DECENTRALIZED SLIDING MODE CONTROL FOR AN …eprints.utm.my/id/eprint/5962/1/HaszuraidahIshakMFKE2007.pdfSliding Mode Control theory and the utilisation of Matlab / Simulink software

DECENTRALIZED SLIDING MODE CONTROL FOR AN

ELECTROHYDRAULIC ROBOT MANIPULATOR

HASZURAIDAH ISHAK

A project report submitted in partial fulfilment of the

requirements for a award of the degree of

Master of Engineering (Electrical-Mechatronics and Automatic Control)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

MAY 2007

iii

This thesis is especially dedicated to my dearest father, mother and family

for their love, blessing and encouragement ...

iv

ACKNOWLEDGEMENT

Alhamdulillah, I am greatly indebted to Allah SWT on His mercy and

blessing for making this project successful.

I would like to express my deepest gratitude and thanks to Professor Dr.

Johari Halim Shah Osman, my honourable supervisor, for his continuous guidance,

committed support and invaluable advice throughout my study.

I wish to thank Associate Professor Dr. Mohamad Noh Ahmad and

Associate Professor Dr. Yahaya Md Sam for their guidance and facilitation on the

Sliding Mode Control theory and the utilisation of Matlab / Simulink software.

I sincerely thank to all lecturers who have taught me, for the lesson that has

been delivered. Not to mention, to all my friends, thank you for sharing useful idea,

information and moral support during the course of study.

Last but not least, I would like to express my sincere appreciation and

gratitude to my parents, who are always there when it matters most.

v

PUBLICATION

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

to conference:

1. J.H.S Osman, H. Ishak. A Decentralized Sliding Mode Tracking Controller

for Hydraulic Robot Manipulators. The 1st International Conference on

Control, Instrumentation, and Mechatronics Engineering (CIM). 2007.

Johor, Malaysia. (Accepted for Oral Presentation and Publication).

2. S.Z Nordin, H. Ishak, J.H.S Osman. Sliding Mode Tracking Controller for

Hydraulic Manipulators with Numerical Analysis. 2ND International

Conference on Mathematical Sciences (ICoMS). 2007. Johor, Malaysia.

(Accepted for Oral Presentation and Publication).

vi

ABSTRACT

This thesis is concerned with the problems of modelling and controlling of a

3 DOF electrohydraulic robot manipulators. The control of electrohydraulic robot

manipulator is challenging due to the dependence of system parameters on variables

such as displacement and velocity, on the geometry and inertia of the links,

uncertainties associated with gravity, coriolis and centrifugal forces, variations in

payload handled by the manipulator, and environmental influences. To overcome

these problems, an integrated mathematical model of the 3 DOF electrohydraulic

robot manipulators is treated as a large-scale uncertain system models using the

known parameters of the robot. Decentralized control concept is used in this study

where the uncertain system is treated as large-scale system which composed of a set

of interconnected uncertain subsystems. A variable structure control (VSC) strategy

is utilized to overcome the inherent high nonlinearity in the system dynamics under

decentralized and centralized frameworks. In each of the approach, a variant of the

VSC known as the Sliding Mode Control (SMC) is adopted to ensure the stability of

the system dynamics during the sliding phase and to render that the system

insensitive to the parametric variations and disturbances. The performance and

robustness of the proposed controller is evaluated through computer simulation by

using Matlab and Simulink. The results proved that the controller has successfully

provided the necessary tracking control for the 3 DOF electrohydraulically driven

robot manipulator system.

vii

ABSTRAK

Tesis ini bertujuan untuk mengenengahkan model matematik dan teknik

kawalan bagi robot berkuasa hidro. Pengawalan robot berkuasa hidro adalah lebih

rumit disebabkan sifat sambungan mekanikal dan motornya yang tidak linear,

parameter yang berubah-ubah, ketidaktentuan beban dan kesan perangkai. Untuk

mengatasi masalah ini, model bersepadu untuk tiga darjah kebebasan robot berkuasa

hidro ditukar menjadi suatu sistem berskala besar tak pasti berdasarkan kepada had-

had parameter sistem. Reka bentuk kawalan berasaskan kepada pendekatan kawalan

ternyahpusat digunakan dalam simulasi ini dengan menganggap sistem robot sebagai

suatu sistem berskala besar, yang mempunyai model bersepadu yang boleh

dipecahkan menjadi beberapa sub-sistem yang saling terhubungkait. Strategi

kawalan struktur berubah (VSC) diadaptasi untuk mengatasi ciri-ciri rumit yang

terdapat dalam robot berkuasa hidro menggunakan konsep ternyahpusat dan sepusat.

Didalam setiap pendekatan ini, dua pengawal penjejakan menggunakan konsep

kawalan gelincir telah dicadangkan, di mana pengawal pertama menggunakan

konsep sepusat, manakala pengawal kedua menggunakan konsep ternyahpusat

Kawalan ragam gelincir (SMC) iaitu variasi daripada kawalan struktur berubah telah

dipilih untuk memastikan kestabilan sistem semasa fasa gelincir tanpa dipengaruhi

parameter yng berubah-ubah dan ketidaktentuan beban. Pencapaian kaedah ini

dinilai melalui simulasi komputer. Keputusan membuktikan bahawa, strategi

kawalan ini berjaya dalam membekalkan kawalan laluan/ trajektori yang diperlukan

untuk sistem lengan robot berkuasa hidro.

viii

CONTENTS

CHAPTER TITLE PAGE

TITLE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

PUBLICATION v

ABSTRACT vi

ABSTRAK vii

CONTENTS viii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF SYMBOLS xviii

LIST OF ABBREVIATIONS xx

1 INTRODUCTION 1

1.1 Robot Manipulator System 1

1.2 Electrohydraulic Robot Manipulator 4

1.3 Research Objective 9

1.4 Scope of Research 10

1.5 Research Methodology 10

1.6 Structure and Layout of Thesis 12

ix

2 MATHEMATICAL MODELING OF ELECTROHYDRAULIC

ROBOT MANIPULATOR 14

2.1 Introduction 14

2.2 Dynamic Equation and State Space Representation

of Electrohydraulic Actuator 15

2.3 Dynamic Equation of Robot Manipulator

Mechanical Linkage 21

2.4 Integrated Dynamic Model of the Electrohydraulic

Robot Manipulator 23

2.5 Dynamic Model of 3 DOF Electrohydraulic

Robot Manipulators 26

2.5.1 Dynamic Equation of the Electrohydraulic

Motors for the 3 DOF Robot Manipulator 28

2.5.2 Dynamic Equation of 3 DOF Robot

Manipulator Mechanical Linkage 31

2.5.3 Integrated Dynamic Model of the Three DOF

Electrohydraulic Robot Manipulator 35

2.6 Summary 40

3 DECENTRALIZED SLIDING MODE

CONTROLLER DESIGN 42

3.1 Introduction 42

3.2 Decentralized Sliding Mode Control Strategies 43

3.3 Electrohydraulic Robot Manipulator as a

Large-Scale Uncertain System 45

3.4 Problem Formulation for Decentralized SMC 52

3.4.1 System Dynamics during Sliding Mode 54

3.4.2 Sliding Mode Tracking Controller Design 55

3.5 Summary 57

x

4 SIMULATION 58

4.1 Introduction 58

4.2 Trajectory Generation 58

4.3 Simulation Study 60

4.4 Controller Parameters Selection 61

4.5 Tuning Algorithm 62

4.6 Simulation using Centralized Sliding Mode

Controller 64

4.61 Numerical Computation and Selection

of Controller Parameters 64

4.7 Simulation Decentralized Sliding Mode

Controller 72

4.71 Numerical Computation and Selection

of Controller Parameters 72

4.7.2 Comparison of the Centralized SMC &

Decentralized SMC 80

4.7.3 Effect of Load Variation 87

4.7.4 Effect of the Controller Parameter 90

4.7.5 Effect of Sliding Surface Constant, C 97

4.7.6 Effect of Sampling Time 102

4.7.7 Effect of Closed-loop Poles 106

4.7.8 Control Input Chattering Suppression 110

4.6 Summary 115

5 CONCLUSION 117

5.1 Conclusion 117

5.2 Suggestion For Future Work 118

REFERENCES 120

xi

LIST OF TABLES

TABLE NUMBER TITLE PAGE

2.1 Range of Operation of the Mechanical Linkage 27

2.2 Parameters of the Mechanical Linkage 27

2.3 Parameters of the Hydraulic Actuator 28

3.1 Value of Elements in Matrices 50

4.1 Order of Extrapolation for Chattering Suppression 110

xii

LIST OF FIGURES

FIGURE NUMBER TITLE PAGE

1.1 Schematic diagram of a hydraulic system and its

components 2

1.2 Schematic diagram of a spool valve in a neutral position 3

2.1 Physical Model of an Electrohydraulic Servo Control

System 16

2.2 Schematic diagram of the Gear Train Connecting the

Motor and the Load 18

2.3 Three DOF Hydraulically Driven Robot Manipulator 26

4.1 Desired Joint Position Profile 59

4.2 Desired Joint Velocity Profile 60

4.3 Simulation Flow Chart 61

4.4 Joint 1 tracking response (angle) using centralized SMC

tracking controller 66





4.7 Joint 1 tracking response (velocity) using centralized

SMC tracking controller 2 67





4.10 Joint 1 control input using centralized SMC


xiii





4.13 Joint 1 sliding surface using centralized SMC






4.16 Joint 1 tracking response (angle) using decentralized

SMC tracking controller 74





4.19 Joint 1 tracking response (velocity) using decentralized






4.22 Joint 1 control input using decentralized SMC






4.25 Joint 1 sliding surface using decentralized SMC






xiv

4.28 Joint 1 tracking error (angle, 0kg) using Centralized

and Decentralized SMC 81





4.31 Joint 1 tracking error (velocity, 0kg) using Centralized


















4.40 Joint 1 tracking error (angle) with mass variation 87



4.43 Joint 1 tracking error (velocity) with mass variation 89



4.46 Joint 1 tracking response (angle) with unsatisfied

controller parameter 91



xv



4.49 Joint 1 tracking error (velocity) with unsatisfied






4.52 Joint 1 control input with unsatisfied






4.55 Joint 1 sliding surface with unsatisfied






4.58 Joint 1 tracking error (angle) with different

sliding surfaces 99


sliding surfaces 99


sliding surfaces 100

4.61 Joint 1 tracking error (velocity) with different






4.64 Joint 1 tracking response (angle) with different

sampling time 103

xvi


sampling time 103


sampling time 104

4.67 Joint 1 tracking response (velocity) with different

sampling time 104


sampling time 105


sampling time 105


closed-loop poles 107











4.76 Control input for each joint using Solver Ode14x Set 1 111



4.79 Joint 1 tracking error (angle) using variation order of

Solver Ode14x 113


Solver Ode14x 113


Solver Ode14x 113

4.82 Joint 1 tracking error (velocity) using variation order of

Solver Ode14x 114

xvii


Solver Ode14x 114


Solver Ode14x 115

xviii

LIST OF SYMBOLS

SYMBOL DESCRIPTION

1. UPPERCASE

A(*,*) system matrix for the integrated direct drive robot arm

ΔA(*,*) matrix representing the uncertainties in the system matrix

B(*,*) input matrix for the intagrated direct drive robot arm

ΔB(*,*) matrix representing the uncertainties in the input matrix

Bmi viscous damping coefficient of ith actuator

C constant matrix of the PI sliding surface

Dmi volumetric displacement of ith actuator

Jmi ith motor inertia

Ii moment of inertia of ith link

Kqi flow gain in ith actuator

Kti total leakage coefficient in ith actuator

Kvi servo valve gain

N number of joints

Psi supply pressure in ith actuator )(tSδ a continuous function used to eliminate chattering

iLT load torque for ith motor

U(*) N x 1 control input vector for a N DOF robot arm

Vti

total compressed volume in ith actuator

X(*) state vector for the integrated electrohydraulic manipulator

Z(*) error state vector between the actual and the desired states of

the overall system

(*)T transpose of (*)

xix

||(*)T|| Euclidean norm of (*)

2. LOWERCASE

aij ijth element of the integrated system matrix A(*,*)

bij ijth element of the integrated input matrix B(*,*)

g gravity acceleration (m.s2)

li length of the ith manipulator link (m)

mi mass of the ith manipulator link (kg)

t time (s)

3. GREEK SYMBOLS

α norm bound of continuous function H(*)

β norm bound of continuous function E(*)

eiβ

effective bulk modulus in ith actuator

θ& joint displacement (rad)

θ&& joint velocity (rad/s)

θ&&& joint acceleration (rad/s2)

dθ& desired joint angle (rad)

dθ&& desired joint velocity (rad/s)

dθ&&& desired joint acceleration (rad/s2)

σ Integral sliding manifold

τ time interval for arm to travel from a given initial position to a final

desired position (seconds)

xx

LIST OF ABBREVIATIONS

CTC Computed Torque Control

DC Direct Current

DOF Degree of Freedom

LHP Left Half Plane

PID Proportional Integral Derivative

SMC Sliding Mode Control

1

CHAPTER 1

INTRODUCTION

1.1 Robot Manipulator System

Industrial robots have gained a wide popularity as essential components for

the realization of automated manufacturing systems. Reduction of manufacturing

costs, increase of productivity, improvement of product quality standards and last

but not least, the possibility of eliminating harmful or alienating tasks for the human

operator in manufacturing system, represent the main factors that have spearhead the

spreading of robotics technology in a wide range of applications in manufacturing

industry [1].

An industrial robot is constituted by a mechanical structure or manipulator

that consists of sequence of rigid bodies (links) connected by means of articulation

whether revolute or prismatic joints and this manipulator is characterized by an arm

that ensures mobility, a wrist that confers dexterity and an end effector that performs

the task required of the robot, actuators that set the manipulator in motion through

actuation of the joints while the motors employed are typically electric and

hydraulic, and occasionally pneumatic, sensors that measure the status of the

manipulator and if necessary the status of the environment and a control system

(computer) that enables control and supervision of manipulator motion [1].

Although electrically driven robots are widely used in an increasing number

of applications, there are many industrial tasks where hydraulic actuators can be

used advantageously. For special applications such as for very large robots and civil

2

service robots, hydraulic actuator may be an appropriate choice [2]. Machinery in

construction, forming, mining, forestry industry, heavy load motion control and

mobile equipment applications as well as large flight simulators take the advantage

of the high power to weight ratio, possible speed reversals and continuous operation,

the stiffness and short response time of hydraulic drives.

Electrohydraulic system uses low power electrical signals for precisely

controlling the movements of large power pistons and motors. The interface between

the electrical equipment and the hydraulic (power) equipment is called ‘hydraulic

servo valve’. These valves used in the system must respond quickly and accurately.

A schematic diagram of a typical hydraulic system is shown in Figure 1.1.

Figure 1.1: Schematic diagram of a hydraulic system and its components

A servo valve is created when a servomotor is attached to the spool valve

and the servo valve. The servo valve together with the hydraulic actuator will form

the hydraulic servomotor. A simple movement of the spool valve controls the

motion of the actuator. As the spool moves up and down, it opens the supply and

returns to the port through which the fluid travels to the cylinder or return to the

reservoir as shown in Figure 1.2. The amount of the supply fluid and the

displacement of the cylinder can be controlled by adjusting the size of these ports

3

opening. Similarly, the flow rate of the supply fluid and the velocity of the cylinder

can be controlled by adjusting the rate of the ports opening [2].

Figure 1.2: Schematic diagram of a spool valve in a neutral position

In electrohydraulic manipulator system, each joint is driven by a hydraulic

servomotor. A higher control input voltage will produce larger valve flow from the

servo valve into the hydraulic motor. This will eventually results in a faster

rotational motion of the motor and thus the path (position and the orientation) of the

manipulator can be done in a specified time. The timed path is called trajectory of

the manipulator’s end effector [3]. However, it is difficult to precisely control the

position of electrohydraulic robot both theoretically and practically due to the

nonlinearities and coupling effects present in the system.

The control variable for the DC motor is either motor voltage or current that

is proportional to the actuation torque. The hydraulic actuator on the other hand, the

control voltage or current signal to the valve of hydraulic actuator controls the speed

of the actuator rather than its force or torque. The system also has large extent of

parametric uncertainties due to the large variations of inertial load and the change of

bulk modulus caused by the entrapped air or change of temperature. Besides, the

system may also have large extent of lumped uncertain nonlinearities including

external disturbances and unmodeled friction forces. Therefore, the

4

electrohydraulically driven revolute robot manipulator dynamics are more complex

than electrically driven manipulator dynamics. All of these factors make the

modeling and control of such system a challenging task [4].

In all industrial robot applications, completion of a generic task requires the

execution of a specific motion that prescribed by the desired path trajectory and

performance. However, when faster trajectories are demanded, the performance of

the manipulator will be worst. Therefore, the correct execution is entrusted to the

control system which shall provide the joint actuators of the manipulator with the

command consistent with the desired motion trajectory. Thus, an accurate analysis

of the characteristics of the manipulator dynamics is therefore a necessary premise

to finding motion control strategies. In general, motion control problem consists of

obtaining the dynamics model of the electrohydraulic robot manipulator in which

these models will be used to determine the control laws or strategies to achieve the

desired system response and performance.

1.2 Electrohydraulic Robot Manipulator

Nowadays, hydraulic robots are widely used in the construction and mining

industries. However, majority of earlier work in the design of the control laws for

manipulators deal with electrically actuated manipulators. In terms of hydraulic

actuators, comparatively less work has been done [5]. However, by taking the

dynamics of the actuator alone is not sufficient to represent the dynamic of hydraulic

manipulator, since it does not take into account the arm dynamic forces such as the

inertia forces, the coriolis and centrifugal effects and also the gravity effects that will

affect the performance of the controller. Tracking performance of the system can be

improved by implementing mechanical linkage dynamic model in the controller

design since it is part of the overall control system. This approach has been

successfully shown in many electrical robots in the past [6].

5

[7] has used 6 DOF hydraulic robot and the models incorporate manipulator

dynamics. The limitation with this project is that it did not include the hydraulic

motor nonlinear spring stiffness, viscous damping and inertia. Same goes with [8]

who has incorporated manipulator dynamics in developing 2 DOF hydraulic robot

arm models, but the hydraulic motor nonlinear spring stiffness, viscous damping and

inertia are not taken into account in the design. [9] on the other hand, have used

hydraulic cylinders with the application to robot manipulators. The problem with the

study is that it did not incorporate the mechanical linkage dynamics in the design

model.

[5] has incorporated both rigid body dynamics and hydraulic actuator

dynamics into the design. However, the mathematical model presented was not in

state-space form. For some recent development on mathematical model derivation of

this type of manipulator, [10] has developed the mathematical model in state-space

form for the electrohydraulic robot manipulator that integrated both the manipulator

dynamics and hydraulic actuator dynamics including the hydraulic motor nonlinear

spring stiffness, viscous damping and inertia.

The mathematical model derived in [10] will be used in this project to

synthesize different control laws in providing the trajectory tracking control of the 3

DOF electrohydraulically driven revolute robot manipulator.

The robot control problem revolves around the computation of the required

actuator inputs in order to maintain the dynamic response of manipulator in

accordance with the desired response and performance. This control problem will

become complex due to the nonlinear dependence of system parameters on variables

such as displacement and velocity, on the geometry and inertia of the links,

uncertainties associated with gravity, coriolis and centrifugal forces, variations in

payload handled by the manipulator, and environmental influences.

In classical control theory, it is assumed that the control actions are

undertaken by a single controller that has all the available information about the

6

system and treat each joint of the manipulator as a simple linear servomechanism as

in most of industrial robots, whereby the simple controller like Independent Joint

Control (IJC), proportional plus derivative (PD), or proportional plus integral plus

derivative (PID) controllers are adopted. In these methods, the nonlinear, coupled

and time-varying dynamics of the mechanical linkage of the robot manipulator have

been excluded and completely ignored, or assumed as disturbances. Manipulators

that have been controlled by this method usually move at slow speeds with

unnecessary vibrations. In general, the method is only suitable for relatively slow

manipulation and limited precision tasks [11]. However, when the manipulator joints

are moving simultaneously and at high speed, the nonlinear coupling effects and the

interaction forces between the manipulator links may affect the performance of the

overall system and increase the tracking error. The disturbances and uncertainties

such as variable payload in a task cycle may also reduce the tracking quality of the

robot manipulator system [12].

Therefore, control strategies for high speed robotic system are of great

interest for both industrial and academic fields, whereby various advanced and

sophisticated control techniques have been proposed by numerous researchers in

providing the necessary tracking trajectory of robot manipulator and at the same

time guaranteeing the stability of the system. In general, these strategies can be

divided into two categories; the non-model based or usually known as Artifical

Intelligence approaches and model based approaches. While for the structures of

these controllers can be grouped into three categories; the centralized, decentralized,

and multilevel hierarchical. For the model based approaches, among the major

control approaches considered in the literature for the uncertainties nonlinear

systems are the Adaptive Control method [13], Lyapunov based control and

Variable Structure Control [14]. While for the non-model based approaches, where

the knowledge of the mathematical model is not needed, Fuzzy Logic system,

Genetic Algorithm and Neural Networks controls have become important research

topics [15].

In [8], PID and Computed Torque Control (CTC) strategies have been

implemented for the hydraulic robot and the performance of both methods did not

7

give satisfactory results. As mentioned earlier, the limitation with PID controllers is

that they are not meant for high speed robots and in situations that require precise

trajectory tracking. While for the CTC, it only can be applied to robots allowing

joint torque control. Moreover, the problem with CTC is essentially based on exact

robot arm dynamic model; the explicit use of an incorrect robot model will affect the

performance of control. He further synthesized the Kinematic Compensation Control

integrating a feedforward kinematic compensation and conventional regulatory

control techniques. Even though the system shows good experimental result, it still

lacks mathematical stability proof.

[16] has proposed a link-space pressure feedback controller for Stewart type

hydraulic manipulator. However, this approach lacks stability proofs that are

important from both theoretical and implementations points of view. [17] has

developed a generalized predictive control algorithm for hydraulic control system

but the limitation of this approach is that it relies heavily on online parameter

estimation and consequently, is computationally expensive. [18] on the other hand,

have adopted a Lyapunov based Model-based Adaptive Control for hydraulic

manipulator. Even though the technique possesses mathematical stability proof but it

needs persistent excitation and pressure feedback. A strategy based on Backstepping

approach has been developed by [19] to provide necessary position tracking for the

hydraulic robot. However, the proposed strategy also relies on online computation

for converting into task-space coordinates. Furthermore, it is said to be sensitive to

sensor noise, hence high-quality measurements are needed. To overcome this

drawback is by introducing heuristic limitation of time derivatives in the control law

so that the influence of sensor noise in the simulations reduces significantly, but may

deteriorate the control performance.

Non-adaptive control techniques such as computed torque methods and

optimal control have serious disadvantages, namely complex controller structure,

excessive on-line computation, and sensitivity to uncertainties and nonlinearities in

the system. These difficulties become more complicated by their being centralized

approaches. Adaptive control methods tackle the robot control problem fairly

effective, but the controller is greatly complicated. In much of the works on adaptive

8

control of manipulators, the justification for this added complexity is not addressed

[20]. Despite the fact that the centralized approaches have attained significant

achievements to improve the tracking performance of robots, but when the degree of

freedom (D.O.F) of robots is large, they stumble upon time consuming computations

and complexity of the controller structure. Furthermore, very few results could be

transferred into practice due to the high implementation cost. Besides, the

centralized approach treats the robot manipulator as a single entity plant, which is

unfavorable and impractical for implementation and maintenance of the controllers

[21]. Therefore control methods that reduce these problems by changing the problem

to control smaller scale subsystems by using the decentralized controllers have the

advantage of computation simplicity and low-cost hardware setup. For this reason,

improving the performance of the trajectory tracking problem of robot manipulator

through decentralized control is an interesting topic.

Variable Structure Control utilizes a high-speed switching control law to

drive the nonlinear plant’s state trajectory onto a specified and user-chosen surface

in the state space and to maintain the plant’s state trajectory on this surface for all

subsequent time [22]. This property of remaining on the switching surface once

intercepted is called a sliding mode. The plant dynamics will be restricted to this

surface to represent the controlled system’s behavior. Hence, it is suitable for

complex systems and is insensitive to parameters variations and uncertainties. SMC is

particularly well suited for the manipulator control problem for the following

reasons. First, the application of SMC does not require an exact knowledge of the

system dynamics, provided there is no un-modeled structural uncertainty. This

property is desirable since the complexity of the manipulator dynamics makes the

exact calculation of the dynamics infeasible if not impossible. Second, when the

SMC is applied, the performance of the system can be made insensitive to bounded

disturbances. This property is important in rejecting effects due to the Coulomb and

viscous frictions. It is also important when the manipulator is carrying payloads

because the payload exerts at the robot end-effector can be translated into forces or

disturbances at each of the joints. Thus, the application of the SMC technique results

in a performance that is robust with respect to disturbances and modeling errors,

while provides accurate tracking [21].

9

This project will extend the control strategies proposed in controlling two

coupled pendulums in [23] to provide trajectory tracking control of a three DOF

electrohydraulically driven revolute robot manipulator. The approach stabilizes a

system through a fast switching global control to render that the system to behave as

a second linear time invariant system which can be chosen to be stable. This method

incorporated the ideas of variable structure system with the technique of pole

placement in a decentralized nature. This is done by constructing a decentralized

sliding mode controller which will force the original nonlinear interconnected

uncertain subsystems to behave as a second linear interconnected uncertain

subsystem which has had its pole placed in the left half of the s-plane by pole

placement method.

1.3 Research Objective

The objectives of this project are:

i) To decompose the 3 degree of freedom (DOF) electrohydraulic robot

manipulator into interconnected uncertain subsystems;

ii) To design a decentralized robust controller based on Sliding Mode Control

(SMC) for the 3 degree of freedom (DOF) electrohydraulic robot

manipulator;

iii) To evaluate the performance of the system based on the proposed controller

and to compare the performance of the decentralized robust controller with a

centralized robust controller.

10

1.4 Scope of Research

The scope of work for this project includes:

i) To decompose the integrated nonlinear dynamic model of the 3 DOF

revolute electrohydraulic robot manipulator as described in [10] into a set of

interconnected subsystem by treating it as a large-scale system. The

interconnected model will be transformed into interconnected uncertain

subsystems models using the known parameters of the robot;

ii) To synthesize a decentralized tracking trajectory controller based on a

variant of the VSC approach, which is the SMC for large-scale uncertain

system. This proposed controller will be applied to the 3 DOF

electrohydraulically driven revolute robot manipulator models developed in

part (i);

iii) A centralized tracking trajectory controller will be designed based on the

deterministic approach for an uncertain system, where the transformation-

free SMC will be utilized;

iv) Simulation studies will be done to investigate the performance of the

proposed controller and the effectiveness of the decentralized SMC as

compared to the centralized SMC in providing the necessary position

tracking control for the system. These will be done using SIMULINK and

MATLAB 7.0.

1.5 Research Methodology

The research work is undertaken in the following three developmental stages:

a) Development of an interconnected uncertain system models of a 3 DOF

revolute hydraulic robot manipulator. The steps taken in this stage are:

11

i) Conduct literature review on the existing electrohydraulic robot

manipulator mathematical model in order to understand the

dynamics behavior of the system. Based on the information

obtained, the integrated model will be decomposed into three

interconnected subsystems in order to apply the decentralized

tracking controller;

ii) Conduct literature review on the existing techniques for

decomposing the system into interconnected uncertain

subsystems.

b) Application of a decentralized robust controller based on VSC technique to

the robotic system. The steps taken in this stage are:

i) Conduct literature review on the existing control technique for

robotic systems;

ii) Conduct literature review on the existing robust control technique

based on decentralized Sliding Mode Control algorithm;

iii) Synthesize the decentralized SMC technique cited from [23] to

the robotic system. The procedures performed in this stage are:

• Decomposition of the complete model into an large-scale

uncertain model

• Definition of each local sliding surface

• Determination of the system dynamics during Sliding Mode

• Establishment of the final control law for each subsystem

c) Perform computer simulation of the proposed controller by using MATLAB

and SIMULINK to investigate the effectiveness of the decentralized SMC as

compared to a centralized SMC.

12

1.6 Structure and Layout of Thesis

This report is organized into five chapters. In Chapter 2, the formulation of

the mathematical modeling of the integrated electrohydraulic robot manipulator, in

which, first, a general dynamic model of a hydraulic actuator dynamics and a rigid

manipulator link are described separately. Then, based on these equations, an

integrated model in state space representation is presented. At the end of the chapter,

the complete integrated dynamic model of three DOF electrohydraulically driven

revolute robot manipulator is determined.

Chapter 3 deals with the controller design using decentralized sliding mode

control strategies with specific application to the plant described in Chapter 2.

Firstly, by treating the electrohydraulic robot manipulator as a large-scale system

and each joint as a subsystem, a linear interconnected uncertain system is developed

to represent the manipulator as interconnected subsystems. Secondly, based on the

known allowable range of operation of the manipulator and the maximum allowable

payloads, the nominal and bounded uncertainties of the system may be developed

and the manipulator can be represented as an interconnected uncertain subsystems.

Finally, the decentralized SMC controller is designed for the system.

Chapter 4 outlines the performance of the proposed control system which is

evaluated by means of computer simulation study through MATLAB/SIMULINK.

The simulation begins with a pre-specified desired trajectory for each of the

manipulator joints in terms of joint displacement, velocities and accelerations. In

order to analyze the effectiveness of the decentralized SMC, centralized SMC

strategy is used as a mean of comparison. Conclusion on the robustness of the

approach in handling the nonlinearities, uncertainties and couplings effect present in

the system and the necessary trajectory tracking control of the plant is also made and

discussed based on the results obtained.

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This thesis ends with Chapter 5, where the summary of the synthesized

approach while undertaking this project is described. Recommendations for future

work are also presented at the end of the chapter.

Documents

DECENTRALIZED SLIDING MODE CONTROL FOR AN …eprints.utm.my/id/eprint/5962/1/HaszuraidahIshakMFKE2007.pdfSliding Mode Control theory and the utilisation of Matlab / Simulink software