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MODELLING MAGNETO-RHEOLOGICAL DAMPER USING RADIAL BASIS
FUNCTION NEURAL NETWORK
MOHD FIKRI BIN ARIFIN
Thesis submitted in fulfillment of the requirements
for the award of the degree of
Bachelor of Mechanical Engineering
Faculty of Mechanical Engineering
UNIVERSITI MALAYSIA PAHANG
JUNE 2013
vii
ABSTRACT
This is a study on modeling the MR damper using RBF. MR damper can be
simplify as a damper that using MR fluids. MR fluid contains magnetic particles which
will react to current flow when power is supplied. The viscosity of the fluid depends on
the current flow. The stiffness of the damper depends on the fluids. This modeling is to
achieve the similarity of the results of the experiment using proper machine and
apparatus and by using MATLAB software. The data that are obtained from the
experiment are used in the MATLAB software to generate graphs. The RBF equations
are used in the m-file to get the similarity as the graph from experiment. Comparisons
between the graphs are decided by inspection and the most accurate, by using the
RMSE graph. The input in m-file is adjusted again and again to get the smallest RMSE
as possible.
viii
ABSTRAK
Ini adalah satu kajian ke atas model peredam MR menggunakan RBF. Peredam
MR dirigkaskan sebagai peredam yang menggunakan cecair MR. Cecair MR
mengandungi zarah-zarah magnetik yang akan bertindak balas ke atas arus elektrik
apabila kuasa dibekalkan. Kelikatan cecair bergantung kepada bekalan kuasa.
Kekukuhan peredam bergantung kepada cecair. Kemodelan ini adalah untuk mencari
persamaan antara keputusan eksperimen yang menggunakan mesin dan peralatan yang
betul dan dengan menggunakan perisian MATLAB. Data yang diperolehi dari
eksperimen akan digunakan didalam perisian MATLAB untuk menjana graf.
Persamaan RBF digunakan didalam m-file untuk mendapatkan persamaan antara graf
dari eksperimen. Perbandigan antara graf diputuskan dari pemerhatian dan yang paling
tepat adalah dari graf RMSE. Input didalam m-file diselaraskan berulang kali untuk
mendapatkan nilai RMSE yang kecil yang mungkin.
ix
TABLE OF CONTENTS
TITLE Page
EXAMINER DECLARATION ii
SUPERVISOR DECLARATION iii
STUDENT DECLARATION iv
DEDICATION v
ACKNOWLEDGEMENTS vi
ABSTRACT vii
ABSTRAK viii
TABLE OF CONTENTS ix
LIST OF TABLES xiii
LIST OF FIGURES xiv
CHAPTER 1 INTRODUCTION
1.1 Introduction 1
1.2 Problem Statement 2
1.3 Objective of Project 2
1.4 Scope of Project 2
x
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction 3
2.2 Types of Damping System 6
2.3 Design of MR Damper 8
2.4 Radial Basis Function Network 9
CHAPTER 3 METHODOLOGY
3.1 Introduction 12
3.2 Flow Chart 12
3.2.1 Flow Chart of Experiment Setup 13
3.2.2 Flow Chart of Final Year Project 1 14
3.2.2 Flow Chart of Final Year Project 2 15
3.3 MR Damper Experiment Setup 16
3.4 MATLAB Software Setup 17
3.4.1 M-file Script 17
3.4.2 Simulink Diagram 19
3.4.3 Plotting Graphs 20
CHAPTER 4 RESULT AND DISCUSSION
4.1 Introduction 22
xi
4.2 Data Analysis 22
4.2.1 Actual MR Force and RBF Force Graph 23
4.2.2 Displacement Graph 23
4.2.3 Velocity Graph 24
4.2.4 Actual MR Force vs Displacement Graph 24
4.2.5 Displacement vs Actual MR Force Graph 25
4.2.6 Velocity vs Actual MR Force Graph 25
4.2.7 Displacement vs Actual MR Force and RBF Force Graph 26
4.2.8 Velocity vs Actual MR Force and RBF Force Graph 26
4.2.9 Actual MR Force Graph 27
4.2.10 RBF Force Graph 27
4.2.11 Root Mean Square Error (RMSE) 28
4.3 Results 28
4.3.1 Results for Non-current (0A) 29
4.3.2 Results for 0.5A 32
4.3.3 Results for 1.0A 35
4.3.4 Results for 1.5A 38
4.3.5 Resultsfor 2.0A 41
4.3.6 RMSE Calculation 43
CHAPTER 5 CONCLUSION AND RECOMMENDATIONS
5.1 Introduction 46
xii
5.2 Conclusion 46
5.3 Future Recommendations 47
REFERENCES 48
xiii
LIST OF TABLES
Table No. Title Page
4.1 RMSE Values of Five Currents 45
xiv
LIST OF FIGURES
Figure No. Title Page
Figure 2.1 MR Fluid When Power is Not Supply. 3
Figure 2.2 MR Fluid When Power is Supply. 4
Figure 2.3 MR Fluid in Squeeze Mode. 5
Figure 2.4 MR Fluid in Shear Mode. 5
Figure 2.5 MR Fluid in Valve Mode. 5
Figure 2.6 Passive Damping System 7
Figure 2.7 Semi-active Damping System 7
Figure 2.8 Active Damping System 7
Figure 2.9 Monotube MR Damper. 8
Figure 2.10 Twin Tube MR Damper. 8
Figure 2.11 Double-ended MR Damper 9
Figure 2.12 Example of RBF Structure. 9
Figure 2.13 Gaussian RBF 11
Figure 2.14 Multiquadratic RBF 11
Figure 3.1 Experiment Flow Chart 13
Figure 3.2 Flow Chart of Final Year Project 1 14
Figure 3.3 Flow Chart of Final Year Project 2 15
Figure 3.4 Equipment for Identification of MR Damper 16
Figure 3.5 MATLAB’s version. 17
Figure 3.6 Simulink Model. 19
xv
Figure 3.7 Sample of Generated Graph. 20
Figure 3.8 MATLAB Command Menu. 21
Figure 4.1 Actual MR Force and RBF Force Graphs 23
Figure 4.2 Displacement Graph. 23
Figure 4.3 Velocity Graph. 24
Figure 4.4 Actual MR Force vs Displacement Graph. 24
Figure 4.5 Displacement vs Actual MR Force Graph. 25
Figure 4.6 Velocity vs Actual MR Force Graph. 25
Figure 4.7 Displacement vs Actual MR Force and RBF Force Graph. 26
Figure 4.8 Velocity vs Actual MR Force and RBF Force Graph. 26
Figure 4.9 Actual MR Force Graph. 27
Figure 4.10 RBF Force Graph. 27
Figure 4.11 Force Graph (RMSE). 28
Figure 4.12 Displacement Graph. 29
Figure 4.13 Velocity Graph. 29
Figure 4.14 Actual MR Force Graph 30
Figure 4.15 RBF Force Graph. 30
Figure 4.16 Actual MR & RBF Force Graph. 31
Figure 4.17 Force (RMSE) Graph. 31
Figure 4.18 Displacement Graph. 32
Figure 4.19 Velocity Graph. 32
Figure 4.20 Actual MR Force Graph. 33
xvi
Figure 4.21 RBF force Graph. 33
Figure 4.22 Actual MR & RBF Force Graph. 34
Figure 4.23 Force (RMSE) Graph. 34
Figure 4.24 Displacement Graph. 35
Figure 4.25 Velocity Graph. 35
Figure 4.26 Actual MR Force Graph. 36
Figure 4.27 RBF Force Graph. 36
Figure 4.28 Actual MR & RBF Force Graph. 37
Figure 4.29 Force (RMSE) Graph. 37
Figure 4.30 Displacement Graph. 38
Figure 4.31 Velocity Graph. 38
Figure 4.32 Actual MR Force Graph. 39
Figure 4.33 RBF Force Graph. 39
Figure 4.34 Actual MR & RBF Force Graph. 40
Figure 4.35 Force (RMSE) Graph. 40
Figure 4.36 Displacement Graph. 41
Figure 4.37 Velocity Graph. 41
Figure 4.38 Actual MR Force Graph. 42
Figure 4.39 RBF Force Graph. 42
Figure 4.40 Actual MR & RBF Force Graph. 43
Figure 4.41 Force (RMSE) Graph. 43
xvii
Figure 4.42 Example of File Listed. 44
Figure 4.43 Listed Values. 44
1
CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION
In vehicles suspension system, there are many differences of damping system or
suspension system between ordinary cars’, four wheel drive vehicles’, luxury cars’ and
other land transports’ such as the spring’s stiffness, the fluids’ stiffness, and more.
Imagine that we can control the stiffness during our ride, it will be much more
comfortable than usual. One of the methods is by using the magneto-rheological
damper.
Magneto-rheological (MR) damper is a damper filled with MR fluids which can
simply know as fluid with magnetic particles. This MR fluid will increase its stiffness
when there is electrical field. The stiffness will increase as the current increase. MR
damper are not restricted just in vehicles’ suspension system but they are also used in
buildings as to stabilize them during earthquake.
MR damper is a semi-active control device and has been characterized by a set
of nonlinear differential equations which represent a model of the MR damper. By
using this mathematical model, the force of the MR damper is directly solved to a given
displacement and applied voltage. However, solving the non-linear equations
describing the performance of the MR damper may be difficult or time consuming to
predict a required voltage. Recently, the artificial neural network has been effectively
applied to model complex systems because of its great training process.
2
1.2 PROBLEM STATEMENT
The problem statements of this project are expressed as follows:
i) To use the MATLAB software for modeling.
ii) To get the similar result as an actual MR damper using Radial Basis Function
(RBF) method.
iii) The result errors must be small.
1.3 OBJECTIVE OF PROJECT
The objectives of this project are as follows:
i) To model MR damper using RBF method.
ii) To get the similar results as the actual MR damper.
iii) To get the small root mean square errors (RMSE).
1.4 SCOPE OF PROJECT
This project is using MATLAB software to create simulation for modeling the MR
damper with Radial Basis Function (RBF) and compared the results between the
theoretical and the experimental. Then, the graph behaviors between those two results
need to be analyzed whether they are similar or not and to check the RMSE by various
input.
3
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
This chapter will tell more details about Magneto Rheological (MR)
Fluids, the uses of MR fluids, types of damping system, design of MR damper.
Magneto-Rheological Fluid or MR fluid as stated by Spencer et. al
(1996) is composed of oil and varying percentage of iron particles that have
been coated with an anti-coagulant material. When the electricity is inactivated,
MR fluid acted like ordinary damper oil (Figure 2.1). When the power is
supplied, it will create a magnetic field, micron-size iron particles that are
dispersed throughout the fluid align themselves along magnetic flux lines
(Figure 2.2). Thus, this will increase the MR fluid’s viscosity. MR fluids are
effective to control vibrations.
Figure 2.1 : MR Fluid When Power is Not Supply.
4
Figure 2.2 : MR Fluid When Power is Supply.
MR fluid can be used in three different ways, all of which can be applied
to MR damper design depending on the damper’s intended use. These modes of
operation are referred to as squeeze mode, valve mode, and shear mode. A
device that uses squeeze mode has a thin film (on the order of 0.020 in.) of MR
fluid that is sandwiched between paramagnetic pole surfaces as shown in Figure
2.3. The MR fluid device is said to operate in shear mode when a thin layer (≈
0.005 to 0.015 in.) of MR fluid is sandwiched between two paramagnetic
moving surfaces. Shear mode (Figure 2.4) is useful primarily for dampers that
are not required to produce large forces and for clutches and brakes. The last
mode of MR damper operation, valve mode (Figure 2.5), is the most widely
used of the three modes. MR device is said to operate in valve mode when the
MR fluid is used to impede the flow of MR fluid from one reservoir to another.
(James, 2001)
5
Figure 2.3 : MR Fluid in Squeeze Mode.
Figure 2.4 : MR Fluid in Shear Mode.
Figure 2.5: MR Fluid in Valve Mode.
Source: James, 2001.
6
2.2 TYPES OF DAMPING SYSTEM
Ashfak et. al (2009) figured the passive suspension’s drawbacks can be
overcome by resorting to one of three techniques, adaptive, semi-active or fully
active suspension. An adaptive suspension utilizes a passive spring and an
adjustable damper with slow response to improve the control of ride and
handling. A semi-active suspension is similar, except that the adjustable damper
has fast response (about 10 milisecond) and the damping force is controlled in
real time. A fully active suspension replace the damper with a hydraulic actuator
which can achieve optimum vehicle control, but expensive. Vibration control is
becoming increasingly important as the design of mechanisms become more
and more precise and less tolerant to transient vibration. Active and semi-active
controls provide an important new tool for the control engineer. Transports,
buildings, and other have already been design using the active and semi-active
damping system.
To simplify, the passive damper system (Figure 2.6) is which the spring
is chose base of the vehicle’s weight and it using either gas or oit to control the
suspension movement. The semi-active (Figure 2.7) system is just like the
passive but the damper is controllable and using the MR fluid. On the other
hand, the active system (Figure 2.8) is using actuator instead of damper.
An actuator is a type of motor for moving or controlling a mechanism or system.
It is operated by a source of energy, usually in the form of an electric
current, hydraulic fluid pressure or pneumatic pressure, and converts that energy
into some kind of motion.
7
Figure 2.6 : Passive Damping System
Figure 2.7 : Semi-active Damping System
Figure 2.8 : Active Damping System
Source: Ashfak et. al, 2009.
8
2.3 DESIGN OF MR DAMPER
So far there are known three designs of MR damper. They are monotubeMR damper (Figure 2.9), twin tube MR damper (Figure 2.10) and double-endedMR damper (Figure 2.11). A monotube MR damper is one that has only onereservoir for the MR fluid and also has some way to allow for the change involume that results from piston rod movement. The twin tube MR damper isone that has two fluid reservoirs, one inside of the other. This inner housing isfilled with MR fluid so that no air pockets exist. The double-ended MR damperhas a piston rod of equal diameter protrudes from both ends of the damperhousing. (James, 2001).
Figure 2.9 : Monotube MR Damper.
Figure 2.10 : Twin Tube MR Damper.
9
Figure 2.11 : Double-ended MR Damper
Source: James, 2001.
2.4 RADIAL BASIS FUNCTION (RBF) NETWORK
Mark (1996) stated that RBF is a real valued function whose value
depends only on the distance from the origin. The basic architecture for a RBF
is a 3-layer network, as shown in Figure 2.12. This is becoming an increasingly
popular neural network with diverse applications and is probably the main rival
to the multi-layered perceptron. Much of the inspiration for RBF networks has
come from traditional statistical pattern classification techniques.
Figure 2.12 : Example of RBF Structure.
Source: Mark, 1996.
10
An RBF network is nonlinear if the basis functions can move or change
size or if there is more than one hidden layer. The single layer networks with
functions is focused on which are fixed in position and size. A nonlinear
optimisation is used but only for the regularisation parameters in ridge
regression section and the optimal subset of basis functions in forward selection
section. The kind of expensive nonlinear gradient descent algorithms is avoided
such as the conjugate gradient and variable metric methods that are employed in
explicitly nonlinear networks. Keep one foot firmly planted in the world of
linear algebra makes analysis easier and computations quicker.
Radial functions are special class of function. Their characteristic feature
is that their response decreases or increases monotonically with distance from a
central point The centre the distance scale and the precise shape of the radial
function are parameters of the model all xed if it is linear A typical radial
function is the Gaussian which in the case of a scalar input is:
ℎ( ) = exp(− ( ) ) (2.1)
Where h(x) is RBF function and x is the input. Its parameters are its
centre, c and its radius, r. Figure 2.13 and Figure 2.14 illustrates a Gaussian
RBF with centre, c = 0 and radius, r = 1. A Gaussian RBF monotonically
decreases with distance from the centre. In contrast a multiquadric RBF which
in the case of scalar input is monotonically increases with distance from
ℎ( ) = ( )(2.2)
the centre (see Figure 2.13), Gaussian like RBFs are local give a significant
response only in a neighbourhood near the centre and are more commonly
used than multiquadric type RBFs (Figure 2.14) which have a global
response They are also more biologically plausible because their response is
infinite. (Mark, 1996).
11
Figure 2.13 : Gaussian RBF
Figure 2.14 : Multiquadratic RBF
Source: Mark, 1996.
Displacement, cm
Displacement, cm
Forc
e, N
Forc
e, N
12
CHAPTER 3
METHODOLOGY
3.1 INTRODUCTION
This project needs to model the MR damper and get the similar result as an
actual MR damper. To do so, it requires modelling and simulating of block diagram by
using MATLAB software. There are three things that need to be considering which are
the inputs, the outputs and the error.
3.2 FLOW CHART
Flow chart can be considered important because it will guide to do the project
properly from the start till the end. The project starts with selecting the project title
which is “Modeling Magneto-Rheological Damper Using Radial Basis Function”. The
supervisor will give the introduction and discussing about the project. We need to use
MATLAB software in this project. Then we need to find the journals for literature
reviews and also to find suitable equation based on our method which is Radial Basis
Function (RBF).
After getting the result of the simulation, we need to discuss about it with the
supervisor so we can know what we are looking for. The process takes plenty of times
to get the best result. In Final Year Project 1 (FYP 1), we need to model the MR