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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 Braking Torque Disturbance 38
5.2.1.1 Lateral/Side slip 38
5.2.1.2 Yaw 40
5.2.1.3 Longitudinal 42
5.2.2 Crosswind Disturbance 44
5.2.2.1 Lateral/Side slip 44
5.2.2.2 Yaw 46
5.2.2.3 Longitudinal 48
5.3 Different Speed 50
5.3.1 Braking Torque Disturbance 50
5.3.1.1 Lateral/Side slip 50
5.3.1.2 Yaw 53
5.3.1.3 Longitudinal 55
5.3.2 Crosswind Disturbance 58
5.3.2.1 Lateral/Side slip 58
5.3.2.2 Yaw 60
5.3.2.3 Longitudinal 63
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
5.7.1 Side slip angle for braking torque at 1 m/s on dry road ( µ = 1) 51
5.7.2 Side slip angle for braking torque at 10 m/s on dry road ( µ = 1) 51
5.7.3 Side slip angle for braking torque at 30 m/s on dry road ( µ = 1) 52
5.7.4 Side slip angle for braking torque at 50 m/s on dry road ( µ = 1) 52
5.8.1 Yaw rate for braking torque at 1 m/s on dry road ( µ = 1) 53
5.8.2 Yaw rate for braking torque at 10 m/s on dry road ( µ = 1) 54
5.8.3 Yaw rate for braking torque at 30 m/s on dry road ( µ = 1) 54
5.8.4 Yaw rate for braking torque at 50 m/s on dry road ( µ = 1) 55
5.9.1 Longitudinal force for braking torque at 1 m/s on dry road ( µ = 1) 56
5.9.2 Longitudinal force for braking torque at 10 m/s on dry road ( µ = 1) 56
5.9.3 Longitudinal force for braking torque at 30 m/s on dry road ( µ = 1) 57
5.9.4 Longitudinal force for braking torque at 50 m/s on dry road ( µ = 1) 57
5.10.1 Side slip angle for crosswind at 1 m/s on dry road ( µ = 1) 58
5.10.2 Side slip angle for crosswind at 10 m/s on dry road ( µ = 1) 59
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5.10.3 Side slip angle for crosswind at 30 m/s on dry road ( µ = 1) 59
5.10.4 Side slip angle for crosswind at 50 m/s on dry road ( µ = 1) 60
5.11.1 Yaw rate for crosswind at 1 m/s on dry road ( µ = 1) 61
5.11.2 Yaw rate for crosswind at 10 m/s on dry road ( µ = 1) 61
5.11.3 Yaw rate for crosswind at 30 m/s on dry road ( µ = 1) 62
5.11.4 Yaw rate for crosswind at 50 m/s on dry road ( µ = 1) 62
5.12.1 Longitudinal force for crosswind at 1 m/s on dry road ( µ = 1) 63
5.12.2 Longitudinal force for braking torque at 10 m/s on dry road ( µ = 1) 64
5.12.3 Longitudinal force for braking torque at 30 m/s on dry road ( µ = 1) 64
5.12.4 Longitudinal force for braking torque at 50 m/s on dry road ( µ = 1) 65
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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.