OPTIMAL DYNAMIC INVERSION BASED CONTROL OF AN OVERHEAD

CRANE

AHMAD EDHAM BIN MOHAMMAD

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

UNIVERSTI TEKNIKAL MALAYSIA MELAKA FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER

BORANG PENGESAHAN STATUS LAPORAN

PROJEK SARJANA MUDA II

Tajuk Projek : OPTIMAL DYNAMIC INVERSION BASED CONTROL

OF AN OVERHEAD CRANE Sesi Pengajian : 2008/2009

Saya AHMAD EDHAM BIN MOHAMMAD 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: LOT P.T 11083, LRG 2 KANAN, JLN. GONG PASIR, 23000, DUNGUN TERENGGANU.

Tarikh: ……………………….. Tarikh: ………………………..

OPTIMAL DYNAMIC INVERSION BASED CONTROL OF AN OVERHEAD

CRANE

AHMAD EDHAM BIN MOHAMMAD

This report is submitted in partial fulfillment of the requirements for the award of

Bachelor of Electronic Engineering (Industrial Electronics) With Honours

Faculty of Electronic and Computer Engineering

Universiti Teknikal Malaysia Melaka

April 2009

iii

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

in the references”

Signature :………………………………………….

Author :AHMAD EDHAM BIN MOHAMMAD

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 :MDM. AZDIANA BINTI MD YUSOP

Date :………………………………………….

v

To my beloved family,

mum, dad, brothers and sisters,

thanks for your support and encouragement

that you have given in my life. Also to my supervisor,

thanks for your guide and the supports that been given

to me in completing this work. And also not

forget to all of my friend and people

around me for your support and

cooperation.

vi

ABSTRACT

A Methodology is proposed to control the transient and residual oscillation of a

payload carried by an overhead crane. The design approach is based on a linearised

model of the crane and consists of dampening the linearised system by an observer-

based controller and applying a dynamic inversion procedure in order to assure a

predetermined oscillation free polynomial motion law for the payload. Polynomials

functions are adopted in order to guarantee that the input function has a continuous

derivative of an arbitrary order. Moreover, the motion time can be minimized, taking

into account constraints on the actuator, by means of a simple bisection algorithm.

Parameter uncertainties are taken into account during the whole design procedure.

Simulation results, based on a nonlinear crane model, show how the method is also

effective when the payload is hoisted or lowered during the motion, and when friction

effects are considered.

vii

ABSTRAK

Satu kaedah telah dicadangkan untuk mengawal ayunan sementara dan ayunan

sisa satu muatan yang dibawa oleh satu kren bergerak ke atas. Pendekatan rekaan ini

adalah diasaskan oleh satu model kren yang dilinearkan dan mengandungi perlembapan

sistem yang dilinearkan secara satu pemerhati berpangkalan pengawal dan menggunakan

satu prosedur songsangan dinamik teratur bagi memastikan satu ayunan yang pratentu

mengikut usul hukum polinomial bebas untuk muatan. Fungsi-fungsi Polynomials

diambil dengan teratur untuk menjamin fungsi input mempunyai satu terbitan yang

berterusan dari satu perintah sembarangan. Tambahan pula, masa usul boleh

dikurangkan jika mengambil kira kekangan-kekangan di penggerak oleh cara sederhana

pembahagian dua sama algoritma. Ketidakpastian parameter juga diambil kira sepanjang

perlaksanaan seluruh reka bentuk. Hasil simulasi adalah berdasarkan satu model tidak

linear dan menunjukkan bagaimana kaedah ini adalah juga berkesan apabila muatan

dinaikkan atau direndahkan, dan apabila kesan-kesan geseran juga diambil kira.

viii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

BORANG PENGESAHAN STATUS LAPORAN i

PAGE TITLE ii

AUTHOR DECLARATION iii

SUPERVISOR DECLARATION iv

DEDICATION v

ABSTRACT vii

ABSTRAK vii

CONTENTS viii

LIST OF TABLES xii

LIST OF FIGURES xiii

LIST OF SYMBOLS xv

LIST OF APPENDIXS xvi

I INTRODUCTION 1

1.1 Introduction 1

1.2 Objective 3

1.3 Problems Statement 3

1.4 Scopes of work 4

1.5 Methodology 5

II LITERATURE REVIEW 7

ix

2.1 Optimal Dynamic Inversion Method 7

2.2 Luenberger Observer 8

2.3 Background on Gantry Crane 8

2.3.1 Types of Gantry Cranes 9

2.4 Motion Control System 11

2.4.1 Stepper Motor 12

2.4.1.1 Fundamentals of Operations 12

2.4.1.2 Stepper Motor Characteristics 12

2.4.1.3 Open-loop versus closed-loop commutation 13

2.4.1.4 Types of Stepper Motor 13

2.4.2 Operation principles of stepper motor 14

2.5 Data Acquisition Board (DAQ) 15

2.5.1 Acquisition of Data 16

2.6 Microcontroller 18

2.6.1 Programming Environment 19

2.7 Overview Microchip PIC 20

2.7.1 Data space (RAM) 21

2.7.2 Code Space 22

2.7.3 Word Size 22

2.7.4 Stacks 22

2.7.5 Limitation 23

2.8 Signal Conditioning (SCC-68) 24

III METHODOLOGY 26

3.1 Methodology 26

3.1.1 Stage 1 26

3.1.2 Stage 2 26

3.1.3 Stage3 28

x

3.1.4 Stage4 28

IV MODELING OF THE GANTRY CRANE SYSTEM 29

4.1 Assumption and Limitation 30

4.2 Modeling of a Gantry Crane 30

4.3 Modeling Techniques 31

4.4 Mathematical Modeling of a Gantry Crane 36

4.5 Controller Design 45

4.5.1 Observability and Controllability Test 45

4.5.2 Pole Placement 46

4.5.3 Dynamic Inversion-Based Control Design 49

4.5.4 State-Feedback Control Design 49

4.5.5 For 20 OS% Ts=5s 50

4.5.6 For 20 OS% Ts=1s 54

V SIMULATION RESULTS AND DISCUSSION 57

5.1 General SIMULINK Model of the Open Loop system 57

5.1.1 Nonlinear Model Function Block Parameters 58

5.2 Simulation Results of Open Loop System 59

5.2.1 Input Force 59

5.2.2 Sway Angle 60

5.2.3 Position of the Trolley 61

5.3 General Model of Closed Loop System 62

5.3.1 State Feedback Controller 63

5.4 Simulation Results of Closed Loop System 64

5.4.1 Graph Position of the Trolley for OS=20% Ts=5s 64

5.4.2 Graph Sway Angle for OS=20% Ts=5s 65

5.4.3 Graph Position of the Trolley for OS=20% Ts=1s 66

xi

5.4.4 Graph Sway Angle for OS=20% Ts=1s 67

5.4.5 Comparison Graph Position of the Trolley for

OS=20% Ts=5s and Ts=1s 68

5.4.6 Comparison Graph Sway Angle for OS=20%

Ts=5s and Ts=1s 69

VI HARDWARE IMPLEMENTATION 71

6.1 Microcontroller 71

6.1.1 Pin description 72

6.1.2 Microcontroller Schematic 74

6.1.3 L293D Motor Driver IC 76

6.1.4 Motor Driver Schematic 77

6.1.5 Rotation for Stepper Motor and Trolley Wheel 79

6.2 Hardware Implementation 79

VII CONCLUSION 90

7.1 Conclusion 90

7.2 Future Works 91

REFERENCES 93

xii

LIST OF TABLES

NO TITLE PAGE

5.1 Simulations result 70

6.1 Pins on PIC 16F84 microcontroller 74

6.2 Connection of Pins PIC 16F84 with other components 75

6.3 The connection of Pins IC L293D and its function 78

xiii

LIST OF FIGURES

NO TITLE PAGE

1.1 Project flow chart 6

2.1 Super-PostPanamax portainer crane 9

2.2 Workstation Gantry crane 10

2.3 Rail Mounted or EOT Gantry Cranes 11

2.4 Operation principles of stepper motor 15

2.5 PIC Microchip 19

2.6 PIC 21

2.7 Signal Conditioning (SCC-68) 24

2.8 SCC-68 Power Distribution Block Diagram 25

4.1 Gantry Crane Model 29

4.2 Block Diagram of Linear System 35

4.3 F(t) Approximated by sequence of pulses 36

4.4 Trolley Free Body Diagram 37

4.5 Load’s Free Body Diagram 37

4.6 Block Diagram Based on State Space Equation 42

4.7 Modified block diagram 42

4.8 Controllability and Observability test using M-file application 46

4.9 Eigenvalues of the crane system 47

4.10 Eigenvalues and eigenvector of the crane system 48

4.11 Find gain, K using M-File 52

4.12 Find integral gain, K5 using M-File 53

xiv

4.13 Find gain, K using M-File 55

4.14 Find integral gain, K5 using M-File 56

5.1 Open loop system for linearized model 58

5.2 Nonlinear Model function block parameters 58

5.3 Graph of Input Force vs. Time 59

5.4 Graph of sway angle vs. Time 60

5.5 Graph Position of the Trolley vs. Time 61

5.6 Nonlinear Model with feedback control system 62

5.7 State Feedback controller 63

5.8 Graph Position of the Trolley vs. Time for OS=20% TS=5s 64

5.9 Graph of Load Sway Angle vs. Time for OS=20% TS=5s 65

5.10 Closed Loop Trolley Position vs. Time OS=20% for Ts=1s 66

5.11 Closed Loop Load Sway Angle vs. Time for OS=20% Ts=1s 67

5.12 Comparison Graph Position of the Trolley Position 68

5.13 Comparison Graph Position of the Payload Sway Angle 69

6.1 PIC16F84A block diagram 72

6.2 Pins description for PIC16F84A 73

6.3 Microcontroller Schematic 74

6.4 IC L293D 76

6.5 Motor driver schematic 77

6.6 Stepper motor and run wheel diagram 79

6.7 Solver Configuration Parameter 80

6.8 Hardware Implementation task pane 81

6.9 Hardware Implementation task pane 81

6.10 Real Time Application task pane 82

6.11 Error Notification 83

6.12 The generating process in the Matlab window 89

xv

LIST OF SYMBOLS

M, mc- Trolley mass

m, ml- Payload mass

l - Length of the hoisting rope

Fx - Input force

G - Gravitational acceleration = 9.81ms-2

G - Centre point

x - Trolley position

.x - Velocity

..x - Acceleration

θ - Sway angle

.θ - Angular velocity

..θ - Angular acceleration

xvi

LIST OF APPENDIX

NO TITLE PAGE

1 Optimal Dynamic Inversion Based of an Overhead Crane 95

2 Anti-Sway Control of Container Cranes: Inclinometer,

Observer, and State Feedback 102

3 Project Gantt Chart 118

CHAPTER I

INTRODUCTION

In this chapter there will be a discussion on this project title of optimal dynamic

inversion based control of an overhead crane. The project introduction, project objective,

problem statement, and scopes of work and methodology will also be presented.

1.1 Introduction

The safety and efficiency of the operation of an overhead crane are generally

reduced by the transient sway and residual oscillation of either the empty hook or the

payload. In general, this problem is tackled by the experience and skill of the operators,

who try to impose a deceleration law that reduces the oscillation caused by the

acceleration. Moreover, a man is often tasked to stop the hook or the payload. Thus, the

performances of the system can be significantly improved by using appropriate

automatic control architecture, which is capable of reducing the swing effect and

minimizing the motion time in order to increase the through put of the crane.

However, the design of the controller is a challenging problem, since the system,

which can be regarded as a single-pendulum, is nonlinear (and hence, if a linearised

2

model is considered for the controller design, then the attained performances have to

verified against a complete nonlinear model) and the value of certain parameters such as

the rope length and the payload mass may significantly vary during the operations.

Moreover, in the minimization of the motion time of the payload the trolley driving

motor constraint have to be taken into account.

In many cases system uncertainties and actuator constraints are not taken into

account and often the controller design is done by optimizing only one side of the

problem either the traveling time of the payload is minimise or the swinging effect is

reduced. Therefore, it seems that a design technique that is capable of achieving

different goals in a unified frame work still lacking.

A methodology based on dynamic inversion, for the design of a robust

feedforward/feedback control scheme which allows us to significantly reduce the

transient sway and residual oscillation of the payload, whilst minimizing the traveling

time and taking into account the trolley’s actuator constraints. The methodology

basically consists of linearising system and dampening it by means of a robust state-

feedback controller. Then, after having defined a family of desired smooth polynomial

motion laws for the payload depend on the motion time, the corresponding family of

reference inputs is subsequently determined by inverting the nominal closed-loop system.

Finally, with a worst case approach, the motion time can be opportunely minimized

ensuring that limits on the trolley’s actuator are not exceeded.

In the literature, the use of dynamics procedures has been proposed for a variety

of output tracking problems for applications to mechanical systems.

3

1.2 Objective

The objective of this project is to develop an optimal dynamic inversion based

control for a gantry crane system where this system can reduce the transient sway,

residual oscillation, traveling time and reach the target position without vibration.

1.3 Problems Statement

Gantry cranes are widely used for factories, transportation, nuclear installation

and also construction. The crane has to move as fast as possible without causing any

excessive movement at the final position or during it moves. However, moving the

payload using the crane is not an easy task especially when strict specifications on the

swing angle and on the transfer time need to be satisfied. The swing motion when

payload is suddenly stopped after a fast motion can be reduced but very wasting time.

Moreover, the gantry crane needs a skilful and experience operator to control manually

for stopping the swing immediately at the right position. Beside this, the operator also

needs time to wait the string stop from vibration after movement the load. The vibration

is a serious problem in a mechanical system. A gantry crane system with inverse

dynamic method can used to solve this problem

If a linearised model is considered for the controller design, the attained

performances have to be verified against a complete non-linear model. The crane has to

move the load as fast as possible without causing any excessive movement at the final

position or during it moves. Moreover, in the minimization of the motion time of the

payload, the trolley driving motor has to be considered. In many cases, system

uncertainties and actuator constraints are not considered and often the controller design

is done by optimizing only one side problems either the traveling time or swinging effect.

So, the design based on dynamic inversion will encounter this problem.

4

1.4 Scopes of Work

During the project, there a scope of work that will guide student in their project.

It’s a guideline which student should attain to fulfill the requirement of project. The

scopes of work are listed as below:

i. Learn the basic concept of a dynamic inversion analysis.

ii. Develops the system based of an optimal dynamic inversion.

iii. Modeling of a gantry crane consists of dynamic derivations of gantry crane

model, dynamic inversion analysis.

iv. Perform a controllability and observability test before designing a controller.

v. Designing a state feedback control using pole placement method related to the

optimal control.

vi. Applying the design of nonlinear gantry crane block in MATLAB SIMULINK to

analyze to simulation result.

vii. Interface the gantry crane system control design in MATLAB Simulink with the

hardware.

viii. Evaluation of any problems in the project.

ix. Come out with the result and analysis of this project.

5

1.5 Methodology

Start

Develops the system based of an optimal dynamic inversion.

(Review of theory related to optimal dynamic inversion, Familiarization of MATLAB

Simulink etc.)

Modeling a gantry crane system consist of dynamic inversion analysis.

(Dynamic derivation of crane model)

Designing a controller by using poles placement method related to the optimal control.

Continue

Apply the design using nonlinear block in the MATLAB Simulink to analyze the simulation result.

NO

YES

6

Continue

Interface the gantry crane system control design in MATLAB Simulink

with the hardware.

Evaluation of any problems in this project and come out with result and analysis of

this project.

End

Figure 1.1: Project flow chart

CHAPTER II

LITERATURE REVIEW

This chapter contains the reviews and information about the project on several

important concepts on optimal dynamic inversion and tools that were used in this project.

Each fact and information is guided by journals and other references. It will be

compared and the best method will be choosing for this project. This literature review

will also include the review of several types of cranes.

2.1 Optimal Dynamic Inversion Method

The control design methodology, consist of first determining state feedback

control law whose aim is to assure the robust stability of the system and to damp it. In

this phase it is necessary to augment the system in order to assure a null steady state

error is achieved at the end of the motion in spite of possible external disturbances (for

example friction effects). Then, after having defined a parameterized family or desired

output function which depends on the motion time, the corresponding family of

command input function is derived by inverting the closed loop system. The motion time

can be minimized taking account actuator constraints and parameter uncertainties.