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DESIGN AND MODELLING OF 6 DOF REVOLUTE ROBOT USING
FUZZY PID CONTROLLER
MOHD RADZI BIN TARMIZI
A project report submitted in partial
fulfillment of the requirement for the award of the
Degree of Master of Electrical Engineering
Faculty of Electrical & Electronic Engineering
Universiti Tun Hussein Onn Malaysia
JANUARI 2014
v
ABSTRACT
Designing a robot manipulator with great performance is one of the fields of interest
in the industry. This is due to the nonlinearities and input couplings presented in the
dynamics of the robot arm. This project report is concerned with the problems of
modelling and control of a 6 degree of freedom direct drive arm. The research work
was undertaken in the following five developmental stages; Firstly, the complete
mathematical model of a 6 DOF direct drive robot arm including the dynamics of the
brushless DC motors actuators in the state variable form is to be developed. In the
second stage, the state variable model is to be decomposed into an uncertain model.
Then, the Fuzzy PID Controller is applied to the robot arm. In the fourth stage, the
simulation is performed. This is done through the simulation on the digital computer
using MATLAB/SIMULINK as the platform. Lastly, the performance of Fuzzy PID
controller is to be compared with the conventional controller which is PID. The
simulation results show that the output performance of Fuzzy PID is greater than the
performance of conventional method of PID controller.
vi
ABSTRAK
Merekabentuk satu tangan robot yang mempunyai kebolehupayaan yang tinggi
merupakan satu bidang yang terpenting di industri. Ini adalah disebabkan oleh
ketaklelurusan dan gandingan masukan yang wujud di dalam dinamik lengan robot.
Laporan projek ini membincangkan mengenai masalah dalam permodelan dan
kawalan lengan robot yang mempunyai 6 darjah kebebasan. Robot tersebut berupaya
untuk membuat kerja dan aplikasi mengambil barang dan meletakkannya kembali.
Kajian ini melibatkan lima peringkat seperti berikut; Pertama, pembangunan model
matematik 6 DOF lengan robot pacuan terus yang lengkap merangkumi dinamik
pemacu motor DC tanpa berus dalam bentuk pembolehubah keadaan. Di peringkat
kedua, model pembolehubah keadaan akan dipisahkan ke model yang tidak tetap.
Kemudian, kawalan Fuzzy PID diguna pakai dalam lengan robot ini. Peringkat
kelima adalah membuat penyelakuan. Simulasi atau penyelakuan ini dijalankan
menggunakan komputer digital dengan bantuan perisian MATLAB/SIMULINK.
Akhir sekali, keupayaan di antara kawalan Fuzzy PID dengan kawalan PID
dibandingkan. Keputusan simulasi menunjukkan pengawal Fuzzy PID mempunyai
keluaran yang lebih baik berbanding dengan pengawal PID.
vii
CONTENTS
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
CONTENTS vii
LIST OF TABLES ix
LIST OF FIGURES x
LIST OF SYMBOLS & ABBREVIATIONS xii
LIST OF APPENDICES xiv
CHAPTER 1 INTRODUCTION 1
1.1 Overview 1
1.2 Problem Statement 2
1.3 Objective 2
1.4 Scope of Project 3
1.5 Research Methodology 3
1.6 Literature Review 4
1.7 Layout of Project Report 5
1.8 Project Planning 6
CHAPTER 2 ROBOT KINEMATICS AND MATHEMATICAL
MODELLING
viii
2.1 Introduction 7
2.2 Robot Kinematic Analysis 10
2.2.1 Forward Kinematic 11
2.2.2 Inverse Kinematic 14
2.3 DC Motor Modelling 15
CHAPTER 3 ROBOT CONTROLLER DESIGN
3.1 Flow Chart 19
3.2 Overview of Controller 21
3.3 PID Structure 21
3.3.1 PID Characteristic Parameters 24
3.4 Fuzzy Logic Controller 26
3.4.1 Fuzzification 27
3.4.2 Rule Base 29
3.4.3 Defuzzification 30
CHAPTER 4 SIMULATION RESULTS
4.1 Introduction 32
4.2 6 DOF Revolute Robot Arm 33
4.3 Simulation Using PID Controller 36
4.4 Simulation Using Fuzzy PID Controller 41
4.5 Simulation Using Fuzzy PID and PID Controller 46
CHAPTER 5 CONCLUSION & FUTURE WORKS
5.1 Conclusion 48
5.2 Suggestion for Future Work 49
REFERENCES 50
APPENDIX 53
ix
LIST OF TABLES
TABLE NUMBER TITLE PAGE
2.1 Summary of arm parameter 12
2.2 DC motor parameter and values 18
3.1 Effect of each PID Parameter 24
3.2 Rule base for fuzzy PID controller 29
4.1 DH parameter of robot arm 34
4.2 Performance of the PID controller 39
4.3 Performance of the Fuzzy PID controller 44
x
LIST OF FIGURES
FIGURE NUMBER TITLE PAGE
1.1 Gantt chart 6
2.1 Symbol of prismatic joint 8
2.2 Symbol of rotary joint 8
2.3 Cartesian robot 9
2.4 Articulated robot 10
2.5 Denavit-Hartenberg frame assignment 11
2.6 Schematic of DC motor system 16
2.7 Block diagram for DC motor system 17
2.8 DC motor subsystem using SIMULINK 18
3.1 Flow Chart of Research methodology 20
3.2 PID controller structure 23
3.3 Unit step response curve 25
3.4 Basic configuration of Fuzzy system 26
3.5 Membership function for input error 28
3.6 Membership function for input error change 28
3.7 Membership function for output u 28
3.8 Centroid defuzzification method 31
4.1 6 DOF robot arm 33
4.2 Frame assignment for the robot arm 34
4.3 Robot arm home position 35
xi
4.4 Robot arm desired position 35
4.5 PID control step response for 1 36
4.6 PID control step response for 2 36
4.7 PID control step response for 3 37
4.8 PID control step response for 4 37
4.9 PID control step response for 5 38
4.10 PID control step response for 6 38
4.11 PID control step response with disturbance for 1 39
4.12 PID control step response with disturbance for 3 40
4.13 PID control step response with disturbance for 6 40
4.14 Fuzzy PID control step response for 1 41
4.15 Fuzzy PID control step response for 2 41
4.16 Fuzzy PID control step response for 3 42
4.17 Fuzzy PID control step response for 4 42
4.18 Fuzzy PID control step response for 5 43
4.19 Fuzzy PID control step response for 6 43
4.20 PID control step response with disturbance for 1 45
4.21 PID control step response with disturbance for 3 45
4.22 PID control step response with disturbance for 6 46
4.23 Output response for 1 for both controllers 46
4.24 Output response for 3 for both controllers 47
xii
LIST OF SYMBOLS AND ABBREVIATIONS
SYMBOL DESCRIPTION
θ Joint angle
d Joint distance
a Link length
Twist angle
1
i
iH Homogeneous transformation matrix
( )m t Motor torque produced by motor shaft
Magnetic flux
( )ai t Armature current
mK Proportional constant
( )b t Back EMF
m Shaft velocity of the motor
( )s
Joint velocity
mJ Moment of inertia
mB Motor friction coefficient
bK Back EMF constant
tK Torque constant
aR Electrical resistance
xiii
aL Electrical inductance
gr Gear ratio
pK Proportional gain
IK Integral gain
DK Derivative gain
Damping ratio
U Universe of discourse
e Error
e Change of error
DC Direct current
EMF Electromagnetic field
FLC Fuzzy logic controller
PID Proportional integral derivative
DOF Degree of freedom
CAD Computer aided design
DH Denavit-Hartenberg
xiv
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Forward and inverse kinematic analysis 53
B Simulink model (Fuzzy PID controller) 59
C Simulink model (PID controller) 60
D Slides presentation (Hand-out) 61
CHAPTER 1
INTRODUCTION
1.1 Overview
Robot manipulator field is one of the challenging fields in industrial automation
systems. Many researchers focus to study the improvement of the robot arm
controller. This is due to the nonlinearities and physical input present in the
dynamics of the robot arm. This thesis presents the design and modelling of a 6 DOF
robot arm controller using fuzzy PID controller. The study of robot manipulator can
be divided into two parts which is the mathematical modelling of the manipulator
and also the control method of the robot arm.
The modelling of robot arm includes the analysis for kinematics and
dynamics computations. The kinematics model is a prerequisite for the dynamic
model and fundamental for practical aspects like motion planning, singularity and
workspace analysis.
2
1.2 Problem statement
Generally, different types of robot controller give different output performance of
robot movement. The performance of a robot arm can be analyzed by evaluating the
movement from an initial position to a final position. Nonlinearities, parameter
uncertainties and external disturbances exist in linear robot controllers. Therefore, it
is difficult to eliminate these undesired effects in order to achieve good stability and
precise tracking control performance. Output response of linear controller would
sometimes deviate from the desired input trajectory. Thus, a robot controller must be
designed to handle both linear and nonlinear systems. The controller is used to
minimize the error between the intended and the actual positions. The controller must
meet certain specifications. These specifications such as reducing overshoot,
minimizing rising time and eliminating the steady state error. In addition the robot
arm should be able to operate as usual when the external disturbance is applied to
any joint of the robot arm.
1.3 Objectives
The designing of 6 degree of freedom robot arm and the control strategy for the robot
are the aims of this research. The robot arm is designed by using computer-aided
design (CAD) software for control development purpose. To achieve these aims, the
objectives of this research are formulated as follow:-
i. To design CAD model of 6 degree of freedom (DOF) of articulated
robot arm using SolidWorks software.
ii. To develop the controller for the robot using the conventional control
system and artificial intelligence control system.
iii. To compare the performance of both conventional control system and
artificial intelligence control system in terms of output response.
iv. To integrate the CAD model of robot arm for pick and place
application using the MATLAB/Simulink environment.
3
1.4 Scope of Project
This project will focus on how to control the robot manipulator by analyzing the
kinematics of the robot arm and applying control strategy. The development stages of
this project are as follow:
i. Design the 6 DOF robot arms in identical size and weight with the
industrial type robot.
ii. Derive the forward and inverse kinematics equations of the robot.
iii. Apply the PID controller to the robot arm with input disturbances.
iv. Apply the combination of fuzzy-PID controller to the robot arm.
The performance of the PID controller is to be compared with fuzzy-PID in
terms of output response with minimal rising time, zero steady state error and
minimal overshoot. MATLAB/Simulink will be used as platform to simulate the
output performance of the robot.
1.5 Research Methodology
The project work was undertaken in the following five developmental stages:
i. Developing complete 6 DOF articulated robot arm including forward
kinematics and dynamics calculation for the robot arm using CAD
model.
ii. Converting the CAD model into Simulink model using SimMechanics
link provided by MathWorks.
iii. Utilizing the PID and Fuzzy PID controller as the robot arm
controller. The controller can be designed in Simulink model for
graphical environment of simulation.
iv. Comparing the performance of Fuzzy PID controller with the
conventional control system such as PID controller.
4
1.6 Literature Review
Industrial robot manipulators are generally used in positioning and handling devices.
Rapid technology changes in industrial robot manipulator urged human to develop
and improve the performance of control strategy which can be used to replace human
in hazardous, complex and boring tasks [1]. Generally, the dynamics behavior of
robot manipulators can be described by the nonlinearity and external input parameter
such as in friction, load and disturbances [2].
In the field of robot manipulators, many researchers have proposed literatures
and discussed the kinematics analysis of industrial robots such as SCARA, PUMA
560 and SG5-UT robot manipulator [7], [19]. Other papers discussed about the
control techniques problems such as PID, FLC, neural network algorithm and also
the combination of the three controllers. Some of the research employed the Denavit
Hartenberg method which it is used to model the mathematical equation of
kinematics [11]. The forward and inverse kinematic equation analysis was generated
and implemented using a simulation program [20], [21].
Nowadays, PID controller is a good control technique in industrial
automation applications due to its simplicity and robustness [3]. Although PID is
most widely used controller in industry, it has several drawbacks. One of the
drawbacks is that the PID controller is not sufficient to obtain the desired tracking
control performance because of the nonlinearity of the robot manipulator [4].
Therefore, PID controller is not a good technique to control a system with nonlinear
environment.
Fuzzy logic controller (FLC) was introduced to overcome the drawbacks of
PID controller. Fuzzy logic was pointed out in 1965 when Lotfi A. Zadeh [18]
presented his milestone paper in fuzzy sets and introduced the concept of linguistic
variable in 1973 [5]. Then, fuzzy logic control was developed by [6] and Assilian.
Fuzzy logic controller can be used to achieve better performance of robot
manipulator because its algorithm can implement a human’s heuristic knowledge on
how to control a system. The regularity use of PID and the good algorithm of FLC
can be combined into a controller to optimize the control performance of robot
manipulator.
5
There are a lot of papers discussed about the PID tuning. Fuzzy gain
scheduling of PID controllers was presented by [7] which proposed the uses of fuzzy
rules and reasoning to determine the PID controller parameter and how to control it
online. This method was also proposed by [8] which discussed about the fuzzy
supervisory control in reducing the amount of additional PID tuning.
An approach to combine a fuzzy logic controller and PID controller was
presented by [9]. In that paper, he replaced the proportional term in the PID with
fuzzy P controller and thus became the fuzzy P+ID controller.
1.7 Layout of Project Report
This section outlines the overall structure of the thesis and provides a brief
explanation for each chapter. This thesis consists of five chapters.
Chapter 2 explains some fundamental aspect about robot manipulators. This
chapter covers the current practical methodologies for kinematics modelling and
computations. The kinematics model represents the motion of the robot arm without
considering the forces that cause the motion. This chapter also presents the modelling
of the DC motor.
Chapter 3 presents the controller used in robot arm. The concepts of
conventional controller system such as PID controller are reviewed. The
characteristics and parameter of PID controller are discussed in detail before they are
applied to the robot arm. Since PID controller can be applied only to the linear
system, then the improvement can be made to the controller for wide range of
application. Fuzzy PID controller is introduced in this chapter and the concept of the
controller is presented. The definition of fuzzy set and some operation of fuzzy logic
are discussed. Explanation about fuzzifier, inference mechanism and defuzzifier are
also presented in this chapter.
Chapter 4 discusses the simulation results. The performance of the Fuzzy
PID controller is evaluated by the simulation study using Matlab/Simulink. For the
comparison purposes, the simulation study of PID controller is also presented.
Chapter 5 summarizes the work undertaken. Recommendations for future
work of this project are presented at the end of the chapter.
6
1.8 Project planning
Figure 1.1: Gantt chart
CHAPTER 2
ROBOT KINEMATICS AND
MATHEMATICAL MODELLING
2.1 Introduction
A robot manipulator system often consists of links, joints, actuators, sensors and
controllers. The links are connected by joints to form an open kinematic chain. Robot
manipulator consists of a collection of n-links to move in the robot workspace. The
total maximum points that the end effector can reach is called robot workspace. Both
end of the robot is attached to the base and another end is equipped with a tool (hand,
gripper or end-effector) to perform an operation or tasks.
The joints used to connect the robot links can be prismatic or rotary.
Prismatic joints can be described as sliding joint which the relative displacement
between links is a translation. Figure 2.1 shows the symbol of prismatic joint. Joint
distance, d is a translation distance of the previous frame (axis x, y & z) along the z
axis.
8
Figure 2.1: The symbol of prismatic joint [10]
Rotary joint can be explained as having revolute joint with angle θ is rotated
with respect to the z axis. Figure 2.2 shows the symbol of rotary joint.
Figure 2.2: The symbol of rotary joint [10]
9
In a robot manipulator, the number of DOF is refers to the number of
independent joint variables that would have to be specified in order to locate all parts
of the mechanism. For example, a robot manipulator is usually defined with a single
variable; the number of joints equals the number of degrees of freedom. If a robot
manipulator has 6 independent joint variables, so that the robot has 6 DOF.
Robot manipulator can be classified based on the geometric types and the
configuration of the robots. For example, if all joints of robot manipulator are
prismatic, the robot is known as Cartesian manipulator while the robot with rotary
joint is known as a revolute robot or articulated robot. Figure 2.3 and Figure 2.4
show the Cartesian robot and articulated robot respectively. There are another three
types of robot geometric configuration which is cylindrical, spherical and SCARA.
This project focused on the analysis of 6DOF robot with articulated robot
configuration.
Figure 2.3: Cartesian robot [10]
10
Figure 2.4: Articulated robot [10]
2.2 Robot Kinematic Analysis
Kinematics is the study of the motion of the robot manipulator without the regard to
the forces or other factors that can change the robot movement [10]. Kinematics
deals with the movement of end effector of the robot manipulator relative to the base
of the manipulator as a function of time. Kinematic analysis of the robot manipulator
can be divided into two categories which is forward kinematics and inverse
kinematics. The forward kinematic solution for robot manipulators can be derived by
using Denavit-Hartenberg algorithm which provides a matrix solution.
Forward kinematics of robot manipulator is for determining the position and
orientation of a robot hand with respect to a reference coordinate system, given the
joint variables and the arm parameters [11]. The forward kinematics problem can be
expressed mathematically as follows [12]:
1 2 3 n dF(θ ,θ ,θ ....θ ) =[x,y,z,R ] (2.1)
where 1 2θ ,θ and nθ are the input variables, [ x,y,z ] are the desired position
and dR is the desired rotation.
11
Inverse kinematics of a robot manipulator deals with the calculation of each
joint variable, given the position and orientation of end effector. The computation of
the inverse kinematics of robot manipulator is quite difficult if compared to the
forward kinematics because of the nonlinearities and multiple solutions involved.
The following equation explains the inverse kinematics problem.
1 2 3 nF(x,y,z,R) =[θ ,θ ,θ ....θ ] (2.2)
2.2.1 Forward Kinematic
The forward kinematic equations describe the functional relationship between the
joint variables and the position and orientation of the end-effector. Consider a robot
manipulator with numbers of links connected by either rotary joints or prismatic
joints. The robot base is defined as the link 0, and the joint 1 connects the base (the
link 0) to the link 1. Figure 2.5 shows a spatial linkage, where the joint i connects the
link i to the link i-1. In order to determine the position and orientation of the link i
relative to its neighbouring link i-1, a Cartesian frame xiyizi is assigned to it.
Figure 2.5: Denavit-Hartenberg frame assignment
12
To obtain the forward kinematic equations the following steps should be
done:
a) Obtain the Arm Parameters
The arm parameter can be computed after a Cartesian frame xiyizi is assigned to the
robot arm. Two parameters of the link i are the link length ai and the twist angle i.
Two joint parameters are the joint angle θ i and the joint distance di as shown in
Figure 2.5. The link length ai and twist angle i are always constant. The summary
of arm parameter is shown in Table 2.1.
Table 2.1: Summary of arm parameter
Arm parameter Symbol Revolute joint Prismatic joint
Link length a Constant Constant
Twist angle Constant Constant
Joint angle θ variable Constant
Joint distance d Constant Variable
b) Obtain link transformation matrices
A homogeneous transformation matrix can be calculated if the frame assignment has
been constructed and the arm parameter has been obtained. The transformation from
the frame xi-1yi-1zi-1 to the frame xiyizi can be obtained by the following sequence of
rotations and translations:
i. Rotation of the frame xi-1yi-1zi-1 about the zi-1.
0 0
0 0( , )
0 0 1 0
0 0 0 1
i i
i i
i
C S
S CRot z
(2.3)
ii. Translation of the frame xi-1yi-1zi-1 along the zi-1 axis by di units.
13
1 0 0 0
0 1 0 0( , )
0 0 1
0 0 0 1
i
i
Trans z dd
(2.4)
iii. Translation of the frame xi-1yi-1zi-1 along the xi axis by ai units.
1 0 0
0 1 0 0( , )
0 0 1 0
0 0 0 1
i
i
a
Trans x a
(2.5)
iv. Rotation of the frame xi-1yi-1zi-1 about the xi axis by an angle i.
1 0 0 0
0 0( , )
0 0
0 0 0 1
i i
i
i i
C SRot x
S C
(2.6)
The transformation matrix for each joint can be calculated as:
1 ( , ) ( , ) ( , ) ( , )i
i i i iH Rot z i Trans z d Trans x a Rot x (2.7)
D-H transformation matrix from the frame xi-1yi-1zi-1 to the frame xiyizi can be
calculated by using post multiplication rule. The result is as follows:
10
0 0 0 1
i i i i i i i
i i i i i i ii
i
i i i
C C S S S a C
S C C S C a SH
S C d
(2.8)
The position and orientation of the robot tool frame with respect to the base
frame can be described by the following matrix:
1 2 3
0 0 1 2 1...n n
nH H H H H (2.9)
14
The transformation matrix 0
nH can be expressed as follows:
00 0 0 1
0 0 0 1
x x x x
y y y yn
z z z z
n s a P
n s a PH
n s a P
n s a P (2.10)
The notation a is called the approach vector, s is the sliding vector and n is
the normal vector. P is the position vector of the robot hand, pointing from the origin
of the robot base frame to the origin of the robot hand frame. The vectors a, s and n
specify the orientation of the robot hand frame and the vector P describes the
position of the robot hand frame in the robot base frame.
2.2.2 Inverse Kinematic
The inverse kinematic equation is to find the joint variables of the robot manipulator
for a given position and orientation of the robot hand. The computation of the inverse
kinematics of the robot manipulator is a difficult task because of the nonlinearities
and multiple solution problems. The steps used to solve the inverse kinematics for
the robot manipulator are as follow:
i. Calculate the forward kinematics matrix of the robot arm using D-H
algorithm as shown in equation (2.8).
ii. Specify the intended position and orientation of the robot hand relative to
the robot base frame. The position is specified in matrix form as shown in
equation (2.10).
iii. Equate the homogeneous transformation matrix to the final
transformation matrix of the robot manipulator.
iv. Find the values of the joint variables which are unknown. Solving the
matrix means to solve 12 equations.
15
2.3 DC Motor Modelling
Modelling refers to the plant system in mathematical terms, which characterizes the
input and output relationship [13]. Direct current (DC) motor is a common actuator
found in many mechanical systems and industrial applications such as industrial and
educational robots [11]. The function of DC motor is to convert the electrical energy
to mechanical energy. The motor has rotary movement, and when combined with
mechanical part it can provide translation movement for the desired link.
Equation (2.11) states the relation between the current and the developed
torque in the motor shaft.
( ) ( )m m at K i t (2.11)
where ( )m t , is the motor torque produced by the motor shaft, , the
magnetic flux, ( )ai t , the armature current, and mK , is a proportional constant.
Equation (2.12) states the relation between the produced EMF and the shaft
velocity:
( )b m mt K (2.12)
where ( )b t , denotes the back EMF, and m , is the shaft velocity of the
motor.
DC motors are important in control systems, so it is necessary to establish
and analyze the mathematical model of the DC motors [13]. Figure 2.6 shows the
schematic diagram of the armature controlled DC motor with a fixed field circuit.
16
Figure 2.6: Schematic diagram of DC motor system
It is modelled as a circuit with resistance and inductance connected in series.
The input voltage ( )ae t , is the voltage supplied by amplifier to move the motor. The
back EMF voltage ( )b t , is induced by the rotation of the armature windings in the
fixed magnetic field. To derive the transfer function of the DC motor, the system is
divided into three major components of equation: electrical equation, mechanical
equation, and electro-mechanical equation [14].
The transfer function of the motor speed is:
( ) 2
( )
( ) ( )
tspeed s
m a a m a a t b
KsG
V s J L s L B R J s K K
(2.13)
In addition, the transfer function of the motor position is determined by
multiplying the transfer function of the motor speed by the term1
s:
( ) 2
( )
( ) ( )
tposition s
m a a m a a t b
KsG
V s J L s L B R J s K K s
(2.14)
where, mJ , and mB , are denoted as the moment of inertia and motor friction
coefficient.
According to the previous discussion, the schematic diagram in Figure 2.6 is
modelled as a block diagram in Figure 2.7. This block diagram represents an open
loop system, and the motor has built-in feedback EMF, which tends to reduce the
current flow.
17
Figure 2.7: Block diagram for DC motor system
The advantage of using the block diagram is that it gives a clear picture of the
transfer function relation between each block of the system. Therefore, based on the
block diagram in Figure 2.7, the transfer function from ( )a s to ( )m s with
( ) 0tD s was illustrated in equation (2.13).
Transfer function from the load torque, ( )a s to ( )m s is given with ( ) 0aV s :
( ) ( ) /
( ) ( )( )
m a a
t m a m a a t b
s L s R gr
D s J s L B L s R K K s
(2.14)
where, gr, is the gear ratio. Deriving equation (2.14) is obtained in Appendix.
Using SIMULINK, the model of the motor may be created. This model
includes all the parameters derived previously. Figure 2.8 shows the SIMULINK
model of DC motor.
18
Figure 2.8: DC motor subsystem using SIMULINK
Table 2.2 shows DC motor parameters and values chosen for motor simulation.
Table 2.2: DC motor parameter and values
Parameter Value
Moment of inertia mJ = 0.000052 Kg.m2
Friction coefficient mB = 0.01 N.ms
Back EMF constant bK = 0.235 V/ms-1
Torque constant tK = 0.235 Nm/A
Electric resistance aR = 2 ohm
Electric inductance aL = 0.23 H
Gear ratio gr
Load torque 1( )t
Angular speed m rad/s
CHAPTER 3
ROBOT CONTROLLER DESIGN
3.1 Flow Chart
In accomplishing this project, the scope of the work has been divided into a few
parts. The first part is to design CAD model of 6 DOF robot arm. The second part is
to design the PID and fuzzy-PID controller for the robot arm for comparison
purpose. The third part is to perform simulation using MATLAB/Simulink. The last
part is to analyze the output performance of both controllers. The research
methodology flow chart is shown in Figure 3.1.
20
Study on Forward and Inverse kinematic of robot
Convert CAD model to xml file
Import xml file in
MATLAB and
convert to STL file
Apply PID controller to the
SimMechanics model
Apply fuzzy-PID controller
to the SimMechanics model
Modify the SimMechanics model
Start
End
Perform simulation using MATLAB
Output response meet
requirement?
Yes
No
Design CAD model of 6 DOF robot arm
Compare the output performance
between two controllers
Figure 3.1: The Flow Chart of Research methodology
21
3.2 Overview of Controller
PID controller is considered the most widely used control technique in control
applications. A high number of applications and control engineers had used the PID
controller in daily life. On the other hand, many research papers, number of master
and doctoral theses and books had highlighted this subject. PID control offers an
easy method of controlling a process by varying its parameters. PID works well in
industrial applications such as in slow industrial manipulators where large
components of joint inertia are added by actuators. Since the invention of PID
control in 1910, and Ziegler-Nichols’ (ZN) tuning method in 1942 [15] and [16], PID
controllers became one of the dominant and popular issues in control theory due to
the simplicity of implementation, the ease of designing, and the ability to be used in a
wide range of applications [17]. Moreover, they are available at low cost. Finally, it
provides robust and reliable performance for most systems if the parameters are
tuned properly. However, the PID controller has its own limitation; the PID
performances can give only satisfactory performance if the requirement is reasonable
and the process parameters variation are limited.
3.3 PID Structure
PID algorithm, assumes that the controlled plant is known, such as a robot
manipulator. The error signal, e (t), is the difference between the set point, r (t), and
the process output, y (t). If the error between the output and the input values is large,
then large input signal is applied to the physical system. If the error is small, a small
input signal is used. As its name suggested, any change in the control signal, u (t) is
directly proportional to change in the error signal for a given proportional gain Kp.
22
Mathematically the output of the proportional controller is given as follows:
( ) ( )pu t K e t (3.1)
where e(t) , the error signal and Kp = u(t)/e(t) indicates the change of the
output signal to the change of the error signal.
Proportional term is not sufficient to be a controller in practical cases to meet
a specified requirement (e.g. small overshoot, good transient response) because the
large proportional gain gives fast rising time with large overshoot and oscillatory
response.
Therefore, a derivative term is added to form the PD controller, which tends
to adjust the response as the process approaches the set point. The output of PD
controller is calculated based on the sum of both current error and change of error
with respect to time. The effects of PD give slower response with less overshoot than
a proportional controller only. Mathematically, PD controller is represented as:
( )( ) ( )p D
de tu t K e t K
dt (3.2)
The main function of the third term is the integral control tends to reduce the
effect of steady state error that may be caused by the proportional gain, where a
smaller integration time result is the faster change in the controlled signal output.
The general form of the PID controller in continuous time formula given as:
1
0
( )( ) ( ) ( )p I D
de tu t K e t K e t dt K
dt (3.3)
Each term of the three components of PID controller is amplified by an
individual gain, the sum of the three terms is applied as an input to the plant to adjust
the process. It will be noted that the purely derivative or integral plus derivative
variations is never used. In all cases except proportional control, the PID
compensator gives at least one pole and one zero.
In real application, PID algorithm can be implemented in different forms
depending on the process and control requirements. The easiest form introduced is
the parallel form, as shown in Figure 3.2, where the P, I and D elements has the same
input signal e(t) .
23
Figure 3.2: PID controller structure
The terms, pK , IK and DK stand for the proportional, integral, and derivative
gains. The terms e (t) and u (t) represent the error and the control signal respectively.
The transfer function of the PID controller in parallel is:
2
_ ( )D p II
PID parallel p D
K s K s KKG s K K s
s s
(3.4)
24
3.3.1 PID Characteristic Parameters
Proportional action P K improves the system rising time, and reduces the steady state
error. This means when there is larger proportional gain, the larger control signal
produced to correct the error. However, the higher value of P K produces large
overshoot and the system may be oscillating; therefore, integral action I K is used to
eliminate the steady state error. Despite the integral control, reducing the steady state
error may make the transient response worsen [16]. Therefore, derivative gain D K
will have the effect of increasing the damping in system, reducing the overshoot, and
improving the transient response.
As discussed previously, each one of the three gains of the classical PID
control has an effect of the response of the closed loop system. Table (3.1)
summarizes the effects of each of PID control parameters. It will be known that any
changing of one of the three gains will affect the characteristic of the system
response.
Table 3.1: Effect of each PID Parameter
Closed-Loop
Response
Rise Time Overshoot Settling Time Steady State
Error
Increase Kp Fast Increase Small/no effect Decrease
Increase Ki Fast Increase Increase Decrease
Increase Kd Small/no effect Decrease Decrease Small/no effect
50
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