A Practical Optimal Controller For Gantry Crane Systems.

A PRACTICAL OPTIMAL COTROLLER FOR GANTRY CRANE SYSTEMS

MOHD ZULKHAIRI BIN RUSLAN

This report is submitted in partial fulfillment of the requirements for the award of Bachelor Electronic Engineering (Industrial Electronics) With Honours.

Faculty of Electronic and Computer Engineering Universiti Teknikal Malaysia Melaka

UNIVERSTI TEKNIKAL MALAYSIA MELAKA

FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER BORANG PENGESAHAN STATUS LAPORAN

PROJEK SARJANA MUDA II

Tajuk Projek : A PRACTICAL OPTIMAL CONTROLLER FOR GANTRY CRANE SYSTEMS

Sesi

Pengajian : 2008/2009

Saya MOHD ZULKHAIRI BIN RUSLAN mengaku membenarkan Laporan Projek Sarjana Muda ini disimpan di Perpustakaan dengan syarat-syarat kegunaan seperti berikut:

1. Laporan adalah hakmilik Universiti Teknikal Malaysia Melaka.

2. Perpustakaan dibenarkan membuat salinan untuk tujuan pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan laporan ini sebagai bahan pertukaran

antara institusi pengajian tinggi.

4. Sila tandakan ( √ ) :

SULIT*

(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972)

TERHAD* (Mengandungi maklumat terhad yang telah ditentukan oleh organisasi/badan di mana penyelidikan dijalankan)

TIDAK TERHAD

Disahkan oleh:

……….. ………..

(TANDATANGAN PENULIS) (COP DAN TANDATANGAN PENYELIA) Alamat Tetap:

NO.26 JLN 12/4, TMN CHERAS JAYA 43200 BATU 9 CHERAS

SELANGOR

iii

“I hereby declare that this report is the result of my own work except for quotes as

cited in the references”

Signature :………

Author : MOHD ZULKHAIRI BIN RUSLAN Date :

iv

“I hereby declare that I have read this report and in my opinion this report is

sufficient in terms of the scope and quality for the award of Bachelor of Electronic

Engineering (Industrial Electronics) with Honours”

Signature :………..

Supervisor’s Name :

v

vi

ACKNOWLEDGEMENT

Alhamdulillah, thanks to ALLAH upon blessing along my project and I am able to finish this project. Although there were troubles along the way, I preserved. I want say thanks to all my family, especially to my parent who are supporting me and give a high devise to complete this project. I would like also say thanks to my

supervisor Puan Azdiana Binti Mohd Yusop who’s guided and give some idea in my

work. Thanks also to my entire friend that has help and supporting me along the course of finishing this project. Thanks you all.

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ABSTRACT

In this project, the optimal controller system is used to fast anti-swaying and precise positioning in gantry crane system with highest speed. The optimal controller in this project can be shown based on the state differential equations for the swaying payload. To guarantee the precise positioning of the cart, the anti-swaying controller is redesigned to adapt both the requirement. A linear quadratic regulator (LQR) system is design by using MATLAB programming as a practical optimal controller in gantry crane system. So, the payload can be placed at the appropriate position with high efficiency.

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ABSTRAK

Teknik kawalan optimal di dalam projek ini digunakan adalah untuk menghapuskan ayunan beban dan mengawal kren gantri supaya dapat meletakkan beban tepat pada tempatnya dengan kalajuan yang tertinggi. Di dalam projek ini, teknik kawalan optimal dapat ditunjukkan melalui persamaan pembezaan terhadap ayunan beban. Sebagai jaminan pedati dapat digerakkan tepat pada tempat yang

dikehendaki, sebuah sistem “linear quadratic regulator” (LQR) direka untuk

mengawal “gantry crane” pada tahap kawalan optimal dengan menggunankan

perisian MATLAB. Oleh yang demikian, beban dapat diletakkan pada tempat yang sesuai dengan ketepatan yang tinggi dan tanpa ayunan pada beban.

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TABLE OF CONTENTS

CHAPTER CONTENTS PAGES

PROJECT TITLE i

DECLARATION iii

DEDICATION v

ACKNOWLEDGEMENT vi

ABSTRACT vii

ABSTRAK viii

TABLE OF CONTENTS ix

LIST OF TABLE xii

LIST OF FIGURE xiii

LIST OF APPENDIX xiv

I INTRODUCTION 1

1.1 Project Introduction 1

1.2 Objective 3

1.3 Problem Statement 3

1.4 Scope Project 4

1.5 Methodology Flowchart 5

x

II LITERATURE REVIEW 7

2.1 The Gantry Crane Overview 7

2.2 Optimal Control Theory 10

2.3 The Optimal Linear Regulator 12

III RESEARCH METHODOLOGY 14

3.1 The Gantry Crane Model 14

3.2 System Dynamics 16

3.3 Mathematical Modeling Techniques 18

3.3.1 Newton’s law of motion 18

3.3.2 The energy method 19

3.4 Derivation of the Equation of Motion 21

3.5 Simulation System Block 28

3.6 Interfacing 29

3.7 RTWT Set Up 30

IV RESULT AND DISCUSSION 31

4.1 Input Signal 31

4.2 Cording Command 32

4.3 The Output Position and Sway Angle 35

V CONCLUSION AND SUGGESTION 43

5.1 Conclusion 43

xi

REFERENCE 45

xii

LIST OF TABLE

NO TITLE PAGES

3.1 Parameter value for gantry crane 17 4.1 Analysis Parameter Optimal Control Graph 38 4.2 Analysis Parameter PID Controller Graph 41

xiii

LIST OF FIGURE

NO TITLE PAGES

1.1 The Gantry Crane 2

1.2 Methodology flowchart 5

2.1 A real-world crane system in the harbor 8

2.2 The Model of Gantry Crane 9

3.1 Model of gantry crane 15

3.2 Flowchart of Gantry Crane interface 16

3.3 The modeling of the Gantry Crane 17

3.4 Closed-loop Block system with LQR feedback controller 28

3.5 Interfacing connection 29

3.6 RTWT block system interfacing 30

4.1 Input signal 32

4.2 Output position for LQR controller 36 4.3 Output sway angle for LQR controller 37

4.4 Output position for PID controller 39

xiv

LIST OF APPENDIX

NO TITLE PAGES

A COMPONENTS OF TROLLEY 47

CHAPTER I

INTRODUCTION

1.1 Project Introduction

The crane is a name of machine that used to lift the payload at one location to desire locations. In mechanical sector, their have many type of crane. The type of crane that has used in this project is a gantry crane. In many case, many engineer were design a system of gantry crane to solve the problem that has occur before. The problem that has to solve is vibration and swing payload when operating. The gantry

crane can’t operate properly during lift a payload and maybe an accident will be happen. So, the system that has design of engineer is an initiative to solve that’s

problem.

In this project, the optimal controller systems is used to control the gantry crane system to eliminate swaying angle as fast as possible and place the payload at appropriate location by control the speed of crane. In industrial sector, the optimal control techniques have apply in many function of system such as power supply, motor torque, amplifier and others. While in gantry crane systems, this technique is implementing to manage the time of accelerating and decelerating crane. Where this technique exactly focus on decelerating time when the gantry crane is braking. After the gantry crane is move at high speed, payload is potentially producing the sway angle when the gantry crane is braking. So, the gantry crane systems should be design to control the speed decelerating time to avoid the swaying angle. In other

2

condition, the linear quadratic regulator is used to constant the speed during the gantry crane is decelerating.

Figure 1.1: The Gantry Crane

Figure 1.1 shows one example of gantry crane that is use at a harbor. This gantry crane actually picks up a container from ships to base or from base to a ship and then store it properly. The gantry crane always uses to hoist a big payload such as container at harbor. So, in this project a gantry crane model is redesign as similar with real gantry crane.

3

1.2 Objective

The objective of this project is to apply the technique of the optimal controller into the gantry crane and to move the payload to the required positions as fast as possible without swaying payload.

1.3 Problem Statement

In many mechanical and electrical parts that used a motor to control performance of machine has a problem to stop at desire level with high efficiency and safety. An optimal control strategy is important to control the acceleration and deceleration motor speed. In gantry crane system, the high speed in moving a payload will be provide a large swaying angle along travel to desire location. In high speed moving of crane, the speed of payload also increase base on speed of crane. So, swaying angle of payload is potential to become large from initial condition. This situation will cause an accident or crush to the payload.

Sometime a person has high skill and experience able to control the speed of crane to avoid large swaying angle. To overcome this problem, the optimal control technique is applied to the gantry crane system to control the speed of the gantry crane. Which mean this technique is required to control or manage accelerating and decelerating of speed gantry crane.

4

1.4 Scope Project

The scope of this project includes:

i). Do research about gantry crane characteristics

ii). Research and study of system dynamics in gantry crane. iii). Research and study about the optimal controller technique. iv). Study and design to create block input system.

5

1.5 Methodology Flowchart

Figure 1.2: Methodology flowchart Study the basic concept of gantry crane. Study and do research about optimal controller.

Simulation result Start

Derive state differential equation of payload.

Set the configuration parameter

Expect result Interface with MATLAB

Real time implementation.

Troubleshooting Experimental testing

Finish

NO YES

YES

NO Design optimal controller block system

6

1.6 Project Outline

This report describes the optimal control technique and how to apply the technique onto the gantry crane. In this report, it is consists of five chapters. Where in the chapter 1 is a brief introduction about the project including the objectives, problem statement, scope and methodology of project. Chapter 2 described about a literature review of recent work on optimal controller and application system and the factor sway angle. Chapter 3 is a part that shows detail about the project process constructed and how the equation is derived that used in this project also this chapter discusses what in methodology planning. The result of optimal control system will be describe in chapter 4 while comparison between optimal control (LQR) and PID controller will be compare in this chapter. Finally, chapter 5 is explaining about future work related with optimal control system and conclusion of entire project.

CHAPTER II

LITERATURE REVIEW

2.1 The Gantry Crane Overview

Cranes as one of the major equipments in industries, exists in most places from domestic industries to naval yards to warehouses, as one example shown in Figure 2.1. In these places the productivity of the activities depends on how efficiently the cranes are managed. One of the challenging in the control of the cranes is to deal with swaying phenomenon introduced by the trolley motion. This swaying not only reduces the efficiency of the cranes, but also can cause safety problem in the complicated working environment. In figure, it is a one the model of gantry crane that has design to do an experiment for control the Gantry Crane systems [19].

8

Figure 2.1: A real-world crane system in the harbor

Gantry cranes are widely used for transporting heavy loads and hazardous materials in building constructions. The crane should move the load as fast as possible without having any excessive payload motion at the final position. However, most of the common gantry cranes result in a swing motion when payload is suddenly stopped after a fast motion [20]. The swing motion can be reduced however; it is often time consuming processes which eventually affect the productivity (operational efficiency) in building constructions. Moreover, the gantry crane needs a skilful operator to manually control it using an experience to immediately stop the swing at the right position. Furthermore to unload, the operator has to wait until the load stops swinging. The failure in controlling crane might also cause accident and harm people.

The gantry crane systems also are widely used in harbors and factories for loading and unloading of goods. The crane systems are desired to be able to move the required positions as fast and as accurately as possible while placing the payload at the appropriate position. In addition to these two requirements, the payload swing angle should be kept as small as possible; otherwise, large payload swing during transport may cause damage to the payload itself and surrounding equipments or personnel. It is essential that pendulum oscillations are constrained both for safety reasons and for higher task execution speed [21].

9

Figure 2.2: The Model of Gantry Crane.

Figure 2.2 shows an example of a gantry crane model that is use to test a crane technique before it is implemented into real gantry crane machine. To obtain the best result Figure 2.2 is constructed with fully metal similar with a real gantry crane. The base of this gantry crane model must be firm to avoid vibration when moving the payload.

The gantry crane systems are constrained in terms of gantry travel and pendulum extension. The governing state equations for a gantry crane system with varying pendulum length are nonlinear and highly coupled. The challenges in the control design task of gantry crane system arise from the nonlinear coupling nature of the system. The gantry crane system has three degrees of freedom that need to be controlled-cart position, cord length and angular oscillations of the payload. However, there typically exist only two independent actuate on systems-motors to control cart position and pendulum length respectively [22].

10

2.2 Optimal control theory

Optimal control system is a one of technique that used in many type of control systems. As a theoretical, the linear quadratic control problem has its origins in the celebrated work of N. Wiener on mean-square filtering for weapon fire control during World War II (1940-45) [2, 3]. Wiener solved the problem of designing filters that minimize a mean-square-error criterion (performance measure) of the form

) ( 2 t e E

J (2.1)

where, e(t) is the error, and E{x} represents the expected value of the random variable x. For a deterministic case, the above error criterion is generalized as an integral quadratic term as

0 e'(t)Qe(t)dt

J (2.2)

where, Q is some positive definite matrix. R. Bellman in 1957 [4] introduced the technique of dynamic programming to solve discrete-time optimal control problem. But, the important contribution to optimal control systems was made in 1956 [6] by L. S. Pontryagin (formerly of the United Soviet Socialistic Republic (USSR)) and his associated, in development of his celebrated maximum principle described in detail

in their book [7]. Also, see a very interesting article on the “discovery of the

Maximum Principle” by R. V. Gamkrelidze [5], one of the authors of the original

book [7]. At this time in the United States, R. E. Kalman in 1960 [8] provided linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) theory to design optimal feedback controls. He went on to present optimal filtering and estimation theory leading to his famous discrete Kalman filter [9] and the continuous Kalman filter with Bucy [10]. Kalman had a profound effect on optimal control theory and the Kalman filter is one of the most widely used technique in application of control theory to real world problem in a variety of fields.

1.5 Methodology Flowchart

Figure 1.2: Methodology flowchart Study the basic concept of gantry crane.

Study and do research about optimal controller.

Simulation result Start

Derive state differential equation of payload.

Set the configuration parameter

Expect result Interface with MATLAB

Real time implementation.

Troubleshooting

Experimental testing

Finish

NO YES

YES

NO Design optimal controller block system

6

1.6 Project Outline

This report describes the optimal control technique and how to apply the technique onto the gantry crane. In this report, it is consists of five chapters. Where in the chapter 1 is a brief introduction about the project including the objectives, problem statement, scope and methodology of project. Chapter 2 described about a literature review of recent work on optimal controller and application system and the factor sway angle. Chapter 3 is a part that shows detail about the project process constructed and how the equation is derived that used in this project also this chapter discusses what in methodology planning. The result of optimal control system will be describe in chapter 4 while comparison between optimal control (LQR) and PID controller will be compare in this chapter. Finally, chapter 5 is explaining about future work related with optimal control system and conclusion of entire project.

CHAPTER II

LITERATURE REVIEW

2.1 The Gantry Crane Overview

Cranes as one of the major equipments in industries, exists in most places from domestic industries to naval yards to warehouses, as one example shown in Figure 2.1. In these places the productivity of the activities depends on how efficiently the cranes are managed. One of the challenging in the control of the cranes is to deal with swaying phenomenon introduced by the trolley motion. This swaying not only reduces the efficiency of the cranes, but also can cause safety problem in the complicated working environment. In figure, it is a one the model of gantry crane that has design to do an experiment for control the Gantry Crane systems [19].

8

Figure 2.1: A real-world crane system in the harbor

Gantry cranes are widely used for transporting heavy loads and hazardous materials in building constructions. The crane should move the load as fast as possible without having any excessive payload motion at the final position. However, most of the common gantry cranes result in a swing motion when payload is suddenly stopped after a fast motion [20]. The swing motion can be reduced however; it is often time consuming processes which eventually affect the productivity (operational efficiency) in building constructions. Moreover, the gantry crane needs a skilful operator to manually control it using an experience to immediately stop the swing at the right position. Furthermore to unload, the operator has to wait until the load stops swinging. The failure in controlling crane might also cause accident and harm people.

The gantry crane systems also are widely used in harbors and factories for loading and unloading of goods. The crane systems are desired to be able to move the required positions as fast and as accurately as possible while placing the payload at the appropriate position. In addition to these two requirements, the payload swing angle should be kept as small as possible; otherwise, large payload swing during transport may cause damage to the payload itself and surrounding equipments or personnel. It is essential that pendulum oscillations are constrained both for safety reasons and for higher task execution speed [21].

Figure 2.2: The Model of Gantry Crane.

Figure 2.2 shows an example of a gantry crane model that is use to test a crane technique before it is implemented into real gantry crane machine. To obtain the best result Figure 2.2 is constructed with fully metal similar with a real gantry crane. The base of this gantry crane model must be firm to avoid vibration when moving the payload.

The gantry crane systems are constrained in terms of gantry travel and pendulum extension. The governing state equations for a gantry crane system with varying pendulum length are nonlinear and highly coupled. The challenges in the control design task of gantry crane system arise from the nonlinear coupling nature of the system. The gantry crane system has three degrees of freedom that need to be controlled-cart position, cord length and angular oscillations of the payload. However, there typically exist only two independent actuate on systems-motors to control cart position and pendulum length respectively [22].

10

2.2 Optimal control theory

Optimal control system is a one of technique that used in many type of control systems. As a theoretical, the linear quadratic control problem has its origins in the celebrated work of N. Wiener on mean-square filtering for weapon fire control during World War II (1940-45) [2, 3]. Wiener solved the problem of designing filters that minimize a mean-square-error criterion (performance measure) of the form

) ( 2 t e E

J (2.1)

where, e(t) is the error, and E{x} represents the expected value of the random variable x. For a deterministic case, the above error criterion is generalized as an integral quadratic term as

0 e'(t)Qe(t)dt

J (2.2)

where, Q is some positive definite matrix. R. Bellman in 1957 [4] introduced the technique of dynamic programming to solve discrete-time optimal control problem. But, the important contribution to optimal control systems was made in 1956 [6] by L. S. Pontryagin (formerly of the United Soviet Socialistic Republic (USSR)) and his associated, in development of his celebrated maximum principle described in detail in their book [7]. Also, see a very interesting article on the “discovery of the

Maximum Principle” by R. V. Gamkrelidze [5], one of the authors of the original

book [7]. At this time in the United States, R. E. Kalman in 1960 [8] provided linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) theory to design optimal feedback controls. He went on to present optimal filtering and estimation theory leading to his famous discrete Kalman filter [9] and the continuous Kalman filter with Bucy [10]. Kalman had a profound effect on optimal control theory and the Kalman filter is one of the most widely used technique in application of control theory to real world problem in a variety of fields.