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AN OBSERVER DESIGN FOR ACTIVE SUSPENSION SYSTEM

ADIZUL AHMAD

This project report is submitted in partial of the fulfillment of the

requirement for the award of the Master of Engineering (Electrical - Mechatronics &

Automatic Control)”

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

NOVEMBER, 2005

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DEDICATION

This thesis is dedicated to my beloved parent, Ahmad Bin Razak and Halimah Binti Haji

Dris, my sisters, Noormadiad and Zuhana,to my brother Azman and not forgotten to all

my friend, thank you for the sacrifice and support.

May Allah bless all of you. Amin!

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ACKNOWLEDGEMENT

In the name of ALLAH SWT, the most Gracious, who has given me the strength

and ability to complete this study. All perfect praises belong to ALLAH SWT, lord of

the universe. May His blessing upon the prophet Muhammad SAW and member of his

family and companions.

I gratefully acknowledge the co-operation of Associate Professor Dr. Yahaya

Md. Sam who has provided me with the reference, guidance, encouragement and support

in completing this thesis. All the regular discussion sessions that we had throughout the

period of study have contributed to the completion of this project.

Thank you to my classmate for providing an enjoyable study environment.

Finally, I would like to thank my family for their encouragement, support and patience.

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PUBLICATION

The following paper, based on the work described in this thesis, has been

submitted for publishing:

1. Adizul Ahmad, Yahaya Md. Sam and Nor Maniha Abd. Ghani . “An

Observer Design for Active Suspension System” Accepted for oral

presentation in The International Conference on Mechatronics

Technology (ICMT05), Kuala Lumpur, Malaysia, 5-8 December 2005.

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ABSTRACT

The purpose of this project is to construct an active suspension control for a

quarter car model subject to excitation from a road profile using an improved sliding

mode control with an observer design. The proportional-integral sliding mode was

chosen as a control strategy, and the road profile is estimated by using an observer

design. The performance of controller will be compared with the LQR controller. There

are three parameters to be observed in this study namely, wheel deflection, the body

acceleration and the suspension travel. The performance of this controller will be

determined by performing computer simulations using the MATLAB and SIMULINK

toolbox.

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ABSTRAK

Cadangan untuk projek ini adalah untuk membina model sistem gantungan aktif

yang subjek keatas permukaan jalan dengan menggunakan kawalan ragam gelincir yang

di pertingkatkan keupayaan dengan penggunaan pemerhati. Kawalan ragam gelincir

berkadaran-kamiran di pilih sebangai pengawal dan permukaan jalan di perhati dengan

menggunakan pemerhati. Prestasi pengawal yang di perkenalkan di analisis prestasi

dengan pegawal jenis LQR. Tiga parameter output diperhatikan yang di namai, pantulan

tayar, halaju badan dan pergerakan gantungan. Prestasi pengawal akan di analisis dengan

menggunakan penyelakuan komputer aturcara MATLAB dengan SIMULINK yang

mudah di guna pakai.

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TABLE OF CONTENTS

CHAPTER TITLE

PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

PUBLICATION v

ABSTRACT vi

ABSTRAK x

TABLE OF CONTENT viii

LIST OF TABLE xvi

LIST OF FIGURES xvii

1 INTRODUCTION

1.1 Suspension System 1

1.2 Active Suspension System Control Strategies 5

1.3 Objective of Study 5

1.4 Scope of Work 6

1.5 Structure and Layout of Thesis 7

2 SYSTEM MODEL

2.1 Introduction 8

2.2 Car Suspension System 9

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2.2.1 Passive Suspension System 9

2.2.2 Active suspension System 12

2.3 Road Profile 16

2.4 Conclusion 17

3 PROPORTIONAL INTEGRAL SLIDING MODE CONTROL

3.1 Introduction 18

3.2 Proportional Integral Sliding Mode Control Design 19

3.2.1 Switching Surface design 20

3.2.2 Stability During Sliding Mode 22

3.2.3 Controller Design 24

3.3 Improve Performance 25

3.4 Conclusion 26

4 OBSERVER DESIGN

4.1 Introduction 27

4.2 Literature Review on Observer Design 27

4.3 Observer design 29

5 SIMULATION

5.1 Simulations 34

5.1.1 Performance of PISMC on Road Handling and Ride

Comfort 36

5.1.2 Effect of the Suspension Performance on Various

Road Profiles 46

5.1.3 Effect of the reaching Mode condition on varying Design

Parameter, ρ 49

5.2 Conclusion 53

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6 CONCLUSION AND SUGGESTIONS

6.1 Conclusion 54

6.2 Suggestion For Future Research 55

REFERENCES 56

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LIST OF TABLES

TABLE TITLE

PAGE

2.1 Parameter value for quarter car model 9

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LIST OF FIGURES

FIGURE TITLE

PAGE

1.1 The passive suspension system 2

1.2 The semi-active suspension system 3

1.3 The active suspension system 4

2.1 The passive suspension system 10

2.2 The active suspension for the quarter car model 13

2.3 Road profile represented a 10 cm bump 16

5.1 Road profile that generated to the system 38

5.2 Estimated road profile for the system using PISMC 39

5.3 Estimated road profile for the system using LQR controller 39

5.4 Wheel deflection fro active suspension system 40

5.5 Body acceleration for active suspension system 40

5.6 Suspension travel of active suspension 41

5.7 Sliding surface 41

5.8 Control input ot the active suspension 42

5.9 Wheel deflection between plant observer using LQR controller 43

5.10 Wheel deflection between plant observer using PISMC 43

5.11 Body acceleration between plant observer using LQR controller 44

5.12 Body acceleration between plant observer using PISMC 44

5.13 Suspension travel between plant observer using LQR controller 45

5.14 Suspension travel between plant observer using PISMC 45

5.15 Body acceleration for active suspension system for road profile 1 46

5.16 Suspension travel of active suspension for road profile 1 47

5.17 Wheel deflection of active suspension for road profile 1 47

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5.18 Body acceleration for active suspension system for road profile 2 48

5.19 Wheel deflection of active suspension for road profile 2 48

5.20 Suspension travel of active suspension for road profile 2 49

5.21 Body acceleration for varying the parameter

ρ( positive sliding gain) 50

5.22 Body acceleration for varying the parameter

ρ( negative sliding gain) 50

5.23 Suspension travel for varying the parameter

ρ( positive sliding gain) 51

5.24 Suspension travel for varying the parameter

ρ( negative sliding gain) 51

5.25 Wheel deflection for varying the parameter

ρ( positive sliding gain) 52

5.26 Wheel deflection for varying the parameter

ρ( negative sliding gain) 52

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CHAPTER 1

INTRODUCTION

1.1 Suspension System

Comfort and road-handling performance are the characteristics that have to be

considered in order to achieve a good suspension system. Ideally, the suspension should

isolate the body from road disturbance and inertial disturbances associated with

cornering and braking or acceleration. The suspension must also be able to minimize the

vertical force transmitted to the passengers for their comfort. This objective can be

achieved by minimizing the vertical car body acceleration [1].

Generally, a suspension system for a car is categorized as passive, semi-active

and active suspension system. A passive system is a conventional suspension that

consists of the conventional spring and shock absorber as shown in figure 1.1. The

springs are assumed to have almost linear characteristics; while, most of the shock

absorbers exhibit nonlinear relationship between force and velocity. In passive system,

these elements have fixed characteristics. When the suspension system must operate

over a wide range of conditions, there should be a compromise in choosing the spring

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stiffness and damping parameters. In other words, it is desirable that the above

parameters could be adjustable to improve the performance of the system.

Figure 1.1: The passive suspension system.

The performance of passive suspension system can be improved by using the

semi-active suspension system as shown in figure 1.2. Semi-active suspensions provide

real-time dissipation of energy, which is achieved through a mechanical device called an

active damper. The active damper is installed in parallel with a conventional spring. The

main feature of this system is the ability to adjust the damping of the suspension system,

without any use of actuator. This type of system requires some form of measurement

with a controller board in order to properly tune the damping force.

3

Figure 1.2: The semi-active suspension system

The demand of better ride comfort and controllability of road vehicles has

motivated many automotive industries to consider the use of active suspension. Active

suspension employs pneumatic or hydraulic actuators which in turn creates the desired

force in suspension system as shown in figure 1.3. The actuator is secured in parallel

with spring and shock absorber. Active suspension requires 2 accelerometers that

mounted at sprung and unsprung mass, and a unit of displacement transducer to measure

the motions of the body, suspension system and the unsprung mass. This information is

used by the online controller to command the actuator in order to provide the optimum

target force. Active suspension may consume large amounts of energy in providing the

control force. Therefore, in the of active suspension system the power consumptions of

actuator should also be considered as an important factor. In analysis of suspension

system, there are varieties of performance criteria which need to be optimized. There are

three performances criteria which should be considered carefully in designing a

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suspension system; namely, body acceleration, suspension travel and wheel deflection.

The performance of the system can be further improved by introducing the suitable

controller into the active suspension system.

Figure 1.3: The active suspension system

1.2 Active Suspension System Control Strategies

The objective of the active suspension system is to improve the suspension

system performance by directly controlled the suspension forces to suit with the

performance characteristics. There are various linear control strategies have been

established by previous researchers in the design of the active suspension system.

Amongst them are a fuzzy reasoning [4], robust linear control [7], H∞ [8], and adaptive

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observer [9]. The results of the study have demonstrated that active suspension system is

more effective in the vibration isolation of the car body is compared with passive

system.

The purpose of this study is to utilize the concept of proportional integral sliding

mode control in active suspension system [1, 2, 5, 6,] with observer design for road

estimator. Therefore, the estimated road disturbance will be another state for the system.

1.3 Objective of study

The objectives of this research are as follows:

I. To develop the mathematical model of quarter car active suspension system with

an observer.

II. To design an observer that act as a road profile estimator for the active

suspension system.

III. To design a Proportional Integral Sliding Mode Control (PISMC) for the quarter

car active suspension system.

IV. To study the performance of the PISMC with a disturbance observer.

Theoretical verification of the proposed controller and observer on its stability and

reachability will be accomplished by using a Lyapunov’s second method. The

performance of the active suspension system will be observed by using extensive

computer simulation that will be performed using MATLAB software and SIMULINK

Toolbox subjected to various types of road profiles and parameter value.

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1.4 Scope of work

The scopes of work for this study are as follows:

I. Familiarization of a quarter car active suspension system with Proportional-

Integral Sliding Mode Controller

II. Mathematical derivation of an observer for a quarter car active suspension

system.

III. Design an Observer for a quarter car active suspension system using Sliding

Mode Control technique.

IV. Perform a simulation works by using a MATLAB/Simulink to observe

effectiveness of the observer.

V. Compare the performance of the proposed PISMC with Observer design with

Validate with a Linear Quadratic Regulator (LQR) technique.

1.5 Structure and Layout of Thesis

The necessary components for achieving objective of the study are given in the

succeeding chapters. The mathematical modeling of a quarter car is derived in chapter 2.

The state space representation of the dynamic model of the passive, semi active and

active suspension system are outlined. Finally, various road profiles that represent the

uncertainty in the suspension systems will be represented.

In chapter 3, the proposed controller, proportional integral sliding mode control

with disturbance observer is presented. By using a Lyapunov’s stability theory, it will be

shown that for the system with mismatched uncertain, the system is bounded stable. In

chapter 4 discussion on an observer design is performed. The literature review and

mathematical model will discuss in this chapter.

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Chapter 5 represents the computer simulation for the proposed observer and

controller. In this chapter, the performance of road handling and ride comfort will be

compared with the LQR controller. To assure the robustness of the proposed observer,

various road profiles will be applied in the system. The chattering and boundary layer

effect of the controller will be presented by varying the parameter in the continuous

switching gain.

The summary of the result and future research based on this study will be

presented in chapter 6.

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REFERENCES

[1] Yahaya Md Sam. (2004).“Modeling and Control of Active Suspension System Using

PI Sliding Mode control”, Universiti Teknologi Malaysia, PhD Thesis.

[2] Yahaya Md Sam, Johari Halim Shah Osman., and Mohd Ruddin Abd Ghani. ( 2003),

“A Class of Proportional Integral Sliding Mode Control with Application to Active

Suspension System”, System and Control Letter,pp.217-223

[3] Yahaya Md Sam, Johari Halim Shah Osman., and Mohd Ruddin Abd Ghani. (2002),

“A Class Of Sliding Mode Control for Mismatched Uncertain Systems”, Student

Conference On Research and Development Proceedings (SCOReD 2002), Shah Alam,

Malaysia, pp.31-4.

[4] T. Yoshimura, A. Nakminami, M. Kurimoto And J. Hino. (1999), “Active

Suspension of Passenger Cars Using Linear and Fuzzy logic Control”, Control

Engineering Practice, pp 41-47

[5] T. Yoshimura, A. Kume, M. Kurimoto And J. Hino. (2001), “Construction of an

Active Suspension System of a Quarter Car Model Using the Concept of Sliding Mode

Control”, Journal of Sound and Vibration, pp 187-199

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[6] T. Yoshimura, S. Matumura, M. Kurimoto and J. Hino. (2002), “Active Suspension

System of One-Wheel Car Models Using The Sliding Mode Control with VSS

Observer”, International Journal of Vehicle Autonomous Systems, Vol 1, No 1.

[7] Christophe Lauwerys, Jan Swever, Paul Sas, “Robust Linear Control of an Active

Suspension System on a Quarter Car Test-rig”, Control Engineering Practice.

[8] S. Ohsaku, T. Nakayama, I. Kamimura, Y. Motozono. (1999), “Nonlinear H∞ Con

trol For Semi-active”, JSAE Review 20, pp. 447-452

[9] Rajesh Rajamani, and J. Karl Hedrick. (1995), “Adaptive Observer for Active

Automotive Suspension: Theory and Experiment” IEEE Transactions on Control System

Technology, Vol. 3, No 1 March

[10] Christopher Edwards and Sarah K. Spurgeon. (1998), “Sliding Mode Control:

Theory and Applications”, London: Taylor & Francis Group Ltd.

[11] Vadim Utkin, Jurgen Guldner, Jingxin Shi. (1999), “Sliding Mode Control in

Electromechanical Systems”, Taylor & Francis Group Ltd.

[12] H.D. Taghirad, E. Esmailzadeh. (1995), “ Passenger Ride Comfort Through

Observer Based Control” ASME Conference on Mechanical Vibaration and Noise

[13] Fan Yu, Wei Ping Sha, S. El-Demerdash, “ Estimation Accuracy and Robustness

Analysis of a State Observer for an Active Vehicle Suspension”