STEERING CONTROL FOR A CAR USING BACKSTEPPING...

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STEERING CONTROL FOR A CAR USING BACKSTEPPING CONTROL

STRATEGY

LEONG SENG WAH

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

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STEERING CONTROL FOR A CAR USING

BACKSTEPPING CONTROL STRATEGY

LEONG SENG WAH

This report is submitted in partial fulfillment of the requirements for the award of

Bachelor of Electronic Engineering (Industrial Electronics)

With Honours

Faculty of Electronic and Computer Engineering

Universiti Teknikal Malaysia Melaka

April 2009

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UNIVERSTI TEKNIKAL MALAYSIA MELAKA FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER

BORANG PENGESAHAN STATUS LAPORAN

PROJEK SARJANA MUDA II

Tajuk Projek : ………………………………………………………………………………

Sesi

Pengajian : ………………………………………………………………………………

Saya …………………………………………………………………………………………………..

(HURUF BESAR)

mengaku membenarkan Laporan Projek Sarjana Muda ini disimpan di Perpustakaan dengan syarat-

syarat kegunaan seperti berikut:

1. Laporan adalah hakmilik Universiti Teknikal Malaysia Melaka.

2. Perpustakaan dibenarkan membuat salinan untuk tujuan pengajian sahaja.

3. Perpustakaan dibenarkan membuat salinan laporan ini sebagai bahan pertukaran antara institusi

pengajian tinggi.

4. Sila tandakan ( √ ) :

SULIT*

(Mengandungi maklumat yang berdarjah keselamatan atau

kepentingan Malaysia seperti yang termaktub di dalam AKTA

RAHSIA RASMI 1972)

TERHAD*

(Mengandungi maklumat terhad yang telah ditentukan oleh

organisasi/badan di mana penyelidikan dijalankan)

TIDAK TERHAD

Disahkan oleh:

__________________________ ___________________________________

(TANDATANGAN PENULIS) (COP DAN TANDATANGAN PENYELIA)

Alamat Tetap: ……………………………......

……………………………......

Tarikh: ……………………….. Tarikh: ………………………..

STEERING CONTROL FOR A CAR USING BACKSTEPPING CONTROL STRATEGY

2008 / 2009

LEONG SENG WAH

61, JALAN TUPAI,

34000 TAIPING,

PERAK

APRIL 2009

√√√√

APRIL 2009

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“I hereby declare that this report is the result of my own work except for quotes as

cited in the references”

Signature : .……………………………..:

Author : LEONG SENG WAH

Date : APRIL 2009

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“I hereby declare that I have read this report and in my opinion this report is

sufficient in terms of the scope and quality for the award of Bachelor of Electronic

Engineering (Industrial Electronics) With Honours”

Signature : …………………………………………………

Supervisor’s Name : EN AHMAD SADHIQIN BIN MOHD ISIRA

Date : …………………………………………………

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Dedicated to my beloved parents, family and fellow friends, who had strongly

encouraged and supported me in my entire journey of learning…

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ACKNOWLEDGEMENT

I have successfully completed my thesis which is a partial fulfillment of

requirements for the Bachelor of Electronic Engineering (Industrial Electronic) With

Honours.

I would like to take this opportunity to express my gratitude and thanks to my

supervisor, En. Ahmad Sadhiqin bin Mohd Isira for his guidance that had allowed me to

complete this final year project. I would also like to thank Faculty of Electronic and

Computer Engineering (FKEKK) and Universiti Teknikal Malaysia Melaka (UTeM) for

giving me an opportunity to further my studies here.

To my parents, I would like to express a million of thanks to them for their

support and their love to me. Last but not least, I would like to thank all of my friends

for their support through the times of difficulty and joy throughout the four years in

Melaka.

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ABSTRACT

This project is to design an active steering controller for the car steering. The

controller built is based on the backstepping control technique which is a state feedback

system. The steering control is commonly known as the active steering in the automotive

industry. An active steering is capable of controlling and correcting the vehicle’s

trajectory when the system is subjected to an external interference. In most crosswind

cases, the vehicle may not be able to travel in a straight line. The crosswind causes the

vehicle to change its trajectory and becomes unstable. For such case, the active steering

can help realign the vehicle’s steering thus allowing the vehicle to travel in its intended

path safely.

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ABSTRAK

Projek ini adalah untuk merekabentuk satu sistem kawalan untuk sistem stering

kereta. Alat kawalan tersebut direkabentuk berasaskan teknik backstepping, iaitu

merupakan salah satu bentuk sistem suap balik. Alat kawalan stering kereta lebih

dikenali sebagai stering aktif dalam industry automotif. Stering aktif ini berkebolehan

untuk mengawal dan membetulkan halatuju kereta tersebut apabila sistem kenderaan

mengesan berlakunya perubahan halatuju tanpa perubahan sudut stering. Kebanyakan

kes angin lintang, kereta biasanya tidak dapat bergerak dalam garisan lurus. Angin

lintang ini akan menyebabkan kereta itu mengubah halatuju dan menjadi kurang stabil.

Dalam keadaan ini, stering aktif ini boleh membetulkan stering kereta dan seterusnya

membolehkan kereta tersebut bergerak dalam halatuju yang diinginkan dengan selamat.

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CONTENT

CHAPTER ITEM PAGE

PROJECT TITLE i

REPORT STATUS APPROVAL FORM ii

DECLARATION iii

SUPERVISOR APPROVAL iv

DEDICATION v

ACKNOWLEDGEMENT vi

ABSTRACT vii

ABSTRAK viii

CONTENT ix

LIST OF TABLE xiii

LIST OF FIGURE xiv

LIST OF ABBREVIATION xvii

I INTRODUCTION 1

1.1 Introduction of the Project 1

1.2 Objectives 2

1.3 Problem Statement 2

1.4 Scope 3

1.5 Outline of Methodology 3

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II LITERATURE REVIEW 6

2.1 Introduction 6

2.2 BMW’s Active Steering 7

2.3 Delphi’s Quadrasteer 8

2.4 Literature Review 9

2.4.1 Mathematical Modeling 9

2.4.2 Track Modeling 10

2.4.3 Disturbances 11

2.4.4 Controllers 11

III MATHEMATICAL MODEL 13

3.1 Introduction 13

3.2 The Single Track Model 13

3.3 The Simulink Modeling in MATLAB 19

3.4 The Vehicle Numerical Values 21

3.5 Controllability 22

3.6 The Disturbances 23

3.6.1 Braking Torque Disturbance 23

3.6.2 Crosswind Disturbance 24

IV CONTROLLER MODEL 26

4.1 Introduction 26

4.2 Integrator Backstepping 26

4.3 Single Integrator Backstepping 27

4.4 Realization of the Steering Controller 31

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4.5 Linear Quadratic Regulator 33

V SIMULATION AND RESULT 37

5.1 Introduction 37

5.2 Different Road Conditions 37


5.2.1.1 Lateral/Side slip 38

5.2.1.2 Yaw 40

5.2.1.3 Longitudinal 42



5.2.2.2 Yaw 46


5.3 Different Speed 50



5.3.1.2 Yaw 53




5.3.2.2 Yaw 60


VI DISCUSSION AND FUTURE RECOMMENDATION 66

6.1 Introduction 66

6.2 Discussion 66

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6.2.1 Results for Different Road Conditions

with Braking Torque Disturbance 67

6.2.2 Results for Different Road Conditions

with Crosswind Disturbance 68

6.2.3 Results for Different Vehicle Speeds 68

6.3 Future Recommendation 69

VII CONCLUSION 70

REFERENCES 71

APPENDIX A 72

APPENDIX B 74

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LIST OF TABLE

No. TITLE PAGE

3.1 Numerical values of the BMW 735i 21

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LIST OF FIGURE

No. TITLE PAGE

1.1 The methodology flow of the process. 4

2.1 BMW’s Active Steering System 7

2.2 The Quadrasteer v2.0 Four Wheel Steering System 9

2.3 Example of a two track model. 10

2.4 Example of a single track or bicycle model. 11

3.1 Single track model for car steering 14

3.2 Block diagram of a car steering 14

3.3 Kinematics variables 15

3.4 Simulink simulation together with the controller 20

3.5 The controllability output by MATLAB 23

3.6 Braking torque disturbance signal 24

3.7 Crosswind disturbance signal 25

5.1.1 Side slip angle for braking torque at 70 m/s on dry road ( µ = 1) 38

5.1.2 Side slip angle for braking torque at 70 m/s on wet road ( µ = 0.5) 39

5.1.3 Side slip angle for braking torque at 70 m/s on slippery

road ( µ = 0.15) 39

5.2.1 Yaw rate for braking torque at 70 m/s on dry road ( µ = 1) 40

5.2.2 Yaw rate for braking torque at 70 m/s on wet road ( µ = 0.5) 41

5.2.3 Yaw rate for braking torque at 70 m/s on slippery road ( µ = 0.15) 41

5.3.1 Longitudinal force for braking torque at 70 m/s on dry road ( µ = 1) 42

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5.3.2 Longitudinal force for braking torque at 70 m/s on wet road ( µ = 0.5) 43

5.3.3 Longitudinal force for braking torque at 70 m/s on slippery

road( µ = 0.15) 43

5.4.1 Side slip angle for crosswind at 70 m/s on dry road ( µ = 1) 44

5.4.2 Side slip angle for crosswind at 70 m/s on wet road ( µ = 0.5) 45

5.4.3 Side slip angle for crosswind at 70 m/s on dry road ( µ = 0.15) 45

5.5.1 Yaw rate for crosswind at 70 m/s on dry road ( µ = 1) 46

5.5.2 Yaw rate for crosswind at 70 m/s on wet road ( µ = 0.5) 47

5.5.3 Yaw rate for crosswind at 70 m/s on slippery road ( µ = 0.15) 47

5.6.1 Longitudinal force for crosswind at 70 m/s on dry road ( µ = 1) 48

5.6.2 Longitudinal force for crosswind at 70 m/s on wet road ( µ =0.5) 49

5.6.3 Longitudinal force for crosswind at 70 m/s on slippery

road ( µ = 0.15) 49















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5.12.1 Longitudinal force for crosswind at 1 m/s on dry road ( µ = 1) 63




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LIST OF ABBREVIATION

IEEE - Institute of Electrical and Electronics Engineers

LQR - Linear Quadratic Regulator

DOF - Degree Of Freedom

SBW - Steer by Wire

MP - Momentary Pole

CG - Center of Gravity

m - Mass of Vehicle

v - Velocity of Vehicle

β - Sideslip of Body

ψ - Yaw Angle

r - Yaw Rate

yFF - Front Axle Lateral Force in Chassis Coordinate

yRF - Rear Axle Lateral Force in Chassis Coordinate

xF - Retarding Force

J - Moment of Inertia

Fl - Length between Front Axle to the Center of Gravity

Rl - Length between Rear Axle to the Center of Gravity

zDM - Disturbance Torque

Fβ - Sideslip Angle at Front Axle

Rβ - Sideslip Angle at Rear Axle

Fα - Front Tire Sideslip Angle

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Rα - Rear Tire Sideslip Angle

Fδ - Front Steering Angle

Rδ - Rear Steering Angle

ytFF - Lateral Force in Front Tire Coordinate

ytRF - Lateral Force in Rear Tire Coordinate

µ - Adhesion Coefficient

FC - Front Tire Cornering Stiffness

RC - Rear Tire Cornering Stiffness

Co - Controllability

km/h - Kilometers per Hour

m/s Meters per Second

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CHAPTER I

INTRODUCTION

1.1 Introduction of the Project

Losing control of a car at high speeds is a common problem. These accidents

occur because of the driver’s failure to understand the many situations that could result

in loss of control. They have failed to understand the limit of their vehicle. A city car

which is small is not designed to be driven at highway speeds while tires with poor grip

increase the chances of losing control. Such problems are due to the driver’s negligence

to do proper maintenance. A new driver would not even be able to fully control the car,

let alone to understand the hidden dangers of disturbances.

A well maintained vehicle can also lose control due to external factors. The

external disturbance that causes a car to lose control includes but not limited to

crosswind and unstable braking torque. These factors cannot be visible but the driver can

feel its effects. Although many controllers are being installed on a vehicle such as

antilock brake system, traction control, dynamic stability control and active steering,

these system is still unable to defy extreme forces such a full thrust from a Boeing 747

that is about to take off. Such systems are only aimed to improve the drivability of a

vehicle during difficult driving situations such as poor road adhesion and crosswinds.

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1.2 Objectives

The objective of this project is being defined as below:

i. To identify the method of producing a mathematical model of a car steering.

ii. To identify and simulate the disturbance signal

iii. To identify the effects of disturbance towards the vehicle’s sideslip angle and

yaw.

iv. To identify the requirements of the backstepping controller’s requirement and its

implementation.

v. To design a steering control system for a car using the backstepping control

strategy.

1.3 Problem Statement

Driving a car at high speed requires a lot of concentration a vehicle can easily

lose control due to multiple disturbances. The most common problems are the existence

of crosswinds. These crosswinds can easily throw a vehicle off balance, resulting in the

vehicle to veer off course. The driver will have to counter steer in order to maintain the

correct path, else the vehicle may crash. Counter steering is not an easy task as too much

will result in a spin, and too little may not be enough to correct the path. Even high

speed braking is dangerous as the brakes applied are not necessarily same as there are

different amount of forces acting. This will result in the vehicle to move sideways.

Therefore, a controller is required to be implemented to reduce these disturbances to

make driving a safer task. Many controllers are implemented such as antilock brake

system and traction control. It is believed that adding a steering control or active steering

can further enhance the safety level. It must be taken into consideration that the

controllers implemented on the car are only to improve the vehicles handling and it does

not defy the law of physics.

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1.4 Scope

The scope of this project is to focus on the method of developing the vehicle’s

mathematical model especially that of the steering system. The mathematical model will

then be transferred into Simulink in MATLAB for simulation. The graphs relating to the

yaw and sideslip are then generated by adding a simulated disturbance. On the second

part of the project, the focus will be on developing a back stepping controller and will

then be integrated into the mathematical model to improve vehicle stability. This project

will only focus on simulation and does not involve any hardware.

1.5 Outline of Methodology

Literature reviews are conducted to further understand the development of

steering control. The project will simply focus on the construction of the mathematical

model of a vehicle steering. From there, a state feedback strategy controller is designed

and attached to the vehicle steering which is known as the active steering. This project

will not involve any hardware building as is only a simulation. Majority of this

information are referred to the book titled Robust Control: The Parameter Space

Approach [1].

The project was started of with the literature review. In order to understand the

basics of the steering system, a literature review has to be made on the steering system

and the many systems involved in building the state space model that is required to be

simulated in the Simulink of MATLAB. MATLAB is a very powerful simulation tool.

While it was being taught in the syllabus, refreshment is required as it has been quite

some time ago since it was last applied. The MATLAB has many other multiple tools

under Simulink and the multiple commands that can be very useful in the simulation

process. Therefore a clear understanding is required in order to fully utilize the software.

Additional assistance can easily be found under its help file.

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Having to understand the basics, some research was done on active steering

through multiple sources including the IEEE’s journals. From these journals, much

information can be gathered to further understand the problems and solutions applied to

the same concept of active steering. The journals can only give a simple overview of the

research done as most information still requires the readers to further their research by

referring their respective references books. This is to ensure that the readers can fully

understand the entire system more clearly.

Figure 1.1: The methodology flow of the process.

Start

End

Identify Various

Parameters

Establish

Mathematical Model

Control Strategy:

Backstepping & LQR

Understanding

Simulation Tools

Literature Study

Evaluate & Verify

(Using MATLAB)

Establish

Mathematical Model

Research on Active

Steering

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Chapter 2 of the project is to identify the nature of the project which is a

simulation type only. After completing the literature study, a research on the current

Active Steering technology and its many research which can be found in the IEEE’s

website. By doing so, we are able to identify the method used to simulate the system.

In chapter 3, by referring to the references, a standard mathematical modeling for

a car steering is established. The modeling is only limited to three degree of freedom

which is sufficient to represent the vehicle’s steering characteristics. The vehicle

simulation is verified by comparison with the references.

In chapter 4, the type of controller to be implemented is chosen. The

backstepping controller is capable of controlling multiple types of condition at one

moment, thus improving system efficiency. The design and implementation of the

backstepping controller is studied carefully and executed. The mathematical model is

combined with the backstepping controller which results in the active steering. The

controller is verified by adding the Linear Quadratic Regulator (LQR).

Chapter 5 consists of the simulation and results. The simulation is executed with

many types of variables being used as to show the performance of the controller at

different types of conditions. By matching the pattern of the controllers and the

uncontrolled model, it proves that the results are correct and that the simulation is in line

with other types of simulation for vehicle steering.

Chapter 6 is about the discussion and future recommendation. The discussion is

for the results generated. The future recommendation for this project is also discussed

here as this project can be further develop to complete a vehicle simulation.

Finally in chapter 7, the conclusion for this report is noted here. The initial

objectives are reviewed in order to obtain the success level of this project.

STEERING CONTROL FOR A CAR USING BACKSTEPPING...

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