4.5.2 Lateral transient response testing . . . . . . . . . . . . 103

4.5.3 Driver model verication . . . . . . . . . . . . . . . . . 106

5 Control 109

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.2.1 Fundamental vehicle responses . . . . . . . . . . . . . . 110

5.2.2 Eect of steering dynamics on a vehicle's behaviour . . 113

5.2.3 Driver's reaction with the steer-by-wire vehicle . . . . . 115

5.3 Control Objective and Strategy . . . . . . . . . . . . . . . . . 116

5.3.1 Linear quadratic regulator (LQR) . . . . . . . . . . . . 117

5.3.2 Sliding mode control (SMC) . . . . . . . . . . . . . . . 119

5.3.3 Control strategy . . . . . . . . . . . . . . . . . . . . . . 122

5.4 Simulation Results and Discussion . . . . . . . . . . . . . . . . 129

5.4.1 J-Turn manoeuvre with a constant speed . . . . . . . . 129

5.4.2 Sine steer manoeuvre . . . . . . . . . . . . . . . . . . . 132

5.4.3 Driver in-loop simulations . . . . . . . . . . . . . . . . 135

5.4.4 Integration of the proposed controller with the eight

DOF model . . . . . . . . . . . . . . . . . . . . . . . . 138

6 Conclusions 141

6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

6.3 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

A LabVIEW model 145

B Non-linear vehi