STATIC AND DYNAMIC CONTROL OF NETWORK BASED

ROTARY INVERTED PENDULUM SYSTEM

ZAID BIN YAAKOB

A project report submitted in partial fulfilment of the

requirements for the award of the degree of

Master of Engineering (Electrical-Mechatronics & Automation Control)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

JUNE 2013

iii

Dedicated to …..

My beloved wife, Kahtijah

Who has so much faith in me

My son Adam

Who is in the phase of growing up perfectly

Love you always

Also to my beloved father and mother, Yaakob and Robisah

I could have never done it without you

To all my friends, who have stood by me through thin and tick

I treasure you all

Thanks for showering me with love, support and encouragement

Life has been wonderfully coloured by all of you

Alhamdulillah...Syukur kepada ALLAH s.w.t

iv

ACKNOWLEDGEMENT

I would like to thank to Allah Almighty for blessing and giving me strength to

accomplish this thesis and to the Prophet Rasulullah Muhammad SAW. Firstly, I would

like to express my sincere appreciation to my supervisor Dr. Abdul Rashid Husain, for

the encouragement, guidance, critics, advices, motivation, idea, and friendship from the

beginning to the end of this project. Without having his continual support and interest,

this thesis would not have been the same as present here.

Special thanks to my wife Kahtijah bt Muhammad and my son Adam b Zaid. My

colleagues in Process Control Research room: Amirah and Badrul; for the collaboration

in knowledge-sharing with each other, their views and tips are useful indeed. My sincere

appreciation also extends to all of the lecturers in CIED department FKE UTM, who

have opened my mind seeing the wonderful world of Control System and

Instrumentation. I am also grateful to all my friends in MARA Japan Industrial

Institute(MJII) and Damai group who have stood by me through thin and tick .

Finally, my heartfelt thanks go to all of my family, whose sacrifice, support,

love, caring inspired me to overcome all the difficulties throughout my entire academic

life. This project report processes would not be successful without having their patience,

love, and dedication.

v

ABSTRACT

The control of the Rotary Inverted Pendulum (RIP) is a classic control problem

that is explored often as a project in control courses due to its easily developed dynamics

combined with its complexity of control design. The aim of this project is to delve into

the control of this system to achiev2 the control objectives which is balancing the

inverted pendulum base on CAN Network Control System. This system is composed of

a pendulum attached to the end of a rotary arm controlled by a motor. The motor used is

a Quanser SRV-02, whose characteristics are known completely. The motor consists of a

servomotor coupled with a gear-chain. The aim is to keep the motor at a particular

provided angular position. However, the major disadvantages of using NCS application

are the delay introduced by the network traffic and package drop-out. Many researchers

have directed their works towards solving these two issues by proposing new control

algorithms or optimization of scheduling methods due to the fact that advantages offered

by NCS far outweigh its centralized counterpart. In this thesis, investigation of the

impact of network induced delays on the step response performance aspects of state

space control designs LQR for a NCS with time delays. The vector of state-feedback

control gains ‘K’ is used to deal with the degrade performance of a rotary inverted

pendulum and also deal with the network traffic in network control system. Thus s

simulation performed to show the effectiveness of the system. Eventually the result

prove that the proposed controller gains improve the performance if RIP in a network

induce delay.

vi

ABSTRAK

Pendulum Songsang Bermotor adalah masalah kawalan klasik yang

sering diterokai sebagai projek dalam kursus-kursus kawalan kerana dinamik yang

dibangunkan dengan mudah digabungkan dengan kerumitan reka bentuk kawalan.

Dalam projek ini, kami menyelidiki kawalan sistem ini untuk mencapai objektif-objektif

kawalan yang mengimbangi asas bandul terbalik dengan menggunakan Rangkaian

Kawalan Sistem CAN. Sistem ini terdiri daripada bandul disertakan dengan hujung

lengan putar dikawal oleh motor. Motor yang kita gunakan adalah Quanser SRV-02

Loji, yang ciri-ciri yang dikenali sepenuhnya. Motor terdiri daripada servo motor

ditambah dengan gear rantai. Tujuannya adalah untuk memastikan motor pada

kedudukan tertentu disediakan sudut. Walau bagaimanapun, kelemahan utama

menggunakan aplikasi NCS adalah kelewatan yang diperkenalkan oleh trafik rangkaian

dan pakej keciciran. Ramai penyelidik telah mengarahkan kerja-kerja mereka ke arah

menyelesaikan kedua-dua isu-isu dengan mencadangkan algoritma kawalan baru atau

pengoptimuman kaedah penjadualan kerana hakikat bahawa kelebihan yang ditawarkan

oleh NCS jauh melebihi rakan berpusat. Tesis ini, mengkaji kesan kelewatan disebabkan

rangkaian kepada aspek langkah prestasi sambutan negeri kawalan ruang reka bentuk

LQR untuk sistem kawalan rangkaian dengan kelewatan masa. Vektor gain matrik 'K'

yang digunakan untuk meningkatkan prestasi system disebabkan kelewatan pada system

dan juga pada keaadaan apabila trafik rangkaian tinggi pada rangkaian

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

TITLE

DECLARATION

DEDICATION

ACKNOWLEDGEMENTS

ABSTRACT

ABSTRAK

TABLE OF CONTENTS

LIST OF FIGURE

LIST OF SYMBOL

LIST OF APPENDICES

i

ii

iv

v

vi

vii

viii

xi

xiii

xiv

1. INTRODUCTION

1.1 Background

1.2 Problem Statement

1.3 Objective of Project

1.4 Scope of Project

1.5 Significant of Project

1.6 Thesis Outline

1

1

2

3

4

4

5

2. LITERATURE REVIEW

2.1 Review of previous research in NCS

2.2 Description of Network Control System

6

6

8

viii

2.2.1 Field Bus

2.2.2 Delay in Network Control System

2.2.3 Network Induced Delay in NCS

2.2.3 Packets Dropouts

2.2.4 Effects of delays in the loop

2.2.6 NCSs Structures

2.3 Control Area Network (CAN)

2.4 TRUETIME Toolbox

2.4.1 Adding disturbing traffic over the

network

2.5 Inverted Pendulum

9

10

13

14

15

15

17

17

19

19

3. METHODOLOGY

3.1 Project Implementation

3.2 Inverted Pendulum

3.2.1 Rotary Inverted Pendulum SRV02-Series

3.2.2 RIP Mathematical Modelling

3.2.2.1 Free Body Diagram Method

3.2.2.2 Lagranian Formulation method

3.2.2.3 Output Torque formulation

3.2.2.4 Linearization

3.2.2.5 State Space representation

3.3 Controller Design

3.3.1 Open Loop Poles

3.3.1 Linear Quadratic Regulation (LQR)

3.3.2 Observer Based control

3.4 Simulink modelling

3.4.1 Simulink Model of Linearize Plant

3.4.2 Simulink Model of Non Linearize Plant

3.4.3 Verification Linear and Non Linear Simulink

model

22

22

24

27

28

30

33

34

35

35

38

39

39

40

44

44

45

46

47

ix

3.4.4 Full State Feedback Control Simulink Model

3.4.5 Full State Estimator control Simulink model

3.4.6 NCS Full State Feedback Control Simulink

Model

3.4.6 NCS Full State Estimator Control Simulink

Model

48

49

50

51

4. RESULT AND DISCUSSION

4.1 Verification of the linear model against the

nonlinear model

4.2 Verification System with Controller

4.3 RIP Full State Feedback With and Without

NCS

4.4 Configuration With Delay State Variable

4.4.1 Gain Matrix Selection, K

4.5 RIP Full State Estimator With NCS

4.5.1 Configuration With Bandwidth

Network Disturbance

4.6 Summary

51

51

53

55

57

59

60

62

63

5. CONCLUSION AND FUTURE WORKS

5.1 Conclusion

5.2 Future Works

65

65

66

REFERENCES

Appendices A-D

68

71-76

x

LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 List of the terminology used in IPC 24

3.2 RIP Symbol description parameter 30

3.3 Typical parameter configuration of the system 37

4.1 Summary of the step response with and without NCS 57

4.2 Summary of the step response for different K value 60

4.3 Summary of the step response for FSF and FSE 61

4.4 Differentiation of the system with and without network traffic 63

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Example of a NCS application 2

1.2 Response feedback control system subject to delay in loop 3

2.1 Block diagram of a typical NCS. 7

2.2 Configuration and network delays for NCS formulation 7

2.3 NCS with various system components (controllers, actuators,

sensor etc.,)

9

2.4 Network connection(a) typical connection.(b) connection via

filed bus

10

2.5 Configuration of network topologies 10

2.6 A Typical Networked Control System 11

2.7 Timing Diagram of NCS Delay Propagation 12

2.8 Time Delay in NCS (Number 1,2,3…8 represent the a sequence

of data packets to be send to the controller).

13

2.9 Missing Data due to packet Drop Out 14

2.10 Data Out of Oder due to packet Drop Out 15

2.11 System performance degradations caused by delays in the loop 15

2.12 (a) Direct Structure of NCS, (b) Hierarchical Structure of NCS 17

2.13 CAN Bus Data Frame 18

2.14 TRUETIME Block Library 19

2.15 Block Kernel of interference 19

xii

2.16 The Broomstick Balancing Problem 20

2.17 Inverted Pendulum on Cart Problem 20

2.18 Real-world example that relates behaviour of an inverted

pendulums problem.(a): Rocket MAXUS 1 in starting position,

(b): Segway self-balancing vehicle.

21

3.1 Project implementation flow chat 23

3.2

free-body diagrams of the two elements of the inverted

pendulum system

24

3.3 Quanser-SRV-02 Rotary Inverted pendulum 28

3.4 Simplified model of the rotary inverted pendulum system 29

3.5 Free Body Diagram of the rotary inverted pendulum system 31

3.6 Full state feedback control system 38

3.7 Full State estimator using observer base design 41

3.8 The implementation of observer design 43

3.9 Linearize model of Rotary Inverted Pendulum 45

3.10 Non-Linear model of Rotary Inverted Pendulum 46

3.11 Verification of linear and non-linear plant 47

3.12 Full State Feedback Simulink design 48

3.13 Full State Estimator Simulink design 49

3.14 Conceptual design of the full state feedback 49

3.15 Conceptual design of the Observer system with NCS 50

4.1 Overlapped plot of Linear and Non-Linear model, theta θ 52

4.2 Overlapped plot of Linear and Non-Linear model, alpha α 52

4.3 Overlapped plot of alpha α and theta θ 53

4.4 Network scheduling signals 54

4.5 With and without NCS step response 55

4.6 Focusing step response over shoot 56

4.7 Focusing step response undershoot 56

4.8 State feedback is delay in the system, τs 57

4.9 Applying execution time 0.06 second to the system 58

4.10 Applying execution time 0.06 second to the system 59

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4.11 Differentiate the step response of the each setting of K. 60

4.12 Step response of the FSF versus FSE 61

4.13 Step response of the FSF versus FSE with interferences. 62

4.14 System with Rate of CAN speed reduce to 125k (bits/s) 63

5.1 Propose controller for future work 65

5.2 Proposed Two Rotary Inverted pendulum system for future

work

66

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LIST OF SYMBOLS

퐿 - Length of the pendulum

푚 - Mass of the pendulum arm

푟 - Mass of the pendulum arm

휃 - Servo gear angle

훼 - Pendulum angle

ℎ - Distance of pendulum

퐽 - Pendulum inertia

푉 - Velocity of Pendulum centre x-direction

푉 - Velocity of Pendulum centre y-direction

푔 - Standard gravity

휂 - Gearbox efficiency

휂 - Motor efficiency

퐾 - Motor torque constant

퐾 - Back emf constant

퐾 - Total gearbox ratio

푅 - Cylinder differential pressure

Vt - Motor armature resistance

xv

LIST OF APPENDICES

APPENDIX TITLE PAGE

A RIP Full State Feedback Control with NCS 71

B RIP Full State Estimator Feedback Control with NCS 73

C MATLAB source code for nonlinear RIP parameter 75

D MATLAB source code for RIP controlled with NCS 76

CHAPTER 1

INTRODUCTION

1.1 Background

Networked Control Systems (NCS) accumulates various field of study in

control system theory, data transmission and networking. The defining feature of an

NCS is that the data containing information is exchanged by a network between

control system nodes (sensors, controller, and actuator). Because NCS offers

feedback control system via a communication channel it has become one of the main

research focuses in academic studies and industry for many decades. Figure 1.1 is an

example of a system that incorporates with a communication network in the feedback

control loops. As a result makes the design and analysis more complex. Common

control theories with many ideal assumptions, such as synchronized control and non-

delayed sensing and actuation, must be re-evaluated before they can be applied to

NCSs. The issues that needs to be addressed while designing an NCS include,

network-induced delays that occurs while exchanging data among devices connected

to the shared medium, and packet losses, because of the unreliable network

transmission path, where packets not only suffer transmission delays but, even

worse, can be lost during transmission

2

Figure 1.1: Example of a NCS application

Many researchers have directed their works towards solving delay introduced by

the network traffic and package drop-out by proposing new control algorithms or

optimization of scheduling methods due to the fact that advantages offered by NCS

far outweigh its centralized counterpart[1]. This thesis examines the impact of

network induced delays on the step response performance aspects of state space

control designs with Linear Quadratic Regulator (LQR) for networked control

systems with time delays. The vector of state-feedback control gains ‘K’ is used to

deal with the degrade performance of a rotary inverted pendulum and also deal with

high network traffic in network control system.

1.2 Problem Statement

The existences of the NCS introduce time delay by the communication

messages or data between the NCS components. This delay will lead to the

instability of the system performance due to network traffic or data loss during the

transmission. Figure 1.2 response feedback control system subject to delay in loop.

3

Figure 1.2 Response feedback control system subject to delay in loop

The goal is to identify parameters that can be applied to optimize the

performance of the system. The performance of the controllers is illustrated using

RIP as it is an ideal experiment device to test the correctness and feasibility of new

control theory[2]. Furthermore, with the increasing trend in rising fieldbus and

industrial real time Ethernet technology, it is a meaningful research to connect the

RIP with the NCS.

1.3 Objectives of Project

The objectives of this project are:

1. To develop a nonlinear model of Rotary Inverted Pendulum

2. To develop a network RIP base on CAN network.

3. To analyze performance of the system for static and dynamic control

under various condition

4

1.4 Scope of Project

The scopes of this project can be outlined as:

1. Modeling of Rotary Inverted Pendulum in NCS based on CAN.

A motor driven SIMO dynamic system model of NCS based on CAN will

be developed. This is done based on existing model found in established

work.

2. Comparative Assessment and result analysis.

Various network-induced delay parameters will be introduced and a

comparative assessment between offline controls as reference is done to

analyze the control performance.

3. Computer simulation

The simulation will be performed using MATLAB and TRUETIME

Toolbox.

1.5 Significance of Project The existences of the control loop in network introduce time delay by the

communication messages/data between the NCS components. This delay will lead to

the instability of the system performance due to network traffic or data loss during

the transmission. When applying state space control designs with network control

system, parameters determining the state feedback control can be identified and

applied to optimize the performance of the system. By using Linear Quadratic

Regulation (LQR) method, the state-feedback control gain ‘K’ can be obtained and

those parameters will be used to control and achieve the desired performance of

Rotary Inverted pendulum with different delay parameter condition in a Network

5

Control System. In addition, to address the situation where not all state variables are

measured, a state estimator is designed and compared with different network

bandwidth disturbance percentage.

1.6 Thesis Outline This thesis consists of five chapters. It begins with the introductory chapter.

This chapter gives the brief description of the problem statement and background of

the Rotary Inverted Pendulum in Network control system, objectives, scope and

significance of the project.

Chapter two discusses the literature review and others related works from

previous existing modeling paradigm and technique to calculate and estimate the

delay parameters in Network Control System.

Chapter three includes design and methodology of the study. It contains

design of the system, modeling and procedure to design the static and dynamic

controller based on Rotary Inverted Pendulum.

Chapter four contains the results and discussion of the study for the system.

Verification of the plant, delay parameter implementation and propose parameter

value to optimize performance is described here.

Then, chapter six describes the conclusion and suggestion of the work for

future development.

68

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