SANAZ YADEGAR - psasir.upm.edu.my

UNIVERSITI PUTRA MALAYSIA

SANAZ YADEGAR

FK 2015 71

CHATTER-FREE AND EQUIVALENT ESTIMATOR FUZZY MODEL-BASED SLIDING MODE CONTROLLER FOR SERIAL LINKS 6 DOF

ROBOT MANIPULATOR

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CHATTER-FREE AND EQUIVALENT ESTIMATOR FUZZY MODEL-BASED

SLIDING MODE CONTROLLER FOR SERIAL LINKS 6 DOF

ROBOT MANIPULATOR

By

SANAZ YADEGAR

Thesis Submitted to the School of Graduate Studies, University Putra Malaysia, in

Fulfilment of the Requirement for the Degree of Master of Science

May 2015

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COPYRIGHT

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photographs and all other artwork, is copyright material of Universiti Putra Malaysia

unless otherwise stated. Use may be made of any material contained within the thesis

for non-commercial purposes from the copyright holder. Commercial use of material

may only be made with the express, prior, written permission of Universiti Putra

Malaysia.

Copyright © Universiti Putra Malaysia

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Dedicate

To

My dearest parents

For their extensively love and

Their endless care

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Abstract of thesis presented to the senate of Universiti Putra Malaysia in fulfillment of

the requirements of the degree of Master Science

CHATTER-FREE AND EQUIVALENT ESTIMATOR FUZZY MODEL-BASED

SLIDING MODE CONTROLLER FOR SERIAL LINKS 6 DOF ROBOT

MANIPULATOR

By

SANAZ YADEGAR

May 2015

Chairman: Azura Binti Che Soh,Phd

Faculty: Engineering

Design of a robust controller for multi input-multi output (MIMO) nonlinear uncertain

dynamical system could be a challenging work. This thesis focuses on the design and

analysis of a high performance Proportional-Integral-Derivative (PID)-like fuzzy sliding

mode control for second order nonlinear uncertain system, in presence of uncertainties.

In this research, sliding mode controller is a robust and stable nonlinear controller, which

selected to control of robot manipulator. The proposed approach effectively combines of

design methods from switching sliding mode controller, adaptive controller, fuzzy logic

theory and linear Proportional-Derivative (PD) control to improve the performance,

stability and robustness of the sliding mode controller.

This sliding mode controller has two important subparts, switching and equivalent.

Switching part (discontinuous part) is very important in uncertain condition but it causes

chattering phenomenon. To solve the chattering, the most common method used is linear

boundary layer saturation method, but this method lost the stability. To reduce the

chattering with respect to stability and robustness; linear controller is added to the

switching part of the sliding mode controller. The linear controller is to reduce the role of

sliding surface slope and switching (sign) function. The nonlinearity term of the sliding

mode controller is used to eliminate the decoupling and nonlinear term of link’s dynamic

parameters. However nonlinearity term of sliding mode controller is very essential to

reliability but in uncertain condition or highly nonlinear dynamic systems it can cause

some problems. To solve this challenge the PID fuzzy logic controller is used as a model-

based PID like fuzzy sliding mode controller. The PID like fuzzy sliding mode controller

is updated based on online tuning sliding surface slope. In order to reduce the online

computation burden, the PID like fuzzy logic controller is also used to sliding surface

slope online tuning. As a result, in proposed method fuzzy logic controller is used to

dynamic estimation and also online tuning. This controller improves the stability and

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robustness, reduces the chattering as well and reduces the level of energy due to the

torque performance as well.

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Abstrak tesis ini dikemunkakan kepada senat Universiti Putra Malaysia sebagai

memenuhi keperluan untuk ijazah master sains

GELATUK-BEBAS DAN PENGANGGAR SETARA MODEL KABUR

BERDASARKAN PENGAWAL MOD GELONGSOR UNTUK PAUTAN

BERSIRI 6 DOF PENGOLAH ROBOT

Oleh

SANAZ YADEGAR

Mei 2015

Pengerusi: Azura Binti Che Soh,Phd

Fakulti: Kejuruteraan

Reka bentuk pengawal teguh untuk sistem dinamik tidak menentu tidak lelurus berbilang

masukan berbilang keluaran (MIMO) boleh menjadi satu kerja yang mencabar. Tesis ini

memberi tumpuan kepada reka bentuk dan analisis prestasi yang tinggi kawalan mod

berkadaran-kamiran-terbitan(PID) seperti gelongsor kabur untuk sistem peringkat kedua

tak lelurus tidak menentu, di hadapan yang tidak menentu. Dalam kajian ini, pengawal

mod gelongsor adalah pengawal tak lelurus yang teguh dan stabil yang dipilih untuk

mengawal pengolah robot. Pendekatan yang dicadangkan berkesan dengan

menggabungkan kaedah dari pengawal mod gelongsor pensuisan, pengawal suai, teori

logik kabur dan pengawal lelurus berkadaran-terbitan (PD) untuk meningkatkan prestasi,

kestabilan dan keteguhan pengawal mod gelongsor.

Pengawal mod gelongsor mempunyai dua sub-bahagian penting, pensuisan dan setara.

Bahagian pensuisan (bahagian tidak berterusan) adalah sangat penting dalam keadaan

yang tidak menentu tetapi ia menyebabkan fenomena gelatukan. Untuk menyelesaikan

gelatukan, kaedah yang paling biasa digunakan adalah kaedah lelurus lapisan sempadan

tepu, tetapi kaedah ini menghilangkan kestabilan. Untuk mengurangkan gelatukan yang

berkaitan dengan kestabilan dan keteguhan; pengawal lelurus ditambah kepada bahagian

pensuisan pengawal mod gelongsor. Pengawal lelurus adalah untuk mengurangkan

peranan gelongsor cerun permukaan dan fungsi pensuisan(tanda). Istilah ketaklelurusan

pengawal mod gelongsor digunakan untuk menghapuskan nyahgandingan dan pautan tak

lelurus parameter dinamik ini. Walaubagaimanapun ketaklelurusan pengawal mod

gelongsor adalah sangat penting untuk kebolehpercayaan tetapi dalam keadaan yang

tidak menentu atau sistem dinamik yang sangat tak lelurus ia boleh menyebabkan

beberapa masalah. Untuk menyelesaikan cabaran ini, pengawal PID logik kabur

digunakan berdasarkan model pengawal mod PID seperti gelongsor kabur. Bagi

pengawal mod PID seperti gelongsor kabur dikemaskini berdasarkan penalaan atas talian

gelongsor permukaan cerun. Dalam usaha untuk mengurangkan beban pengiraan atas

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talian, pengawal PID seperti logik kabur juga digunakan untuk penalaan atas talian

gelongsor permukaan cerun. Oleh itu, dalam kaedah yang dicadangkan, pengawal logik

kabur digunakan untuk anggaran dinamik dan juga penalaan atas talian. Pengawal ini

meningkatkan kestabilan dan kemantapan, mengurangkan gelatukan dan juga

mengurangkan tahap tenaga disebabkan oleh prestasi tork juga.

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ACKNOWLEDGEMENT

First of all, I would like to express my sincere thanks to my supervisor, Dr. Azura Binti

Che Soh who has given the knowledge and the ability to observe, think and develop. I

would like express my sincere gratitude to my co-supervisors, Dr. Siti Anom Binti

Ahmad and Dr. Asnor Juraiza Dato’Hj. Ishak for their valuable guide and advice and

encouragement.

I am grateful to my co-supervisors, Dr. Siti Anom Binti Ahmad for her insightful support

and comments.

Most of all, I am deeply indebted to my parents. Their love, dedication and help were

always the foundation of my work and patient during this long course of learning. I also

want to express my thanks to my family for their unconditional care, patient and help.

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I certify that an Examination Committee has met on to conduct the final

examination of Sanaz Yadegar on his Master of Science thesis entitled "CHATTER-

FREE AND EQUIVALENT ESTIMATOR FUZZY MODEL-BASED SLIDING MODE

CONTROLLER FOR SERIAL LINKS 6 DOF ROBOT MANIPULATOR” in

accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti

Pertanian Malaysia (Higher Degree) Regulations 1981. The Committee recommends that

the candidate be awarded the relevant degree. Members of the Examination Committee

are as follows:

Mohd Khair Hassan, PhD

Senior Lecturer

Faculty of Graduate Studies

Universiti Putra Malaysia

(Chairman)

Nasri Sulaiman, PhD

Senior Lecturer

Faculty of Engineering


(Internal Examiner)

Zaharuddin Mohamed, PhD

Associate Professor

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

(External Examiner)

___________________

Seow Heng Fong, PhD

Professor/Deputy Dean

School of Graduate Studies


Date:

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This thesis was submitted to the Senate of Universiti Putra Malaysia and has been

accepted as fulfillment of the requirement for the degree of Master of Science. The

members of the Supervisory Committee are as follows:

Azura Binti Che Soh, PhD Senior Lecturer



(Chairman)

Siti Anom Binti Ahmad, PhD

Senior Lecturer



(Member)

Asnor Juraiza Bt.Dato’Hj. Ishak, PhD

Senior Lecturer



(Member)

___________________

BUJANG BIN HIM HUAT, PhD

Professor and Dean

School of Graduate Studies


Date:

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Declaration by Graduate Student

I hereby confirm that:

this thesis is my original work;

quotations, illustrations and citations have been duly referenced;

this thesis has not been submitted previously or concurrently for any other degree at

any other institutions;

intellectual property from the thesis and copyright of thesis are fully-owned by

Universiti Putra Malaysia, as according to the Universiti Putra Malaysia (Research)

Rules 2012;

written permission must be obtained from supervisor and the office of Deputy Vice-

Chancellor (Research and Innovation) before thesis is published (in the form of

written, printed or in electronic form) including books, journals, modules,

proceedings, popular writings, seminar papers, manuscripts, posters, reports, lecture

notes, learning modules or any other materials as stated in the Universiti Putra

Malaysia ( Research) Rules 2012;

there is no plagiarism or data falsification/fabrication in the thesis, and scholarly

integrity is upheld as according to the Universiti Putra Malaysia (Graduate Studies)

Rules 2003 (Revision 2012-2013) and the Universiti Putra Malaysia (Research)

Rules 2012. The thesis has undergone plagiarism detection software.

Signature: _______________________ Date: _______________

Name and Matric No: _________________________________________

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Declaration by Members of Supervisory Committee

This is confirm that:

the research conducted and writing of this thesis was under our supervision;

supervision responsibilities as stated in the Universiti Putra Malaysia (Graduate

Studies) Rules 2003 (Revision 2012-2013) are adhered to.

Signature: _____________________ Signature: ___________________

Name of Name of

Chairman of Member of

Supervisory Supervisory

Committee: _____________________ Committee: ___________________

Signature: _____________________ Signature: ___________________

Name of Name of

Member of Member of

Supervisory Supervisory

Committee: _____________________ Committee: ___________________

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TABLE OF CONTENTS

Page

ABSTRACT i

ABSTRAK ii

AKNOWLEDGEMENT iv

APRROVAL vi

DECLARATION viii

LIST OF TABLES xiii

LIST OF FIGURES xv

LIST OF ABBREVIATIONS xix

CHAPTER

1 INTRODUCTION 1 1.1 Motivation and Background 1

1.2 Problem Statement 4

1.3 Objectives 6

1.4 The Scope of Work 6

1.5 Contributions 7

1.6 Thesis Outline 7

2 LITERATURE REVIEW 9 2.1 Introduction 9

2.2 PUMA Robot Manipulator (Arm) 9

2.2.1 System Kinematics

2.2.2 Dynamic of a PUMA Arm 17

2.3 Control Theory 27

2.4 Linear Control of a Robot Arm 27

2.5 Non-linear Control of a Robot Arm

2.5.1 Feedback Linearisation (Computed-Torque Controller) 28

2.5.2 Sliding Mode Controller 29

2.6 Summary 34

3 METHODOLOGY 35 3.1 Introduction 35

3.2 Comparison Studies Between Different Controllers 37

3.2.1 Proportional-Integral-Derivative (PID) 37

3.2.2 Computed Torque Control (CTC) 38

3.2.3 Conventional Sliding Mode Control (SMC) 42

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3.3 Solve Chattering Problem 48

3.3.1 Boundary Layer Method 49

3.3.2 Chatter Attenuation Using a Parallel Linear Method 50

3.4 Dynamic Estimation Using PID-like FLC 55

3.4.1 Design of a PD-like FLC 56

3.4.2 Design of the PI-like FLC 64

3.4.3 Design of a PID-like FLC 65

3.5 Proposed Design of a Chatter-free Model-based PID-like FSMC 67

3.6 On-line Tuning of the Sliding Surface Slope 71

3.7 Proof of The Stability of Chatter-free Model-based PID-like

FSMC 73

3.7 Summary 77

4 RESULTS AND DISCUSSION 78

4.1 Comparison of a conventional PID, CTC and SMC 78

4.1.1 Comparison of the Tracking Data and Information 79

4.1.2 Comparison of the Actuation Torque (τi) 80

4.1.3 Comparison of the Disturbance Rejection

4.1.4 Tracking Error Comparison 83

4.2 Comparison of a Conventional SMC with a Boundary Layer SMC 86

4.2.1 Comparison of Tracking Data and Information 93

4.2.2 Comparison the Sliding Surface (S) 95


4.2.4 Comparison of the Disturbance Rejection 97

4.2.5 Comparison of the Tracking Error 100

4.3 Comparison of Chattering Free Parallel Linear SMC with Boundary

Layer SMC 103


4.3.2 Comparison of The Sliding Surface (S) 108




4.4 Comparison of PID-like FSMC with Chattering-free Parallel Linear

SMC 115


4.4.2 Comparison of the Sliding Surface (S) 119




4.5 Comparison of the Online Sliding Surface Slope Tuning PID-like FSMC

with Offline Sliding Surface Slope Tuning PID-like FSMC 126

4.5.1 Comparison of the Tracking Data and Information: 127

4.5.2 Comparison of Sliding Surface (S) 129

4.5.3 Comparison the Actuation Torque (τi) 130



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5 CONCLUSIONS AND RECOMMENDATION 138 5.1 Conclusions 138

5.2 Recommendation 139

REFERENCES 140 APPENDIX A 144 APPENDIX B 145 BIODATA OF THE AUTHOR 148 LIST OF PUBLICATION 149

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LIST OF TABLES

Table Page

2.1: Comparative evaluation of a serial and parallel link Robot arm [8] 11

2.2: The Denavit Hartenberg Parameters 13

2.3: PUMA D-H Notations [6] 15

2.4: Inertial constant reference (Kg.m2) 25

2.5: Gravitation constants (Nm) 26

3.1: Rule table for the PD-like FLC 61

3.2: Lookup Table for the PD-like FLC 64

3.3: Rule Table for the PID-like FLC 67

4.1: Comparison of rise time between PID, CTC and Conventional SMC 80

4.2: Comparison of overshoot between PID, CTC and Conventional SMC 80

4.3: Conventional SMC Coefficients 87

4.4: Boundary layer SMC coefficients 91

4.5: Comparison of rise time between Conventional SMC and boundary layer

SMC 94

4.6: Comparison of overshoot between SMC and boundary layer SMC 95

4.7: Comparison of steady state error between Conventional SMC and boundary

layer SMC 95

4.8: Chatter-free parallel linear SMC 103

4.9: Comparison of rise time between boundary layer SMC and parallel linear SMC

(Proposed SMC) 106

4.10: Comparison of overshoot between boundary layer SMC and parallel linear

SMC (Proposed SMC) 107

4.11: Comparison of steady state error between boundary layer SMC and parallel

linear SMC (Proposed SMC) 107

4.12: PID-like FSMC coefficients 115

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4.13: Comparison of rise time between boundary layer SMC, parallel linear SMC

and PID-like FSMC 118

4.14: Comparison of overshoot between boundary layer SMC, parallel linear SMC

and PID-like FSMC 119

4.15: Comparison of steady state error between boundary layer SMC, parallel linear

SMC and PID-like FSMC 119

4.16: Comparison of rise time between offline tuning PID-like FSMC and online

tuning PID-like FSMC 128

4.17: Comparison of overshoot between offline tuning PID-like FSMC and online

tuning PID-like FSMC 129

4.18: Comparison of steady state error between offline tuning PID-like FSMC and

online tuning PID-like FSMC 129

4.19: Comparison of steady state error between offline tuning PID-like FSMC and

online tuning PID-like FSMC 133

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LIST OF FIGURES

Figure Page

2-1: Robot arm [5] 10

2-2: The application of Forward and Inverse Kinematics 12

2-3: D-H notation for a PUMA arm [5] 14

2-4: Block diagram of a Conventional SMC 29

2-5: Sliding Surface and the Chatter Phenomenon [3] 30

2-6: Linear Saturation Boundary Layer Functions [3] 31

2-7: Non-linear Fuzzy Saturation Boundary Layer Functions [25] 32

3-1: Flowchart of Proposed Methodology 36

3-2: Block Diagram of PID Control of PUMA arm 38

3-3: Block Diagram of PD-CTC 41

3-4: Block Diagram of PD-SMC for PUMA arm 48

3-5: Block Diagram of Chatter-free Parallel Linear PD-SMC for PUMA arm 53

3-6: Membership Function, Scaling and Linguistic variable for error 58

3-7: Membership Function, Scaling and Linguistic variable for change of error 58

3-8: Membership Function, Scaling and Linguistic variable for PD fuzzy output 59

3-9: Rule Viewer in the PD-like FLC 63

3-10: PD-like FLC 63

3-11: Design of PI controller Based on PD controller 65

3-12: Design of a PI-like FLC Based on a PD-like FLC 65

3-13: Design of a PID-like FLC 66

3-14: Design of a PID-like FSMC 70

3-15: Design of Online Tuning sliding Surface Slope PID-like FSMC 71

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4-1: Trajectory Following: PID, CTC and Conventional SMC 79

4-2: Torque performance: PID, CTC and Conventional SMC 81

4-3: Comparison of disturbance rejection: PID, CTC and Conventional SMC in the

presence of uncertainty 82

4-4: Torque performance: PID, CTC and Conventional SMC in the presence of

uncertainty 83

4-5: Steady state error: PID, CTC and Conventional SMC in the presence of

uncertainty 84

4-6: RMS error: PID, CTC and Conventional SMC in the presence of uncertainty 85

4-7: Slope of the sliding surface and controller gain optimization 86

4-8: Tracking accuracy in classical SMC (λ = 50) 87

4-9: Sliding surface tracking (λ = 50) 88

4-10: Torque control (λ = 50) 88

4-11:Tracking accuracy in classical SMC (λ = 500) 89

4-12: Sliding surface tracking (λ = 500) 89

4-13: Torque control (λ = 500) 90

4-14: Sliding surface slope and controller gain optimisation in the boundary layer

SMC 91

4-15: Tracking accuracy in the boundary layer SMC 92

4-16: Sliding surface tracking 92

4-17: Torque control 93

4-18: Trajectory following: Conventional SMC and boundary layer SMC 94

4-19: Comparison of sliding surface: Conventional SMC and boundary layer

SMC 96

4-20: Comparison the actuation torque: Conventional SMC and boundary layer

SMC 97

4-21: Comparison of disturbance rejection: Conventional SMC and boundary layer

SMC in the presence of uncertainty 98

4-22: Comparison of sliding surface: Conventional SMC and boundary layer SMC in

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the presence of uncertainty 99

4-23: Comparison of the actuation torque: conventional SMC and boundary layer


4-24: Comparison of steady state error: Conventional SMC and boundary layer SMC

in the presence of uncertainty 101

4-25: Comparison of RMS error: Conventional SMC and boundary layer SMC in the


4-26: Tracking accuracy in the parallel linear SMC 103

4-27: Sliding surface tracking in the parallel linear SMC 104

4-28: Torque control in the parallel linear SMC 105

4-29: Trajectory following: boundary layer SMC and parallel linear SMC 106

4-30: Comparison of sliding surface: boundary layer SMC and parallel linear

SMC 108

4-31: Comparison of actuation torque: boundary layer SMC and parallel linear

SMC 109

4-32: Comparison of disturbance rejection: boundary layer SMC and parallel linear


4-33: Comparison of sliding surface: boundary layer SMC and parallel linear SMC in

the presence of uncertainty 111

4-34: Comparison of actuation torque: boundary layer SMC and parallel linear SMC


4-35: Comparison of steady state error: boundary layer SMC and parallel linear SMC


4-36: Comparison of RMS error: boundary layer SMC and parallel linear SMC in the


4-37: Tracking accuracy in the PID-like FSMC 116

4-38: Sliding surface tracking in the PID-like FSMC 116

4-39: Torque control in the PID-like FSMC 117

4-40: Trajectory following: PID-like FSMC, boundary layer SMC and parallel linear

SMC 118

4-41: Comparison of sliding surface: PID-like FSMC, boundary layer SMC and

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parallel linear SMC 120

4-42: Comparison of actuation torque: PID-like FSMC, boundary layer SMC and

parallel linear SMC 121

4-43: Comparison of disturbance rejection: PID-like FSMC, boundary layer SMC

and parallel linear SMC in the presence of uncertainty 122

4-44: Comparison of sliding surface: PID-like FSMC, boundary layer SMC and

parallel linear SMC in the presence of uncertainty 123

4-45: Comparison of actuation torque: PID-like FSMC, boundary layer SMC and


4-46: Comparison of steady state error: PID-like FSMC, boundary layer SMC and


4-47: Comparison of RMS error: PID-like FSMC, boundary layer SMC and parallel

linear SMC in the presence of uncertainty 126

4-48: Trajectory following: offline tuning PID-like FSMC and online tuning PID-like

FSMC 128

4-49: Comparison of sliding surface: offline tuning PID-like FSMC and online PID-

like FSMC 130

4-50: Comparison of actuation torque: offline PID-like FSMC and online PID-like

FSMC 131

4-51: Comparison of disturbance rejection: offline PID-like FSMC and online PID-

like FSMC in the presence of uncertainty 132

4-52: Comparison of sliding surface: offline PID-like FSMC and online PID-like

FSMC in the presence of uncertainty 133

4-53: Comparison of actuation torque: offline PID-like FSMC and online PID-like


4-54: Comparison of steady state error: offline PID-like FSMC and online PID-like


4-55: Comparison of RMS error: offline PID-like FSMC and online PID-like FSMC


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LIST OF ABBREVIATIONS

SMC Sliding Mode Controller

FSMC Fuzzy Sliding Mode Controller

FLC Fuzzy Logic Controller

CTC Computed Torque Controller

FCTC Fuzzy Computed Torque Controller

PD Proportional plus Derivative

PI Proportional plus Integral

PID Proportional-Integral-Derivative

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CHAPTER 1

INTRODUCTION

1.1 Motivation and Background

A critical component to any robot is the controllers that control the motion of the system.

These controllers sit between the high level task and path planning and the actuators that

comprise the physical robot. When functioning properly, they rarely define the system to

the same level as the high level software, which determines the tasks the robot can

complete, or the actuators that define the physical performance, but without highly

capable controllers, the full potential of both these systems will never be realized. In this

research main challenge is to design of a robust controller for multi input and multi

output (MIMO), non-linear, and time variant, uncertain dynamic systems. The

complexities of the tasks require the design of mechanical architectures and robot arm

with non-linear behaviour. These factors are:

Time-varying parameters based on tear and wear.

Simplifying assumptions in system modelling which give rise to un-

modelled dynamic parameters.

External disturbances and noise measurement, which generate

uncertainties.

Robot Manipulator is divided into two main groups, namely, serial link robot

manipulators and parallel link robot manipulators. The PUMA robot Manipulator is from

the serial link group and in this type of robot the links and joints are serially connected

between the base and end-effector. The study of robot Manipulator is sorted into two

main subjects, which are kinematics and dynamics. The study of kinematics part is

important for the design of controllers that can be used in pragmatic applications.

Dynamic modelling is used to illustrate the behaviour of robot Manipulator (e.g., MIMO,

non-linear, uncertain parameters), to assist in the design of non-linear conventional

controllers such as a conventional CTC and a SMC and is also used for simulation.

Dynamic Modelling can explain some of the dynamic parameters, which affect system

behaviours. According to the Armstrong [1], control of PUMA arm with a linear

behaviour is one of the difficult aspects of this research.

To control a PUMA arm, three aspects are very important:

Stability: A system is called stable if for any bounded input signal the

output of the system will stay bounded. Therefore the limitation of

output deviation is very important in any design.

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Robustness: A robust method achieves a robust and stable performance

in the presence of uncertainty and external disturbance. A system is

robust when it works well under different conditions and external

disturbances.

Reliability: Reliability is when a system demonstrates resistance to

failure and is dependable. As part of the control of non-linear and

uncertain systems, reliability plays an important role and most of model-

based controllers are reliable.

As a result, the design of a controller based on these three factors is the main challenge in

this work. Based on control theory, controllers for PUMA arm are divided into two main

groups, namely, conventional control theory and intelligent control theory. In

conventional control theory a system performs based on the non-linear dynamic

parameters of the PUMA arm and these are subdivided into two main categories: the

linear control method and the non-linear control method. In contrast, intelligent control

theory works based on the application of Artificial Intelligence (AI) to control situations

and it is free of the non-linear dynamic parameters of PUMA arm. An important aspect

of this part of the research is to select the best methodology when so many control

techniques are available.

According to the dynamic formulation of PUMA arm, they are uncertain and there exists

strong coupling effects between the joints. The problem of coupling effects plays an

important role to obtain the best performance from a PUMA arm. In a linear controller

this difficulty can be reduced by using the following two methods:

Limiting the performance of the system according to the required

velocities and accelerations. However, modern applications demand

faster and lighter robot manipulators.

Use a high gear ratio (e.g., 250 to 1) at the mechanical design step. In this

method the financial price paid is increased due to the extra gears.

Therefore the linear type of controller such as a PD, PI or PID is considered as unlikely

to provide good results and performance.

Conventional non-linear control theories are highly sensitive to the behaviour of a system

and work based on cancelling the decoupling and non-linear terms of the dynamic

parameters of equipment such as robot arm. CTC and SMC are two non-linear

conventional controllers, which have been introduced by many researchers to the control

of robot manipulators [3-8].

The CTC is one of the effective non-linear controllers, which can be applied to control a

robot Manipulator [3,7,8]. Consequently, to achieve good performance, linearisation and

decoupling without using many gears, feedback linearisation (CTC) methodologies are

presented. To design a CTC, an accurate dynamic model of a PUMA arm plays an

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important role. To model an accurate dynamic system, the modelling of complex

parameters is needed to form the structure of the dynamic model of the system. It may be

very difficult to include all the complexities in the system dynamic model [14-16].

Dynamic parameters may not be constant over time and measuring the acceleration term

can be very expensive. Thus this problem is a significant aspect of the study to select a

suitable CTC as the main controller in this research. To solve the problems associated

with a pure CTC, an intelligent CTC such as a FCTC [14, 16] or other type of

conventional controller such as a SMC can be applied.

To eliminate the actual acceleration measurement and also the computation burden as

well as achieve stability, efficiency and a robust controller, a SMC is introduced in this

section. This controller works very well in certain and partly uncertain conditions [8,

18,19] and has two important subparts, a switching part and an equivalent part. The

switching part of the controller is used to design suitable tracking performance based on

very fast switching and plays an essential role to achieve good trajectory performance in

all the joints. However this part is very important in uncertain conditions but it is liable to

the chatter phenomenon, which can degrade system performance. The chatter

phenomenon can cause some important mechanical problems [18]. The second subpart in

a SMC is the equivalent part, especially in uncertain conditions. The SMC is a non-linear

model based controller and the equivalent part is a dynamic formulation of a PUMA arm

which is used in the control formulation to eliminate the decoupling and non-linear terms

of the dynamic parameters of each link [8, 19]. However this part is essential for

reliability but under uncertain conditions or highly non-linear dynamic systems it can

cause problems. It is known that the conventional SMC is a robust, stable and reliable

controller but there are three main issues that limit its use, namely, the equivalent part

related to the dynamic equation of the PUMA arm, the computation of the bounds of

uncertainties and the chatter phenomenon [20-22].

The problem of the equivalent non-linear dynamic formulation of a PUMA arm is not a

simple task and in this research FLC is used to reduce the difficulties associated with this

issue. According to the literature, the fuzzy logic methodology is used to solve the chatter

phenomenon and also the non-linear dynamic formulation under uncertain conditions.

Pure FLC have problems in the presence of uncertainty conditions (robustness) and pre-

define the inputs/output gain updating factors. To solve the conventional SMC and pure

FLC issues, two main methodologies have been introduced by researchers [21-22]. These

are:

The design of a Fuzzy sliding mode controller (FSMC)

The design of a sliding mode Fuzzy controller (SMFC)

Most of the researchers have used FLC as an intelligent methodology. According to the

literature the FSMC is a robust, non-linear controller and it works based on the sliding

mode theory to eliminate the non-linear dynamic formulation [26]. The SMFC is also a

robust controller and the main controller is used to increase the system robustness [25].

According to the literature in a comparison between a SMFC and a FSMC, the number of

rule based situations in the SMFC is lower than for the FSMC but it is sensitive to the

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sliding surface slope coefficient and implementation of this method is inappropriate

compared to the FSMC.

The literature describes two main methodologies to reduce or eliminate chatter [23-25]:

The linear (saturation) boundary layer method

The non-linear artificial intelligence based method

However, eliminating the switching discontinuous function in a SMC is used in much of

the earlier research but it can cause a loss of robustness of control and accuracy.

Uncertainties are very important challenges and cause overestimation of the bounds. At

this point if the sliding surface is equal to zero and if it is chosen as the desired sliding

surface, the dynamics of the PUMA arm are derived for a sliding surface and if a

switching function is used to reduce the problem of uncertainty then the linearisation and

decoupling through the use of feedback, not gears, can be realised. Based on the above

discussion, a SMC is selected as the main controller so as to reduce all the problems to

FLC and linear control theory in the presence of a discontinuous function. This also

allows modification by using an on-line tuning method, which can be designed and

applied to a PUMA arm.

1.2 Problem Statement

The PUMA arm is a serial link device with six degrees of freedom which means the

PUMA dynamic formulation is highly non-linear, time variant, MIMO, uncertain and

there exists strong coupling effects between the joints. The aim is to design a linear

behaviour controller to reduce or cancel the decoupling as well as to improve the

stability, robustness and reliability as the most important objectives. To achieve these

goals, in the first part a linear controller is investigated with two limitations. The first

limitation is reducing the output velocity and acceleration and the second limitation is the

need for a system design based on a high gear ratio. From this a linear type of controller,

such as a PD or PID cannot provide good performance. Hence non-linear control

methodology is investigated to achieve acceptable velocity and acceleration, linearisation

and decoupling without using many gears. A CTC is one of the possible non-linear

controllers that are available. This controller works based on acceleration measurements

but this can be very expensive, which is an issue. The second difficulty when using a

CTC is related to accurate dynamic modelling of the PUMA arm. This is because the

calculation of an accurate dynamic model of the PUMA arm is very important in the

design of a CTC, but it may be very difficult to include all the complexities in the system

dynamic model. To eliminate the actual acceleration measurement and also to ease the

burden of accurate computation of the robot dynamics of the PUMA arm as well as to

gain stability, efficiency and robustness in the controller, a SMC is evaluated in the

following section.

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A conventional SMC is a non-linear, model based, stable, robust and reliable controller.

This controller is a strong candidate in order to design a system to withstand uncertainties

and external disturbances. Although this type of controller is used in many applications,

there are three main issues limiting the application of a conventional SMC in this

research:

The chatter phenomenon

The equivalent part related to the dynamic equation of a PUMA arm

The computation of the uncertainties problem in a chatter-free equivalent

estimation SMC

The first problem in the design of a robust SMC is to reduce or eliminate the chatter

phenomenon, because this problem causes heating and oscillation in the mechanical parts

of the system. Many researchers have found ways to reduce the chatter but they have also

lost system stability based on their methods. In this research the reduction or elimination

of chatter in order to maintain robustness is one of the main objectives. The switching

function causes the chatter but it is one of the significant parts of the design of a robust

and high speed SMC. In the SMC, the slope of the sliding surface (λ) is the second factor

to control the chatter. As a result one of the main tasks in the first objective is to reduce

or eliminate the chatter in the SMC based on the design of parallel linear control

methodology and a discontinuous part. The SMC and linear control methodologies are

robust based on the Lyapunov theory. The stability of the Lyapunov theory has been

proven in proposing a chatter-free SMC based on switching theory.

The second problem for improving the SMC for the PUMA arm is the non-linear

dynamic sliding mode formulation related to the highly non-linear dynamic equation.

This problem is not a simple mission. Consequently, to solve this issue, FLC is used as a

parallel controller with a chatter-free SMC as a model-based FSMC. In a model-based

FSMC, fuzzy logic is used as an estimator to eliminate the dynamic uncertainties. To a

design FLC, a PID-like FLC is evaluated. Such a device has three inputs, Proportional

(P), Derivative (D), and Integrator (I), which causes the number of the rules in the rule

base to increase. This obviously increases the number of calculations required. To solve

the number of rules in the rule base in the fuzzy model-base SMC, a parallel strategy is

evaluated based on a parallel structure of a PD-like FLC and PI-like FLC. In the next

step, the difficulty of the design of the PI and PD fuzzy rule tables will be explored.

The design of two types of rule tables is very difficult. Therefore the PD type rule table is

used and a PI-like FLC is extracted from the PD-like FLC. In this research the PID-like

FLC is replaced by a PD-like FLC with the integral term in the output. This method

requires the design of only a PD type rule table for the PD-like FLC and the PI-like FLC.

The PID-like FSMC can be updated based on an online tuning of the slope of the sliding

surface. In order to reduce the online computational burden, the PID-like FLC is also

used for online tuning of the slope of the sliding surface which improves the stability and

robustness compared to a boundary layer SMC.

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The third challenge in this research is the uncertainty problem. Uncertainty is a very

important issue and causes an extremely high estimation of the bounds. To solve this

problem, the selection of a desired sliding surface and 𝑠𝑖𝑔𝑛 function play a vital role and

if the dynamics of the PUMA arm are derived from the sliding surface then the

linearisation and decoupling through the use of feedback, not gears, can be realised. In

this state, the derivative of the sliding surface can help to decouple and linearise the

closed-loop PUMA arm that would be expected in CTC. Linearisation and decoupling by

the above method can be obtained in spite of the lack of quality of the PUMA arm

dynamic model, which is in contrast to the CTC that requires an exact dynamic model of

the system. It is a well-known fact that the uncertainties can be very well compensated by

an on-line tuning PID-like FLC and sliding surface slope tuning. To compensate for the

uncertainties fuzzy logic theory is a good candidate, but the design of a FLC with perfect

dynamic compensation in the presence of uncertainty is not trivial. Therefore, in this

research, uncertainties are estimated by discontinuous feedback control and the linear

part controller is added to eliminate the chatter. To increase the bounds of uncertainty,

fuzzy gains and sliding surface slope coefficients will be tuned by an on-line tuning

method. The above discussion gives the rational for selecting the proposed methodology

in this research.

1.3 Objectives

The design of robust control with the minimum coupling effects forms one of the main

challenges in this study. Therefore this research has the following objectives:

To design a robust chatter-free conventional SMC based on a parallel linear

SMC.

To design a model-reference PID-like FSMC with a minimum rule base in

order to solve the non-linear and uncertain equivalency problems.

To improve the system performance as well as reduce the number of rules

in the rule base of a PID-like FSMC by tuning the slope of the sliding

surface on-line.

1.4 The Scope of Work

This research focuses on the design of a minimum computation burden online-tuning

chatter-free PID-like FSMC with application to control a PUMA arm. We have to use a

system, which identifies very well for the dynamic and kinematic formulation. PUMA

arm is popular in academic and industrial because of MIMO and nonlinear. The dynamic

and kinematic formulations of a PUMA arm are extracted from the Armstrong [1]. All

parts of this research are designed and implemented in MATLAB/SIMULINK software.

This research is tested under conditions of limited uncertainty and external disturbance.

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1.5 Contributions

According to the Armstrong [1], the PUMA arm with serial links and six DOF has highly

non-linear dynamic equations, MIMO, time variant dynamic equations, uncertainty and

there exists strong coupling effects between the joints. Consequently, there is a need for

minimal coupling effects in order to obtain a stable, robust and reliable controller to be

used to control this system. Applying the following four methods can reduce the problem

of the coupling effects:

Limiting the performance of the system according to the required velocities

and accelerations even though current applications demand faster and lighter

robot manipulators.

Using a high gear ratio (e.g., 250 to 1) at the mechanical design step. In this

method the financial price paid is increased due to the gears.

Linearisation and decoupling without using many gears based on feedback

linearisation methodology by measurement actual acceleration.

The proposed methodology

In the linear control methodology, to reduce the coupling effects that limit the

performance usually a high gear ratio is applied. However, this produces an expensive

and slow PUMA arm. To reduce the coupling effects based on a CTC two problems

emerge. These are the need for an accurate dynamic model, which it is very difficult to

achieve, and measurement of the actual acceleration which is very expensive. To reduce

the coupling effects based on the proposed methodology then both of the above issues

have to be handled. In the proposed methodology the desired sliding surface is selected

and a 𝑠𝑖𝑔𝑛 function plays a vital role. If the dynamics of the PUMA arm can be derived

from a sliding surface, then linearisation and decoupling through the use of feedback, not

gears, can be realised. In this state, the derivative of the sliding surface can help to

decouple and linearise the closed-loop PUMA arm dynamics that are expected in CTC.

Linearisation and decoupling by the above method can be realised in spite of the lack of

quality of the PUMA arm dynamic model, which is in contrast to the CTC method that

requires an exact dynamic model of a system. It is a well-known fact that if the

uncertainties are very well compensated there is no need to use the discontinuous part,

which causes chatter. To compensate for the uncertainties then FLC is a good candidate,

although the design of a FLC with perfect dynamic compensation in the presence of

uncertainty is non-trivial and most of the time appears to be impossible. As a result,

uncertainties are estimated by discontinuous feedback control and a linear part controller

is added to eliminate the chatter. To increase the bounds of uncertainty the fuzzy gains

and sliding surface slope coefficients will be tuned by an on-line tuning method.

1.6 Thesis Outline

This research is structured into following chapters:

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Chapter 1: Gives the Motivation and Background of the research, along with the

Problem Statement, Objectives, the Scope of Work, Contributions and the Thesis

Outline.

Chapter 2: This chapter starts with a review of the PUMA robot arm as a system. Then,

it presents the kinematics and dynamic formulation with extracts from the high impact

papers concerning system modelling and implementation. After that, it presents a review

of linear, conventional non-linear and soft computing non-linear controllers for PUMA

arm. The linear controller, CTC and SMC are selected for comparison.

Chapter 3: After comparing between the above PUMA arm controllers, the SMC is

selected. In this chapter the modification of the SMC is the main point of discussion. To

modify this powerful controller, the chatter phenomenon is removed in the presence of

the switching mode (sign) function. Then, the chapter continues by presenting the design

of a PID-like FSMC with a minimum rule base to modify the SMC to be able to cope

with the uncertainties. In the last part of this chapter, the modification of the PID-like

FSMC in the presence of uncertainty using an on-line tuning of the slope of the sliding

surface with a minimum computation burden is discussed.

Chapter 4: Presents the controller test and result analysis. In the first part of this chapter,

three types of conventional controller are compared in order to select the best one. Then,

the chapter continues by modifying the selected controller boundary layer for chatter-free

operation and the proposed chatter-free methods are compared using multi-tests. Next,

the second objective is assessed, namely the PID-like FSMC is tested and evaluated.

Subsequently the third objective is considered in which the online tuning PID-like SMC

is tested and analysed.

Chapter 5: Draws the conclusion and future works.

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