Project Proposal 01
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SIMULATION AND EXPERIMENTAL ANALYSIS OF AN ACTIVE VEHICLE SUSPENSION SYSTEM
SIMULATION AND EXPERIMENTAL ANALYSIS OF AN ACTIVE VEHICLE SUSPENSION SYSTEM
A project report submitted in partial fulfilment of the requirements for the award of the degree of Master of Engineering (Mechanical)
v
ABSTRACT
This project was carried out to study the performance of a two degree-offreedom (DOF) active vehicle suspension system with active force control (AFC) as the main proposed control technique. The overall control system essentially comprises two feedback control loops. First is intermediate AFC control loop for the compensation of the disturbances and second is the outermost Proportional-IntegralDerivative (PID) control loop for the computation of the optimum commanded force. Iterative learning method (ILM) and crude approximation (CA) were used as methods to approximate the estimated mass in the AFC loop. Both simulation and experimental studies were applied in this project. A quarter car model consists of sprung and unsprung masses is considered in developing of the computer simulation model in Simulink and also in the experimental set-up. Both simulation and experimental work were carried out and the results between the two of them are compared. The results of the simulation study show that active suspension system using AFC with CA and ILM gives better performance compared to PID controller and passive suspension system. Experimental results obtained in the study further verified the potential and superiority of the performance of the active suspension system with AFC strategy compared to the PID control.
vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xiv
LIST OF ABBREVIATIONS
xvi
LIST OF APPENDICES
xvii
INTRODUCTION
1
1.1
General Introduction
1
1.2
Objective
2
1.3
Scope of Work
2
1.4
Project Implementation
3
1.5
Organisation of Thesis
7
viii
2
THEORETICAL BACKGROUND AND
8
LITERATURE REVIEW
3
2.1
Introduction
8
2.2
Definition of Suspension System
8
2.3
Functions of a Vehicle Suspension
10
2.4
Types of Suspension System
11
2.4.1 Passive Suspension
12
2.4.2 Semi-active Suspension
13
2.4.3 Active Suspension
13
2.5
PID Controller
15
2.6
Active Force Control (AFC)
17
2.7
Iterative Learning Method
19
2.8
Review on Previous Research
20
2.9
Conclusion
21
MATHEMATICAL MODELLING AND
23
SIMULATION 3.1
Introduction
23
3.2
Quarter Car Model
23
3.3
Disturbance Models
26
3.4
Passive Suspension System Model
28
3.5
Active Suspension System Model
29
3.5.1 Active Suspension System with AFC-CA
30
Strategy 3.5.2 Active Suspension System Model with
31
AFC-ILM
4
3.6
Modelling and Simulation Parameters
33
3.7
Conclusion
37
SIMULATION RESULTS
35
4.1
35
Introduction
ix
5
6
7
4.2
Passive Suspension
35
4.3
Active Suspension
37
4.4
Active Suspension with AFC-CA
38
4.5
Active Suspension with AFC-ILM
40
4.6
Conclusion
41
EXPERIMENTAL SET-UP
42
5.1
Introduction
42
5.2
Simulink Model in Real-Time Workshop (RTW)
42
5.3
Experimental Set-up
47
5.3.1 Mechanical System
49
5.3.2 Electrical/Electronic Device
49
5.3.3 Computer Control
52
5.4
Parameters for Experiments
53
5.5
Conclusion
54
EXPERIMENTAL RESULTS AND DISCUSSION
55
6.1
Introduction
55
6.2
System Response Without Disturbance
56
6.3
System Response with the Sinusoidal Disturbance
59
6.4
System Response with the Step Disturbance
62
6.5
Conclusion
65
CONCLUSION AND RECOMMENDATION
66
7.1
Conclusion
66
7.2
Recommendation for Future Works
67
REFERENCES
68
APPENDICES
71
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
3.1
Parameters for suspension model
33
3.2
Simulation parameters
33
5.1
Suspension and pneumatic actuator parameters
53
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Flow chart of the project implementation
5
1.2
Gantt Chart of the project schedule
6
2.1
A suspension system
10
2.2
Passive suspension system
12
2.3
Semi-active suspension
13
2.4
Active suspension system
14
2.5
A block diagram of suspension system using PID controller
16
2.6
The schematic diagram of AFC strategy
18
2.7
A model of iterative learning method
19
3.1
Quarter car vehicle passive suspension
24
3.2
Quarter car vehicle active suspension
25
3.3 (a)
Step input
27
3.3 (b)
Bump and hole
27
3.3 (c)
Sinusoidal
28
3.4
Simulink model of passive suspension system
29
3.5
Simulink model of active suspension system
30
3.6
Simulink model of active suspension system with AFC-CA
31
3.7
Simulink model of active suspension system with AFC-ILM
32
3.8
Subsystem of iterative learning method in AFC
32
4.1 (a)
Passive suspension response to step input disturbance
36
4.1 (b)
Passive suspension response to sinusoidal disturbance
36
4.2 (a)
Active suspension response to step input disturbance.
37
4.2 (b)
Active suspension response to sinusoidal disturbance
38
xii 4.3 (a)
AFC-CA suspension response to step input disturbance
39
4.3 (b)
AFC-CA suspension response to sinusoidal disturbance
39
4.4 (a)
AFC-ILM suspension response to step input disturbance
40
4.4 (b)
AFC-ILM suspension response to sinusoidal disturbance
41
5.1
Simulink model with RTW related to PID and AFC-ILM
43
control 5.2
Active suspension Simulink model in RTW
44
5.3
Pneumatic actuator subsystem
44
5.4
Body acceleration subsystem
45
5.5
Tyre acceleration subsystem
45
5.6
Disturbance subsystem
45
5.7
Suspension deflection system
46
5.8
Force tracking subsystem
46
5.9
AFC with ILM subsystem
47
5.10
Fotograph of the suspension system
48
5.11
The schematic of the experimental set-up
48
5.12
Accelerometer to measure body acceleration
50
5.13
Laser sensor to measure suspension deflection
50
5.14
LVDT to measure disturbance
51
5.15
Pressure sensor to measure actuator force
51
5.16
A computer set as the main controller
52
5.17
DAS 1602 interface card slotted in the CPU
53
6.1
Graph for body displacement response without disturbance
56
6.2
The close-up of body displacement response
57
6.3
Body displacement response without disturbance for B vary
58
6.4
Close-up body displacement response without disturbance
58
for B vary 6.5
Disturbance model type sinusoidal
59
6.6
Body displacement response with the sinusoidal disturbance
60
6.7
Body acceleration response with the sinusoidal disturbance
60
6.8
Suspension deflection response with the sinusoidal
61
disturbance 6.9
Tyre deflection response with the sinusoidal disturbance
61
6.10
Disturbance model type step.
62
xiii 6.11
Body displacement response with the step disturbance
63
6.12
Body acceleration response with the step disturbance
63
6.13
Suspension deflection response with the step disturbance
64
6.14
Tyre deflection response with the step disturbance
64
xiv
LIST OF SYMBOLS
a
-
Acceleration of the body
A
-
Proportional learning parameter
B
-
Derivative learning parameter
bs
-
Damping coefficient
D
-
Derivative
-
Error (output – input)
e ( t )
-
Derivative error
fa
-
Actuator force
Fa
-
Actuated force
F*
-
Estimated force
I
-
Integral
Kd
-
Derivative controller gain
Ki
-
Integral controller gain
Kp
-
Proportional controller gain
ks
-
Spring stiffness
kt
-
Tyre stiffness
m (t ) -
Control signal
e (t )
ms
-
Sprung mass
mu
-
Unsprung mass
M*
-
Estimated mass of the body
P
-
Proportional
TEk
-
Error value/current root of sum squared position track error
xv uk
-
Current estimate value
uk +1
-
Next estimated value
zr
-
Displacement of road
zs
-
Displacement of sprung mass
zu
-
Displacement of unsprung mass
zs
-
Velocity of sprung mass
zu
-
Velocity of unsprung mass
zs
-
Acceleration of sprung mass
zu
-
Acceleration of unsprung mass
z s − zu -
Deflection of suspension
zu − z r -
Deflection of tyre
xvi
LIST OF ABBREVIATIONS
ADC
-
Analoque-to-digital converter
AF-AFC
-
Adaptive fuzzy active force control
AFC
-
Active force control
AFC-CA
-
Active force control with crude approximation
AFC-ILM
-
Active force control with iterative learning method
CA
-
Crude approximation
DAS
-
Data acquisition system
DCA
-
Digital-to-analoque converter
DOF
-
Degree of freedom
FLC
-
Fuzzy logic control
I/O
-
Input/output
IAFCRG
-
Intelligent Active Force Control Research Group
ILM
-
Iterative learning method
LVDT
-
Linear variable differential transformer
PC
-
Personal computer
PD
-
Proportional-Derivative
PID
-
Proportional-Integral-Derivative
PLC
-
programmable logic control
RTW
-
Real-Time Workshop
SANAFC
-
Skyhook and adaptive neuro active force control
xvii
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Simulation Result for Various Conditions
71
B
Experimental Results for Various Learning Parameter
72
C
Experimental Results for Different Conditions
80
D
The Sketch of the Experimental Rig
83
E
The LVDT
84
F
The Pressure Sensor
86
G
The Data Acquisition System Card DAS 1602
88
H
The Accelerometer
90
CHAPTER 1
INTRODUCTION
1.1
General Introduction
Traditionally, automotive suspension designs have been a compromise between three conflicting criteria of road holding, load carrying and passenger comfort. The suspension system must support the vehicle, provide directional control during handling manouevres and provide effective isolation of passenger payload from road disturbances [1]. Good ride comfort requires a soft suspension wheras insentivity to applied load requires stiff suspension. Good handling requires a suspension setting somewhere between the two.
Due to these conflicting demands, suspension design has had to be something of a compromise, largely determined by the type of use for which the vehicle was designed. Active suspensions are considered to be a way of increasing the freedom one has to specify independently the characteristics of load carrying, handling and ride quality.
2 A passive suspension system has the ability to storage energy via a spring and to dissipate it via a damper. Its parameters are generally fixed, being chosen to achive a certain level of compromise between road holding, load carrying and comfort.
An active suspension system has the ability to store, dissipate and to introduce energy to the system. It may vary its parameters depending upon operating conditions and can have knowledge other than the strut deflection the passive system is limited to.
1.2
Objective
The main objective of this project is to study the performance of an active suspension system using active force control (AFC) through simulation and experimental works.
1.3
Scope of work
The scope of this study consists of two major parts. The first is simulation works and the second is experimental works. For the simulation works, the scope involve is as follows:
i)
To use an existing mathematical model of an active suspension.
ii)
Apply active force control (AFC) with crude approximation (CA) and
3 iterative learning method (ILM) to active suspension system. iii)
Simulate active suspension system with active force control with crude approximation (AFC-CA) and active force control with iterative learning method (AFC-ILM) strategy incorporated with different road profile.
iv)
Study the performance of active suspension using AFC-CA and AFCILM strategy compare to PID control.
The scopes involved in an experimental works is as follows:
i)
Prepare experimental set-up.
ii)
Develop Simulink model in Real-Time Workshop (RTW).
iii)
Run experiment.
iv)
Study the performance of active suspension system using AFC-ILM strategy compare to PID control with the different disturbance.
v)
Compare simulation results with the experimental results.
In experimental works, AFC strategy is used with iterative learning method (ILM) is applied to approximate the estimated mass. The study in experimental work will compare the result between PID and AFC-ILM only with different type of disturbance. A quarter car model is considered in both simulation and experimental study.
1.4
Project Implementation
The research is started with deriving the mathematical model of the main dynamic system for the vehicle suspension system using Newton’s Second Law. First, dynamic equation for passive suspension system is derived followed by active
4 suspension system. The model used is a two degree of freedom (DOF) system representing a class of passenger car. Disturbances also were modeled mathematically. Then, control scheme was developed and modelled. The schemes include PID and AFC strategy employing both crude estimation and iterative learning method.
Based on the derived models, a simulation study using MATLAB and Simulink was carried out. Started with the passive suspension system with open loop system followed by closed loop system of active suspension system. The results of the simulations were then compared for both passive and active suspension. The simulation results of active suspension system using AFC strategy and PID controller also were compared.
Experimental set-up for the proposed system then was prepared. The work involve during the set-up preparation is to develop experimental modules in the MATLAB which known as Simulink model with Real-Time Workshop (RTW). Then the experiment was carry out and the results obtained are analysed. Then experimental results was compared to simulation results in order to validate the results obtained for both method. This project implementation can be illustrated in a form of a flow chart as shown in Figure 1.1. Gantt Chart of the project schedule is shown in Figure 1.2.
5
Figure 1.1: Flow chart of the project implementation
SEMESTER 1 Activities
No. 1 Brief idea
W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 W16 W17 W18 *
2 Literature review
*
*
*
3 Study dynamic system
*
*
*
*
*
*
4 Modelling proposed system
*
*
*
*
*
*
*
*
5 Simulate proposed system
*
6 Report writing
* *
*
*
7 Presentation
*
SEMESTER 2 No. Activities 1 Prepare experiments 2 Run experiments 3 Analyze result
W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15 W16 W17 W18 *
*
*
* *
*
* *
*
Compare simulation results with 4
experimental results
*
5 Report writing
*
* *
*
*
*
6 Presentation
* Semester break
Figure 1.2: Gantt chart of the project schedule 6
7 1.5
Organisation of Thesis
This thesis is organised into seven chapters. General introduction to the suspension system, the objective and the scope of the project and how the project is implemented is presented in Chapter 1. Chapter 2 discussed about theoretical information and literature review related to the project backgraound. This includes the definition of the suspension systems and its function. Explanation of types of suspension system and the concept of proportional-integral-derivative (PID) controller, active force control (AFC) and iterative learning method (ILM) also done in this chapter. A number of related research is reviewed adequately in this chapter.
Mathematical modelling based on quarter car model is presented in Chapter 3. Disturbances model and proposed simulation models also discussed in detail. Parameters used for simulation is highlighted in this chapter. Chapter 4 presents the simulation results for the different types of suspension system with various control strategies.
In chapter 5, experimental set-up for this project is explained in detail. This includes the development of the Simulink model with Real-Time Workshop (RTW) complete with all related subsystems in the model. Hardware components that used in the set-up also described. Then, parameters for experiment is presented.
Chapter 6 presents experimental results. System response with various conditions are presented and disscussed adequately. Chapter 7 gives the overall conclusion on the study that has been done and recommend of future works could be considered as extension to this study.
CHAPTER 2
THEORETICAL BACKGROUND AND LITERATURE REVIEW
2.1
Introduction
This chapter includes the study of the suspension definition, function of the vehicle suspension and the vehicle dynamics. Three competing types of suspension systems are also described in this chapter which are passive, semi active and active suspension system. PID control, active force control (AFC) strategies and iterative learning method (ILM) are also discussed. Then, the review of the previous research related to the active suspension system is given.
2.2
Definition of Suspension System
Suspension system is a system that supports a load from above and isolates the occupants of a vehicle from the road disturbances. Springs in the suspension system are flexible elements. They able to store the energy applied to them in the form of loads and deflections. They have the ability to absorb energy and bend when
9 they are compressed to shorter lengths. When a tyre meets an obstruction, it is forced upward and the spring absorbs energy of this upward motion.
However, the spring absorbs this energy for a short time only and it will release the energy by extending back to its original condition. When a spring releases its stored energy, it does so with such quickness and momentum that the end of the spring usually extends too far. The spring will go through a series of oscillations, contractions and extension until all of the energy in the spring is released. The natural frequency of the spring and suspension will determine the speed of the oscillations.
The energy that released by spring is converted to heat and dissipated partly by friction in the system by damper. Dampers usually in the form of piston working in cylinders filled with hydraulic fluid. They exert a force which is proportional to the square of the piston velocity. The function of damper is to restrain undesirable bounce characteristic of the sprung mass. It also used to ensure the wheel assembly always contact with the road by being excited at its natural vibration frequency.
Other mechanical elements in a suspension system are the wheel assemblies and control geometry of their movement. Some of these elements are simple links and multi-role members such as transverse torsion bars used to stabilize the vehicle in corners by restricting roll. A suspension system comprises many elements that include spring, damper, tyres, bushes, locating links and anti-roll bars are shown in Figure 2.1.
10
Figure 2.1: A suspension system [2]
2.3
Functions of a Vehicle Suspension
A vehicle suspension system is a complicated system as it has to fulfill a large number of partly contradictory requirements. Ride comfort, safety, handling, body leveling and noise comfort are among the most important requirements that has to fulfill.
Ride comfort can be determined by the acceleration of the vehicle body. Acceleration forces are experienced by the passengers as a disturbance and set demands on the load and the vehicle. The suspension system has the task to isolate these disturbances from the vehicle body which caused by the uneven road profile. The lower the acceleration, the better the rides comfort.
11 The safety of the vehicle during traveling is determined by the wheels ability to transfer the longitudinal and lateral forces onto the road. The vehicle suspension system is required to keep the wheels as close the road surface as possible. Wheel vibration must be dampened and the dangerous lifting the wheels must be avoided. If the dynamic forces occurring between the wheels and the road surface are small, the braking, driving and lateral forces can be transferred to the road in an optimal manner. The necessity of dampening the tyre system is the reason for the known conflict of aims between comfortable and safety tuning.
Another function of the suspension system is the isolation of the vehicle body from high frequency road disturbances. The passengers in the car note these disturbances acoustically and thus the noise comfort is reduced. When there is changes in loading, the suspension system has to keep the vehicle level as constant as possible, so that the complete suspension travel is available for the wheel movements. A lower suspension travel means that lower suspension working space and this is a good suspension design. In order to fulfill all these contradict requirements certain marginal conditions have to be considered.
2.4
Types of Suspension System
Generally there are three types of the suspension system. They are: i)
passive suspension
ii)
semi-active suspension
iii)
active suspension
12 2.4.1 Passive Suspension
Passive suspension system is the conventional suspension system. However it is still to be found on majority of production car. It consists two elements namely dampers and springs. The function of the dampers in this passive suspension is to dissipate the energy and the springs is to store the energy. If a load exerted to the spring, it will compress until the force produced by the compression is equal to the load force. When the load is disturbed by an external force, it will oscillate around its original position for a period of time. Dampers will absorb this oscillation so that it would only bounce for a short period of time. Damping coefficient and spring stiffness for this type of suspension system are fixed so that this is the major weakness as parameters for ride comfort and good handling vary with different road surfaces, vehicle speed and disturbances.
Figure 2.2: Passive suspension system
13 2.4.2 Semi-active Suspension
The element in the semi-active suspension system is same with passive suspension system and it uses the same application of the active suspension system where external energy is needed in the system. The difference is the damping coefficient can be controlled. The fully active suspension is modified so that the actuator is only capable of dissipating power rather than supplying it as well. The actuator then becomes a continuously variable damper which is theoretically capable of tracking force demand signal independently of instantaneous velocity across it [3]. This suspension system exhibits high performance while having low system cost, light system weight and low energy consumption.
Figure 2.3: Semi-active suspension
2.4.3 Active Suspension
The concept of active suspension system was introduced as early as 1958. The difference compare to conventional suspension is active suspension system able
14 to inject energy into vehicle dynamic system via actuators rather than dissipate energy. Active suspension can make use of more degrees of freedom in assigning transfer functions and thus improve performance. The active suspension system consists an extra element in the conventional suspension which is basically an actuator that is controlled by a high frequency response servo valve and which involves a force feedback loop. The demand foce signal, typically generated in a microprocessor, is governed by a control law which is normally obtained by application of various forms of optimal control theory [3]. Theoretically, this suspension provides optimum ride and handling characteristics. It is done by maintaining an approximately constant tire contact force, maintaining a level vehicle geometry and by minimizing vertical accelerations to the vehicle. How ever due to its complexity, cost and power requirements, it has not yet put into mass production. Figure 2.4 shows an active suspension system.
An important issue in active suspension is energy consumption. It is recognized that full active suspension, which must carry the full weight of vehicle, would consume a considerable amount of energy and need high bandwidth actuators (30 Hz) and control valves (100 Hz) [4,5]. Consequently, it was only installed in some expensive and exclusive car or Formula One cars, and has not been mass produced.
Figure 2.4: Active suspension system
15 2.5
PID Controller
PID control is a particular control structure that has become almost universally used in industrial control. The letters ‘PID’ stand for Proportional, Integral and Derivative. They have proven to be quite robust in the control of many important applications for specific operating conditions. It structure is simple but very effective feedback control method applied to dynamical systems. PID also most conveniently integrated with other more advanced control techniques which more often than not results in better overall performance. Pure PID control is excellent for slow speed operation and with very small or no disturbances, the performance severely degrades in the adverse conditions.
However, the simplicity of these controllers is also their weakness where it limits the range of plants that they can control satisfactorily. Indeed, there exists a set of unstable plants that they cannot be stabilized with any member of the PID family. Nevertheless, the versatility of PID control ensures continued relevance and popularity for this controller.
The PID method is error driven and largely relies on the proper tuning of the controller gains and accurate information from the feedback element (sensor). The basic algorithm of the PID is expressed as follows:
m ( t ) = K p e ( t ) + K i ∫ e ( t )dt + K d e ( t ) where,
m ( t ) = control signal
Kp
= proportional controller gain
Ki
= integral controller gain
Kd
= derivative controller gain
(2.1)
16 e (t ) e ( t )
= error (output – input) = derivative error
A simple PID controller applied to a vehicle suspension system can be illustrated as shown in Figure 2.5.
Figure 2.5: A block diagram of suspension system using PID controller.
The effects of the P, I and D parameters to the system are as follows:
a)
Proportional (P) action
This parameter provides a contribution which depends on the instantaneous value of the control error. A proportional controller can control unstable plant but it provides limited performance and non zero steady-state errors. This later limitation is due to the fact that its frequency response is bounded for all frequencies.
b)
Integral (I) action
Integral parameter gives a controller output that is proportional to the accumulated error, which implies that it is a slow reaction mode. This characteristic is also evident in its low-pass frequency response. The integral mode plays a fundamental role in achieving perfect plant inversion at zero frequency.
17 This forces the steady-state error to zero in the presence of a step reference and disturbance.
c)
Derivative (D) action
Derivative action acts on the rate of change of the control error. Consequently, it is a fast mode which ultimately disappears in the presence of constant errors. It sometimes referred to as a predictive mode because of its dependence on the error trend. The main limitation of the derivative mode is its tendency to yield large control signals in response to high-frequency control errors, such as errors induced by set-point changes or measurement noise.
2.6
Active Force Control (AFC)
Active force control strategy applied to dynamic system was proposed in the early 80s by Hewit [6]. High robustness system can be achieved such that the system remains stable and effective even in the presence of known or unknown disturbances, uncertainties and varied operating conditions [7]. One of the succesful AFC strategy applications is controlling robot arm, done by Mailah [8]. The study has been demonstrated that AFC is superior compared to the conventional method in controlling the robot arm.
The essence of the AFC is to determine the estimated force F * by measuring two importants parameters. These parameters are the actuated force, Fa (measured by force sensor) and acceleration of the body, a (measured by accelerometer). An appropriate estimation of the estimated mass of the body, M * was then multiplied with the acceleration of the body, a yielding the estimated force. The mathematical model for AFC can be written as follows:
18 F * = Fa − M * ⋅ a
(2.2)
If equation ( 2.2 ) can be fulfilled, it is expected that very robust system can be achieved. Thus, it is the main aim of the study to apply the AFC method to control a suspension effectively.
Figure 2.6 shows a schematic of the AFC strategy applied to a dynamic system. Note that the estimated mass, M * in Figure 2.5 can be determined by a number of methods such as crude approximation method, neural network, fuzzy logic, iterative learning and genetic algorithms. However in this project, crude approximation (CA) and iterative learning method (ILM) were used.
Figure 2.6: The schematic diagram of AFC strategy
19 2.7
Iterative Learning Method (ILM)
Iterative learning method (ILM) is one of the popular method in estimate the next value. It has been applied to control a number of dynamic system [9]. As the number of iteration increases, the track error converges to near zero datum and the dynamic system is then said to operate effectively. In this project, the proposed iterative learning algorithm takes the following form; uk +1 = uk + A(TEk ) + B
d (TEk ) dt
(2.3)
where uk +1
= next estimated value
uk
= current estimate value
TEk
= error value/current root of sum squared position track error
A, B
= learning parameter
Figure 2.7 shows a graphical representation of the ILM algorithm.
IM 1
IM(uk)
Me(u k+1) Add du/dt Derivative
k
k
A
B
1 TEk
Figure 2.7: A model of iterative learning method
20
2.8
Review on Previous Research
Active suspensions have been extensively studied nowadays compare to passive suspension. Many researchers have studied and proposed a number of control methods for vehicle suspensions. The first preview in the control of an active system for a 1-DOF model was to introduced by Bender in 1967. Bender assumed an integrated white noise terrain profile. He developed an optimal pair of damping coefficient and spring stiffness by using Wiener filter theory to provide a wide range of vibration isolation [10].
Tomizuka applied a discrete time, state space approach to Bender's problem [11]. The optimal control scheme of that study involved both feedforward and feedback elements. Tomizuka suggested his control logic could be realized in practice by moving previewed samples through shift registers. The potential of the preview control was demonstrated by subsequent studies for 2-DOF models by Thomson.
In their paper, D’Amato and Viassolo described that the goal of this paper is to minimize vertical car body acceleration, and to avoid hitting suspension limits using fuzzy logic control (FLC) [12]. A controller consisting of two control loops is proposed to attain this goal. The inner loop controls a nonlinear hydraulic actuator to achieve tracking of a desired actuation force. The outer loop implements a FLC to provide the desired actuation force. Controller parameters are computed by genetic algorithm based optimization. The methodology proved effective when applied to a quarter car model of suspension system.
Omar introduced a novel approach to control vehicle suspension system using AFC strategy [13]. A proportional-derivative (PD) controller was incorporated into the AFC control scheme. Crude approximation and iterative learning method
21 were used to estimated the initial mass in the AFC to effect the control action. The simulation results have shown that the AFC is able to compensate the presence of known or unknown disturbances to ensure that the system achieve the desired input.
Mailah and Priyandoko proposed an adaptive fuzzy active force control (AFAFC) to control vehicle active suspension system [14]. The technique proposed are mainly for simplicity of the control low and to reduce the computational burden. Non linear hydraulic actuator are used in the study. The simulation result shows the performance of the proposed control method is found to be significantly superior compared to the other systems considered in the study.
Priyandoko et al. introduced the practical design of a control technique apply to a vehicle active suspension system [15]. Skyhook and adaptive neuro active force control (SANAFC) are used as a control scheme. From the experimental result it shows that SANAFC controller is very effective in isolating the vibration effects on the sprung mass which in turn considerably improve the overall system performance.
2.9
Conclusion
The theoretical backgrounds and previous research related to this study have been outlined in this chapter. The information of the suspension in term of definition, functions and type of suspension were adequately discussed. The conventional PID controller and the fundamental concept of active force control (AFC) applied to the dynamic system were also explained. Iterative learning method (ILM) that will apply to estimate the estimated mass in AFC also discussed. It is found that, many research papers discussed on optimization of various types of
22 suspension system to improve ride quality and road handling by using various types of control schemes.
CHAPTER 3
MATHEMATICAL MODELLING AND SIMULATION
3.1
Introduction
In this chapter, a full modeling of the system dynamics related to the vehicle suspension system, proposed control strategies and road disturbances are described. This shall provide the basis for the rigorous computer simulation study to be carried out using MATLAB and Simulink software package. The mathematical modelling of the dynamic system is performed using the Newtonian mechanics. The suspension system is modelled based on a quarter car configuration. The active suspension system is specifically designed and modelled with the feedback control element embedded into the system. A number of assumption that are made throughout the modeling and simulation study is also described.
3.2
Quarter Car Model
Quarter car model are used to derive the mathematical model of the active suspension system. The quarter car model is popularly used in suspension analysis
24 and design because it is simple to analyze but yet able to capture many important characteristics of the full model. It is also realistic enough to validate the suspension simulations.
Figure 3.1 shows a quarter car vehicle passive suspension system. Single wheel and axle are connected to the quarter portion of the car body (sprung mass) through a passive spring and damper. The tyre (unsprung mass) is assumed to have only the spring feature and is in contact with the road terrain at the other end. The road terrain serves as an external disturbance input to the system.
Figure 3.1: Quarter car vehicle passive suspension
The equations of motion for the the passive system are based on Newtonian mechanics and given as: [14]
ms z s = − k s ( zs − zu ) − bs ( zs − zu )
mu zu = k s ( z s − zu ) + bs ( zs − zu ) − kt ( zu − zr ) where ms and mu
: sprung mass and unsprung mass respectively
bs
: damping coefficient
(3.1)
25 ks and kt
: stiffness of spring and tyre respectively
z s and zu
: displacement of sprung mass and unsprung mass respectively
zr
: displacement of road
z s − zu
: deflection of suspension
zu − z r
: deflection of tyre
zs and zu
: velocity of sprung mass and unsprung mass respectively
zs and zu
: acceleration of sprung mass and unsprung mass respectively
Active suspension system for a quarter car model can be constructed by adding an actuator parallel to spring and dampe. Figure 3.2 shows a schematic of a quarter car vehicle active suspension system.
Zs
Sprung Mass Ms
Ks
fa Bs Unsprung Mass Mu
Zu
Kt Zr road profile
Figure 3.2: Quarter car vehicle active suspension
The equations of motion for an active system are as follows:
ms z s = − k s ( zs − zu ) − bs ( zs − zu ) + f a
mu zu = k s ( z s − zu ) + bs ( zs − zu ) − kt ( zu − zr ) − f a where fa
: actuator force
Eq.(3.2)
26 Some assumptions are made in the process of modeling the active suspension system. The assumptions are: i.
the behaviour of the vehicle can be represented accurately by a quarter car model.
ii.
the suspension spring stiffness and tyre stiffness are linear in their operation ranges and tyre does not leave the ground. The displacements of both the body and tyre can be measured from the static equilibrium point.
iii.
3.3
The actuator is assumed to be linear with a constant gain.
Disturbance Models
There are three types of disturbances introduced to the vehicle suspension system in this study. They are the step input, bump and hole, and sinusoidal disturbance. Both bump and hole and sinusoidal are called the road disturbances which represent the irregular road profile.
Figures 3.3 (a), (b) and (c) show the disturbances, step input, bump and hole and sinusoidal respectively. The bump followed by a hole disturbance model is adapted from the study by Roh and Park in [16] and the sinusoidal road input is adapted from the work by Roukieh and Titli [17].
27
Figure 3.3 (a): Step input
Figure 3.3 (b): Bump and hole
28
Figure 3.3 (c): Sinusoidal
3.4
Passive Suspension System Model
The suspension system Simulink model is started basically with developing the passive suspension system of a quarter car model. The dynamical system is separated into two systems as the suspension system involves two degrees of freedoms. This passive suspension model was modeled in Simulink form as shown in Figure 3.4. This model was built based on the equation (3.1). There is an open loop system with no feedback element for appropriate adjustment of parameters.
29
Clock zr Road profile
zsdot
zsddot
k2 kt
zuddot 1 zudot 1 1/m2 s s
zu
k1 ks
mu
1/m1
1 s
1 s
zs XY Graph
ms
du/dt b1 Derivative bs
Figure 3.4: Simulink model of passive suspension system
3.5
Active Suspension System Model
Active suspension system requires an actuator force to provide a better ride and handling than the passive suspension system. The actuator force, Fa is an additional input to the suspension system model. The model in Simulink was built based on the equation (3.2) and shown in Figure 3.5. The actuator force is controlled by the PID controller which involves a feedback loop.
30
zr Road disturbance kt
k2 Clock
PID
-K1/m2
ref
PID Controller
actuator
1 s
1 s
k1
1/m1
zu
Derivative
1 s
zs XY Graph
ks
ms
mu
du/dt
1 s
b1 bs
Figure 3.5: Simulink model of active suspension system
3.5.1 Active Suspension System Model with AFC-CA Strategy
Instead of using only PID controller, active suspension system in Simulink model was further develop by introduced active force control with crude approximation (AFC-CA) in the system. This model is shown in Figure 3.6. The AFC-CA control Simulink blocks include the estimated mass gain, parameter 1/Ka gain and the percentage of AFC application gain. The input to the AFC control is the sprung mass acceleration and the output is summed with the PID controller output before multiply with the actuator gain which finally results the generated actuator force. Crude approximation method is used to estimated the estimated mass in the AFC.
31
zr Road disturbance kt
k2 Clock
PID
-K1/m2
ref
PID Controller
actuator
1 s
1 s
k1
1/m1
zu
1 s
1 s
zs XY Graph
ks
ms
mu 1
du/dt -K-
Derivative
b1 bs
-KMe
Figure 3.6: Simulink model of active suspension system with AFC-CA
3.5.2 Active Suspension System Model with AFC-ILM
To estimate the estimated mass for AFC, systematic method such as intelligent method is appropriate to use rather than try and error. One of the intelligent method is iterative learning method (ILM). This type of method applied with AFC can be modelled as shown in Figure 3.7 .
32
zr Road disturbance kt
k2 Clock
PID
-K-
1 s
1/m2 ref
PID Control ler
actuator
1 s
k1
1 s
1/m1
zu
1 s
zs XY Graph
ks
ms
mu 1
du/dt -K-
Derivative
b1 bs
Product
In1 Out1
y(n)=Cx(n)+Du(n) x(n+1)=Ax(n)+Bu(n)
Subsystem
Discrete State-Space1
Figure 3.7: Simulink model of active suspension system with AFC-ILM
Subsytem for iterative learning method is shown in Figure 3.8.
IM 1
IM(uk)
Me(u k+1) Add du/dt Derivative
k
k
A
B
1 TEk
Figure 3.8: Subsystem of iterative learning method in AFC
33 3.6
Modelling and Simulation Parameters
The suspension parameters used in this study are adopted from the previous study [15]. The detail of suspension model parameters are shown in Table 3.1 and the simulation parameters are shown in Table 3.2.
Table 3.1: Parameters for suspension model. Parameters
Value
Sprung mass ( ms )
170 kg
Unsprung mass ( mu )
25 kg
Spring stiffness ( ks )
10,520 N/m
Damping coefficient ( bs )
1,130 Ns/m
Tyre stiffness ( kt )
86,240 N/m
Table 3.2: Simulation parameters Parameters
Value
Solver
Ode45 (Dormand Prince)
Type
Variable-step
Simulation time
10 s
Minimum step size
Auto
Maximum step size
Auto
Initial step size
Auto
Relative tolerance
1e3
Absolute tolerance
Auto
Zero crossing control
use local setting
34 3.7
Conclusion
The mathematical equations of vehicle suspension system are derived using quarter car model based on Newtonian mechanics. Then, the Simulink models for passive and active suspension system were constructed. The disturbances also modelled in the Simulink. The active suspension control systems in particular were fully modelled complete with the control scheme with intelligent element to be simulated to observe their responses. The simulation results for all models are presented in the next chapter.
CHAPTER 4
SIMULATION RESULTS
4.1
Introduction
This chapter presents the simulated suspension responses results for all suspension systems that are described in the previous chapter. The main concern of the simulated suspension system responses results is the sprung mass displacement. Comparisons of the results between types of the suspension system, different type of disturbances and different type of control system are also discussed.
4.2
Passive Suspension
Figure 4.1 (a) and (b) show the response of passive suspension system to the step and sinusoidal inputs respectively. Response shown for the step input is not stable and need some time to settle down while under sinusoidal disturbance the passive suspension could not adapt to the force given. This causes the sprung mass displacement to occur for a long period of time.
36
Body Displacement 1.8 1.6
Displacement (cm)
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.1 (a): Passive suspension response to step input disturbance
Body Displacement 1.5
Displacement (cm)
1
0.5
0
-0.5
-1
-1.5
0
1
2
3
4
5 Time(s)
6
7
8
9
Figure 4.1 (b): Passive suspension response to sinusoidal disturbance
10
37 4.3
Active Suspension
Figure 4.2 (a) and (b) show the response given by active suspension to the step input and sinusoidal respectively. PID controller is used in this suspension and it is a close loop system. PID is tuned optimisely so that the response for the step input disturbance is good. However, for sinusoidal disturbance the response is not good and not much different with the passive suspension. PID gain used are as follows; Kp = 12, Ki = 5 and Kd = 4. These values are remain for the following sub chapter 4.4 and 4.5 to observe their response.
Body Displacement 1.4
1.2
Displacement (cm)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.2 (a): Active suspension response to step input disturbance
38
Body Displacement 1.5
Displacement (cm)
1
0.5
0
-0.5
-1
-1.5
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.2 (b): Active suspension response to sinusoidal disturbance
4.4
Active Suspension with AFC-CA
Figure 4.3 (a) and (b) show the response given by active suspension with AFC strategy and crude approximation method to the step input and sinusoidal respectively. Both response, under step input and sinusoidal disturbance is much better compare to PID controller only. AFC gives a good result although disturbance is change. Estimated mass used in this simulation is 300 kg.
39
Body Displacement 1.4
1.2
Displacement (cm)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.3 (a): AFC-CA suspension response to step input disturbance
Body Displacement 1.4
1.2
Displacement (cm)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.3 (b): AFC-CA suspension response to sinusoidal disturbance
40 4.5
Active Suspension with AFC-ILM
Figure 4.4 (a) and (b) show the response of active suspension with AFC strategy and iterative learning method to the step input and sinusoidal disturbance respectively. The response given for both disturbance also as good as AFC-CA suspension. This condition shows that the active suspension system with AFC strategy still gives a good response although the disturbance is change. In other words the active suspension with AFC is not affected by the changing of the disturbance. Value of learning parameter A is set to 4 and B = 5. Initial condition used is 200.
Body Displacemnt 5 4
Displacement (cm)
3 2 1 0 -1 -2 -3
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.4 (a): AFC-ILM suspension response to step input disturbance
41
Body Displacement 5 4
Displacement (cm)
3 2 1 0 -1 -2 -3
0
1
2
3
4
5 Time(s)
6
7
8
9
10
Figure 4.4 (b): AFC-ILM suspension response to sinusoidal disturbance
4.6
Conclusion
From the results it is proven that by using AFC, active suspension will response much much better than without AFC. Passive suspension is the weakest suspension to absorb any disturbance exerted to the system. Active suspension with PID controller can give good performance if we can tune the PID controller gain optimally. But when there is changes in the disturbances, PID controller is not capable to compensate for that disturbance.
Active suspension with AFC strategy is proven not affected by the changing of the disturbances. This means with AFC the high robust of suspension system can be achieved. The system will remain stable and effective even in the presence of known or unknown disturbance.
CHAPTER 5
EXPERIMENTAL SET-UP
5.1
Introduction
This chapter presents about the experimental work that was done in this project. Experimental rig was developed using MATLAB, Simulink and Real-Time Workshop after which a number of experiments were carried out.
This project used existing rig that was developed by the Intelligent Active Force Control Research Group (IAFCRG). The quarter car rig was developed based on the modified Perodua Kelisa suspension system. The details of the experimental set-up will describe in this chapter.
5.2
Simulink Model in Real-Time Workshop (RTW)
Simulink model with Real-Time Workshop (RTW) developed in MATLAB Software. This is the important element in the experiment because the RTW has an
43 ability to communicate with the outside world (suspension rig in this case) via an interface card such as data acquisition system (DAS). DAS 1602 card is used in this experiment as an interface card. With an aid of Simulink model in RTW and DAS 1602 card, the control of software and hardware of the rig is made possible through the ‘hardware-in-the-loop’ concept.
Figure 5.1 shows the Simulink model with RTW that used in this experiment. This model can be used for PID only control and also PID and AFC with iterative learning method (AFC-ILM). A switch that is inserted into the middle of the model will switch the system from the pure PID controller to the AFC-ILM control scheme. Figure 5.2 shows the Simulink model with RTW for the physical active suspension system.
body acc
tyre deflection
6.5
PID
disturbance
time
u-200
Active Suspension
susp deflection
force
tyre acc
body pos
Iterative Learning-AFC
Figure 5.1: Simulink model with RTW related to PID and AFC-ILM control
44
7
body position
body pos
1
body acceleration
body acceleration
body accelerometer
2
ty re def lection
tyre deflection ty re acc
6 tyre accelerometer
tyre acc
disturbance
3 disturbance
Out2
1
to actuator
desired press
to actuator
disturbance lvdt bddispl
pneumatic actuator
Out1
U( : )
u
4
susp def lc
bddispl.mat
susp deflc susp deflection laser lvdt
5
f orce
force pressure1
force / pressure sensor -K-
|u| Abs
AREA
Figure 5.2: Active suspension Simulink model in RTW
Figures 5.3 to 5.8 show the subsystem models of the pneumatic actuator, body acceleration, tyre accleration, disturbance model, suspension deflection and force tracking model respectively.
actuator
1
-K-
f(u)
|u|
u
Bad Link
to actuator butter f(u) desired pressure1 U( : )
f(u)
1 desired press
Figure 5.3: Pneumatic actuator subsystem
45
butter
butter
1 s
1 s
1 body position
bacc
bpos
bacc.mat
bpos.mat
butter Bad Link
f(u)
U( : )
u
@1
2 body acceleration
Figure 5.4: Body acceleration subsystem
tdef acc
tdef.mat
butter Bad Link
butter f(u)
U( : )
u
butter
1 s
1 s
1 tyre deflection
@3 tacc
tacc.mat
2 tyre acc
Figure 5.5: Tyre acceleration subsystem
distr
distr.mat butter Bad Link
-1
f(u)
U( : )
f(u)
1 disturbance
@4 2 Out2
Figure 5.6: Disturbance subsystem
distubance
46
U( : )
2
u
susp deflc 1
susdef
Out1 susdef.mat
butter Bad Link
-1
f(u) sus deflc
@7
Figure 5.7: Suspension deflection subsystem
U( : )
u
press
butter Bad Link
1 @8
f(u)
press.mat pressure
2 pressure1
-K-
1 force
AREA force1 U( : )
u
force
force.mat
Figure 5.8: Force tracking subsystem.
Figure 5.9 shows the most important element in the control system in the experiment. That is active force control with iterative learning method (AFC-ILM) simulink model.
47
U( : )
u
press
butter Bad Link
1 @8
f(u)
press.mat pressure
2 pressure1
-K-
1 force
AREA force1 U( : )
u
force
force.mat
Figure 5.9: AFC with ILM subsystem
5.3
Experimental Set-up
Figure 5.10 shows a photograph of an actual rig of active suspension system. The schematic of the experimental set-up is shown in Figure 5.11.
Physical sensors required for input/output (I/O) signal were connected to a PC-based data acquisition and control system using Matlab, Simulink and RealTime Workshop (RTW) that essentially constitute a hardware in the loop configuration, implying that the simulation can be effectively converted to the equivalent practical scheme without much fuss. A 100 Hz sampling frequency was used in conjunction with a data acquisition card (DAS 1602) that is fitted into one of the expansion slots of the personal computer (PC). Appropriate signals are processed using the analoque-to-digital converter (ADC) and digital-to-analoque converter (DCA) channels which are already embedded in the DAS card.
48
Figure 5.10: Photograph of the suspension system.
PC-based control MATLAB/CST/ Simulink/RTW DAS1602 I/O card
to pneumatic actuator
Suspension Test Rig
D/A
PID, AFC and ILM,
A/D from sensors (LVDTs, pressure sensor & accelerometers)
Programmable Logic Controller (PLC)
Disturbances Figure 5.11: The schematic of the experimental set-up.
49 Accelerometers were installed at the sprung and unsprung mass of the vehicle suspension system to measure body acceleration and tyre deflection. A laser sensor was placed in the between of the sprung and unsprung mass to measure suspension deflection. A linear variable differential transformer (LVDT) was used to measure the vertical displacement of the road profile or disturbance. The disturbances were used in this experiment was generated by a specially design pneumatic system control by a programmable logic control (PLC).
The experimental set-up in this project is a mechatronics system. It is because it involved an integration of the mechanical parts, electric/electronics devices, and computer control to make the rig function.
5.3.1 Mechanical System
The mechanical system of the experimental set-up consists of the suspension system itself as shown in Figure 5.10.
5.3.2 Electrical/Electronic Device
The electric/electronics devices were used in the experiment basically consist of the sensors. Four types of sensors were used in the set-up, namely; i.
accelerometer
ii.
laser sensors
iii.
linear variable differential transformer (LVDT)
iv.
pressure sensor
50 The location or position where all the sensors were placed can be seen in Figures 5.12 to 5.15.
Accelerometer
Figure 5.12: Accelerometer to measure body acceleration.
Laser sensor
Figure 5.13: Laser sensor to measure suspension deflection
51
Accelerometer
LVDT
Figure 5.14: LVDT to measure disturbance.
Pressure sensor
Figure 5.15: Pressure sensor to measure actuator force.
52 All the signals from the sensors will be sent to the signal conditioners and driver circuits. The circuits will process the signals to produce suitable signals to the DAS Card.
5.3.3 Computer Control
The experimental set-up used a Pentium III computer as the main controller with the software MATLAB/Simulink and RTW facility constituting the PC based digital control. The DAS 1602 card is interfaced to the computer where the input and output devices (actuators and sensors) were connected to the controller. Figure 5.16 shows the computer control system while Figure 5.17 shows the DAS 1602 interface card used in this experiment.
Figure 5.16: A Computer set as the main controller
53
Figure 5.17: DAS 1602 interface card slotted in the CPU.
5.4
Parameters for Experiments
Table 5.1 shows the suspension parameters and pneumatic actuator parameters that have been used in experiment.
Table 5.1: Suspension and pneumatic actuator parameters. Parameters
Value
Sprung mass ( ms )
170 kg
Unsprung mass ( mu )
25 kg
Spring stiffness ( ks )
10520 N/m
Damping coefficient ( bs )
1130 Ns/m
Tyre stiffness ( kt )
86240 N/m
Stroke length
116 mm
Diameter bore
40 mm
Ram area
0.0076 mm2
54 5.5
Conclusion
The Simulink model with RTW was successfully developed. The details of the model are explained and all the subsystem models were clearly shown in this chapter. Then, this Simulink model was integrated to the experimental rig constitutes a full experimental set-up. A number of experiments were carried out. The results obtained will be discussed in the next chapter.
CHAPTER 6
EXPERIMENTAL RESULTS AND DISCUSSION
6.1
Introduction
This chapter presents the results of the experiments that was carried out. Same with the simulation part, in this experiment the main concerned of the suspension system response result is the sprung mass or body displacement. Comparisons of the results between different type of control scheme, there are PID and AFC-ILM will be discussed in this section. The result for different type of disturbances applied to the system also will presented. The results that are discussed in this chapter were assume to give the best results obtained in the experiment using the chosen parameters. Other results for different parameter setting were attached in the appendix.
The results shown in this chapter are divided into two sections. For the first 200 second, the response belongs to PID controller. Then, for the next 200 seconds, AFC-ILM control scheme take over. By doing this, we can see directly the different responses (if any), displayed in single graph.
56 6.2
System Response Without Disturbance
Figure 6.1 shows the body displacement response of an active suspension system without apply any disturbance into it. PID gain were used in this experiment are, Kp = 35, Ki = 1.2 and Kd = 350. Learning parameter for the ILM are set as follows; B=15 and Initial Condition = 25 kg. The value of learning parameter A is set to vary. Results for the body acceleration, suspension deflection and tyre deflection for the same conditions are shown in Appendix B.
Body Displacement 5 A=10 A=20 A=50
4 3
Displacement (cm)
2 1 0 -1 -2 AFC-ILM
-3 -4 -5
PID 0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.1: Graph for body displacement response without disturbance
Figure 6.2 shows the close-up of body displacement response of an active suspension system without disturbance.
57
Body Displacement A=10 A=20 A=50
0.6
Displacement (cm)
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 50
60
70 Time(s)
80
90
100
Figure 6.2: The close-up of body displacement response without disturbance
For this conditions, the results show that the learning parameter A=50 gives the best results. However, there is no significant difference in result between pure PID and AFC-ILM control schemes. The result looks almost similar. This means that AFC-ILM control scheme was reached at the minimum level. Some tuning still has to be done to get the better result for the AFC scheme.
Figure 6.3 shows the body displacement response with the fixed value of A and varied value of B. The rest of the results for the variation of learning parameter B can be found in Appendix B. Figure 6.4 shows the close-up of of the Figure 6.3.
58
Body Displacement 5 B=15 B=20 B=50
4 3
Displacement (cm)
2 1 0 -1 -2 AFC-ILM
-3 PID
-4 -5
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.3: Body displacement response without disturbance for B vary
Body Displacement 2 B=15 B=20 B=50
1.5
Displacement (cm)
1 0.5 0 -0.5 -1 -1.5 -2
40
50
60
70 Time(s)
80
90
100
Figure 6.4: Close-up body displacement response without disturbance for B vary
59 6.3
System Response with the Sinusoidal Disturbance
Disturbances that applied to the active suspension system are step and sinusoidal. The disturbance is generated by a specially design pneumatic system controlled by PLC. Figure 6.5 shows the disturbance model and Figure 6.6 shows the body displacement response to the sinusoidal disturbance. Sinusoidal signal that gives to the system is high amplitude with high speed ( ≈ 2.8 Hz ). Figures 6.7 - 6.9 show the response of the body acceleration, suspension deflection and tyre deflection respectively to the sinusoidal disturbance.
Sinusoidal Disturbance 2.3 2.2
Amplitude (cm)
2.1 2 1.9 1.8 1.7 1.6 1.5 50
55
60
65
70
75 Time(s)
80
85
90
Figure 6.5: Disturbance model type sinusoidal
95
100
60
Body Displacement 5 4 3
Displacement (cm)
2 1 0 -1 -2 AFC-ILM
-3 PID
-4 -5
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.6: Body displacement response with the sinusoidal disturbance
Body Acceleration 5
Acceleration (m/s 2)
0
-5
AFC-ILM -10 PID
-15
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.7: Body acceleration response with the sinusoidal disturbance
61
Suspension Deflection 8 7 6
Deflection (cm)
5 4 3 2 1 AFC-ILM 0 PID
-1 -2
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.8: Suspension deflection response with the sinusoidal disturbance
Tyre Deflection 2 1.5
Deflection (cm)
1 0.5 0 -0.5 -1
AFC-ILM PID
-1.5 -2
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.9: Tyre deflection response with the sinusoidal disturbance
62 6.4
System Response with the Step Disturbance
The disturbance type step also generated by a specially design pneumatic system controlled by PLC. Figure 6.10 shows the disturbance model of the step. The shape of step is not so good due to some leaking at the pneumatic system. It caused the pneumatic system cannot hold the load for a period of time to form a good step. However the disturbance produce still can be used as long as we can put some interruption to the system and observe the response. All the results observed are shown in the Figures 6.11-6.14.
Step Disturbance 8 7 6
Step (cm)
5 4 3 2 1 0 10
20
30
40 Time(s)
50
Figure 6.10: Disturbance model type step
60
70
63
Body displacement 4 3
Displacemnt (cm)
2 1 0 -1 -2 AFC-ILM -3 -4
PID
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.11: Body displacement response with the step disturbance
Body Acceleration 5
0
Acceleration (m/s 2)
-5
-10
-15
-20 AFC-ILM -25
-30
PID
0
50
100
150
200 Time(s)
250
300
350
Figure 6.12: Body acceleration response with the step disturbance
400
64
Suspension Deflection 8 7
Deflection (cm)
6 5 4 3 2
AFC-ILM PID
1 0
0
50
100
150
200 Time(s)
250
300
350
400
Figure 6.13: Suspension deflection response with the step disturbance
Tyre Deflection 2 1.5
Deflection (cm)
1 0.5 0 -0.5 -1
AFC-ILM PID
-1.5 -2
0
50
100
150
200 Time(s)
250
300
350
Figure 6.14: Tyre deflection response with the step disturbance
400
65
The results for other conditions, i.e different value of parameter A and B, different values of Initial Condition and the different type of disturbance, please refer to Appendix C.
6.5
Conclusion
In order to get the best tune for the learning parameter, A and B, the experiments were carried out without apply any disturbance to the suspension system. The system with the set learning parameter then was applied the disturbances. The result show that the active suspension system with pure PID controller gives almost similar response with the AFC-ILM control scheme. AFCILM suppose to give better response than pure PID. It means that AFC-ILM control scheme was reached at the minimum level. Some tuning still has to be done to get the better result for the AFC scheme but due to time constraint existing learning parameters are remained for this project.
CHAPTER 7
CONCLUSION AND RECOMMENDATION
7.1
Conclusion
The implementation of the active force control (AFC) to the vehicle suspension system has been successfully done in simulation study and in experimental work. In simulation study the result shows that the use of AFC make the system robust. It is because AFC can compensate any internal and external disturbances that presence in the suspension system. In experimental work, it should show the same result. However due to highly skill needed to tune the learning parameter in the ILM to estimate initial mass for AFC, the result obtained is just same with the pure PID controller.
The study in simulation demonstrate that AFC-CA and AFC-ILM give better performance compare to pure PID controller. The most important thing in AFC is to estimate the initial mass. If we get the accurate approximate initial mass, AFC will give a better performance. In estimating the initial mass the method use is crude approximation and iterative learning. Crude approximation method is easier than iterative learning as we just have to directly change the value of initial mass. This method however will take long time to get the right value of initial mass. Iterative learning method is more intelligent to estimate the initial mass value as it will iterate
67 repetitively by decrease the error until it get the right value. But the problem in this method is to tune the learning parameter.
Simulation study shows that by using AFC control scheme, the performance of the system (active suspension in this case) will improve tremendously. AFC able to compensate the presence of the known or unknown disturbances.
In experimental works, the experiment was run using the active suspension rig. Two type of control schemes were used, those are PID and AFC-ILM and the results from both were compared. From the experimental work, the results show that the performance of the suspension system for both control scheme almost similar. The theory says that AFC is better than PID. This condition was happen due to learning parameter tuning for ILM is still not satisfy. Fine tune the learning parameter to the right value will change to the better result.
7.2
Recommendation for Future Works
There are few number of future works could be considered as an extension to the present study. They are as follows; i)
consider the use of the percentage AFC to the system.
ii)
the use of self tuning method to estimate the estimated mass in AFC.
iii)
study the effects to the performance of suspension system by increase the sprung mass load.
68
REFERENCES
[1]
P.G. Wright. (1984). The Application of Active Suspension to High Performance Road Vehicles, Microprocessors in Fluid Engineering IMechE Conference Publications.
[2]
http://www.lanciamontecarlo.net/Scorpion/Technical_Suspension.html
[3]
D. A. Crolla. (1988). Theoretical Comparisons of Various Active Suspension Systems in Terms of Performance and Power Requirements. in “Advanced Suspensions”, Suffolk : Mechanical Engineering Publications Limited. pp 1 – 9.
[4]
Alleyne, A., Neuhaus, P.D., Hedrick, J.K (1993). Application of Non Linear Control Theory to Electronically Controlled Suspension, Vehicle System Dynamics Vol. 22, No. 5-6, P.309-320.
[5]
Gopalasamy, S,. et. al.. (1997). Model Predictive Control For Active Suspension. Controller Design and Experimentally Study. Trans. of ASME, Journal of Dynamic Systems and Control, Vol. 61, pp. 725-733.
[6]
Hewit, J.R., (1998). Advances in Teleoperations, Lecture note on Control Aspects, CISM.
[7]
Mailah, M. and Yong, M.O., (2001). Intelligent Adaptive Active Force Control of a Robot Arm With Embedded Iterative Learning Algorithms, Jurnal Teknologi, UTM, No.35(A), pp. 85-98.
69 [ 8]
Musa Mailah. (1999). A Simulation Study on the Intelligent Active Force Control of A Robot Arm Using Neural Network, Jurnal Teknologi (D), Universiti Teknologi Malaysia. pp 55 – 78.
[9]
Arimoto, S., Kawamura, S., and Miyazaki, F. (1986). Convergence, Stability and Robustness of Learning Control Schemes for Robot Manipulators, Recent Trends in Robotics: Modelling, Control and Education, ed. by Jamshidi M., Luh L.Y.S., and Shahinpoor M. 307 – 316.
[10]
Zhang, Y. (2003). A hybrid adaptive and robust control methodology with application to active vibration isolation, University of Illinois, UrbanaChampaign, Ph.D. Thesis.
[11]
Baillie, A.S. (1999). Development of a fuzzy logic controller for an active suspension of an off-road vehicle fitted with terrain preview, Royal Military Collage of Canada, Kingstone, Canada, Ph.D. Thesis.
[12]
D’Amato, F. J. and Viassolo, D. E. (2000). Fuzzy Control for Active Suspensions, Mechatronics, 10: 897-920.
[13]
Omar, Z. (2002). Modelling and Simulation of an Active Suspension System Using Active Force Control Strategy, MSc. Project Report, Universiti Teknologi Malaysia.
[14]
Mailah M., Priyandoko G. (2005). Simulation of a Suspension System with Adaptive Fuzzy Active Force Control, International Journal of Simulation Modelling, Vol.6 No.1, pp 25-36.
[15]
G. Priyandoko, et al. (2007). Skyhook Adaptive Neuro Active Force Control for an Active Suspension System, Procs. Of CIM07, Johor Persada Convention Centre.
70 [16]
Hyoun-Surk Roh and Youngjin Park. (1999). Preview Control of Active Vehicle Suspension Based on a State and Input Estimator, in Ronald K. Jurgen (Ed.).“Electronic Steering and Suspension Systems.” Warrendale : Society of Automotive Engineers, Inc. pp 277 – 284.
[17]
S. Roukieh and A. Titli. (1992). On the Model-Based Design of Semi-Active and Active Suspension for Private Cars, in “Total Vehicle Dynamics.” London : Mechanical Engineering Publications Limited. pp 305 – 318.
71
APPENDIX A
Simulation Result for Various Conditions
a) Passive suspension response for different value of step input Response for different step input for passive suspension 18 1.0 2.0 10.0
16
step input value (cm)
14 12 10 8 6 4 2 0
0
1
2
3
4
5 time (s)
6
7
8
9
10
b) Active suspension response for different value of proportional gain (kp) zs response with PID controller (various kp, ki=5,kd=4) 3 2.5 2
Amplitude
1.5 1 0.5 0 kp=12 -0.5
kp=20
-1
kp=30
-1.5
0
2
4
6 time, t
8
10
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APPENDIX B
Experimental Results for Various Learning Parameter
The graphs show the response and their close-up for body displacement, body acceleration, suspension deflection and tyre deflection respectively. Body Displacement 5 A=10 A=20 A=50
4 3
Displacement (cm)
2 1 0 -1 -2 -3 -4 -5
0
50
100
150
200 Time(s)
250
300
350
400
Body Displacement A=10 A=20 A=50
0.6
Displacement (cm)
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 50
60
70 Time(s)
80
90
100
73
Body Acceleration 10 5
Acceleration (m/s 2)
0 -5 -10 -15 A=10 A=20 A=50
-20 -25 -30
0
50
100
150
200 Time(s)
250
300
350
400
Body Acceleration 6
2
Acceleration (m/s )
5
4
3
2 A=10 A=20 A=50
1
0
0
10
20
30
40
50 Time(s)
60
70
80
90
100
74
Suspension Deflection 8
6
Deflection (cm)
4
2
0
-2 A=10 A=20 A=50
-4
-6
0
50
100
150
200 Time(s)
250
300
350
400
Suspension Deflection 7
6
Deflection (cm)
5
4
3
2 A=10 A=20 A=50
1
0
0
10
20
30
40
50 Time(s)
60
70
80
90
100
75
Tyre Deflection 2 A=10 A=20 A=50
1.5
Deflection (cm)
1 0.5 0 -0.5 -1 -1.5 -2
0
50
100
150
200 Time(s)
250
300
350
400
Tyre Deflection 1.5 A=10 A=20 A=50
Deflection (cm)
1
0.5
0
-0.5
-1
0
10
20
30
40
50 Time(s)
60
70
80
90
100
76
Body Displacement 5 B=15 B=20 B=50
4 3
Displacement (cm)
2 1 0 -1 -2 -3 -4 -5
0
50
100
150
200 Time(s)
250
300
350
400
Body Displacement 2 B=15 B=20 B=50
1.5
Displacement (cm)
1 0.5 0 -0.5 -1 -1.5 -2
40
50
60
70 Time(s)
80
90
100
77
Body Acceleration 10 5
Acceleration (m/s2)
0 -5 -10 -15 -20 B=15 B=20 B=50
-25 -30
0
50
100
150
200 Time(s)
250
300
350
400
Body Acceleration 6 5 4
Acceleration (m/s2)
3 2 1 0 -1 -2 B=15 B=20 B=50
-3 -4 -5
0
10
20
30
40 Time(s)
50
60
70
80
78
Suspension Deflection 8
6
Deflection (cm)
4
2
0
-2 B=15 B=20 B=50
-4
-6
0
50
100
150
200 Time(s)
250
300
350
400
Suspension Deflection 7 6 5
Deflection (cm)
4 3 2 1 0 B=15 B=20 B=50
-1 -2 10
20
30
40
50
60 70 Time(s)
80
90
100
110
120
79
Tyre Deflection 2 B=15 B=20 B=50
1.5
Deflection (cm)
1 0.5 0 -0.5 -1 -1.5 -2
0
50
100
150
200 Time(s)
250
300
350
400
Tyre Deflection 1 B=15 B=20 B=50
0.8 0.6
Deflection (cm)
0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
0
10
20
30
40
50 Time(s)
60
70
80
90
100
80
APPENDIX C
Experimental Results for Different Conditions
Data 1 : A=100, B=90, IC=250 Data 2 : A=150, B=200, IC=500 Disturbance type : High Sin and high speed ( ≈ 1.8Hz)
Body displacement 5 Data1 Data2
4 3
Displacemnt (cm)
2 1 0 -1 -2 AFC-ILM -3 PID
-4 -5
0
50
100
150
200 Time(s)
250
300
350
400
81
Body Acceleration 5 Data1 Data2
4 3
Acceleration (m/s 2)
2 1 0 -1 -2 AFC-ILM -3 PID
-4 -5
0
50
100
150
200 Time(s)
250
300
350
400
Suspension Deflection 8 Data1 Data2
7
Deflection (cm)
6 5 4 3 2
AFC-ILM PID
1 0
0
50
100
150
200 Time(s)
250
300
350
400
82
Tyre Deflection 5 Data1 Data2
4 3
Deflection (cm)
2 1 0 -1 -2 AFC-ILM -3 PID
-4 -5
0
50
100
150
200 Time(s)
250
300
350
400
83
APPENDIX D
The Sketch of the Experimental Rig
Load
Body Pneumatic actuator Tyre
Motor
Pneumatic to generate disturbance
84
APPENDIX E
The LVDT
The LVDT used in this project is AML/IEU+/-75mm-X-10.
85
86
APPENDIX F
The Pressure Sensor
The pressure sensor used in this project is model DP2-22.
87
88
APPENDIX G
The Data Acquisition System Card DAS 1602
89
90
APPENDIX H
The Accelerometer
The accelerometer used in this project is ADXL-105EM-1.
91
92
93
94
95
96
97
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