AN ADAPTIVE ALGORITHM FOR THE TUNING OF TWO INPUT SHAPING METHODS NUR HAFIZAH BINTI HASSAN
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1 AN ADAPTIVE ALGORITHM FOR THE TUNING OF TWO INPUT SHAPING METHODS NUR HAFIZAH BINTI HASSAN This report is submitted in partial fulfilment of requirements for the Bachelor Degree of Electronic Engineering (Industrial Electronic) With Honours Faculty of Electronic and Computer Engineering Universiti Teknikal Malaysia Melaka April 2011
2 UNIVERSTI TEKNIKAL MALAYSIA MELAKA FAKULTI KEJURUTERAAN ELEKTRONIK DAN KEJURUTERAAN KOMPUTER BORANG PENGESAHAN STATUS LAPORAN PROJEK SARJANA MUDA II Tajuk Projek : Sesi Pengajian AN ADAPTIVE ALGORITHM FOR THE TUNING OF TWO INPUT SHAPING METHODS : 1 0 / 1 1 Saya NUR HAFIZAH BINTI HASSAN 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) Tarikh:.. Tarikh:..
3 iii I hereby declare that this report is the result of my own work except for quotes as cited in the reference Signature Author Date :.. : NUR HAFIZAH BINTI HASSAN :..
4 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 award of Bachelor of Electronic Engineering (Industrial Electronics) with Honours Signature Supervisor s Name Date :. : PN AZDIANA BT MD YUSOP :.
5 Dedicated to my family especially my parent, sister, brothers, and all of my friends. v
6 vi ACKNOWLEDMENT I would like to thank God for His blessing and strengths to endure and carry on my final year project up to completion. Next, I would like to thank my supervisor, Pn Azdiana bt Md Yusop, for all her teachings and guidance, and her experience help on this work. It has been a hardship for you, sorry and thank you so much. I would also like to thank all other colleagues and friends for their help, discussions and information sharing. Finally I would like to thank my father and mother for all their love, sacrifice, understanding and support.
7 vii ABSTRACT The project presents an adaptive algorithm for the tuning of two input shaping methods designed to prevent the excitation of oscillatory modes in resonant systems. The first method produces a control signal that is the linear combination of delayed versions of the reference input. The transfer function of the control system has an infinite number of complex zeros, with some of them placed exactly at the locations of the resonant modes of the plant. In contrast, the second method is based on a pole/zero cancellation of the resonant modes using a finite-dimensional controller. An adaptive algorithm is used for the tuning of both methods. In this project, the problem of controlling systems with resonant modes is considered. For simplicity, attention is focused on second-order systems. The system is developed and simulated by using MATLAB software. The control performance is shown graphically to be comparable for both methods and the adaptive algorithm is found to be both simple and effective for fast adaptation.
8 viii ABSTRAK Projek ini mempamerkan satu algoritma adaptif untuk penetapan dari dua kaedah membentuk input yang direka untuk mencegah eksitasi mod ayunan pada sistem resonan. Kaedah pertama menghasilkan isyarat kawalan yang merupakan gabungan linear daripada versi tertunda dari masukan rujukan. Fungsi pemindahan dari sistem kawalan mempunyai jumlah infiniti sifar kompleks, dengan beberapa daripadanya ditempatkan secara tepat di lokasi mod sistem resonan. Sebaliknya, kaedah kedua adalah berdasarkan pembatalan pole / zero dari mod resonan menggunakan pengawal dimensi terhad. Algoritma adaptif digunakan untuk penetapan kedua-dua kaedah. Dalam projek ini, masalah pengendalian sistem dengan mod resonan dikaji. Untuk kemudahan, perhatian difokuskan pada sistem turutan kedua. Sistem ini dibangunkan dan disimulasikan dengan menggunakan perisian MATLAB. Prestasi kawalan ditunjukkan secara grafik untuk dibandingkan terhadap kedua-dua kaedah dan algoritma adaptif didapati memudahkan dan berkesan untuk diadaptasi dengan cepat.
9 ix CONTENTS CHAPTER TITLE PAGE PAGE TITLE BORANG PENGESAHAN STATUS LAPORAN DECLARATION SUPERVISOR VERIFICATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS i ii iii iv v vi vii viii ix xiii xiv xvii I PROJECT INTRODUCTION 1.1 Introduction Objective Problem Statement Scope of Work Methodology Report Structure 7
10 x II LITERATURE REVIEW 2.1 Definition of Crane Control System Open-loop and Close-loop Control System Manually and Automatic Control Input Shaping Methods Definition of Input Shaping Posicast Control Command Shaping Method Bang-bang Control System Inversion Based Method Delayed Input Method Pole/Zero Cancellation Method Advantages of Input Shaping Adaptive Algorithm 22 III MATHEMATICAL MODELING 3.1 Nonlinear Feedback Control of a Gantry Crane Desired Motion Modeling of the Gantry Crane Derivation of the Equation of Motion Linearization 30
11 xi IV INPUT SHAPING ANALYSIS 4.1 Input Shaper Analysis Delayed Input Method Pole/Zero Cancellation Method Adaptive Algorithm 36 V SIMULATION RESULT AND ANALYSIS 5.1 MATLAB and SIMULINK MATLAB SIMULINK SIMULINK Model for the Gantry Crane in 2 nd Order System System Model Pole/Zero Cancellation Input Shaper Delayed Input Method Input Shaper SIMULINK Model for the Gantry Crane in 4 th Order System Generation of Bang-bang Input Force Generalize Model Sway Motion of a Gantry Crane Sway Angle Position of the Trolley Pole / Zero Cancellation with Inverse Dynamic Analysis Pole / Zero Cancellation with Inverse Dynamic Analysis for Closed- Loop System 74
12 xii VI CONCLUSION 6.1 Conclusion Future Works Experimental Setup Design of the Close-loop Control System Tower Crane 81 REFERENCES 83
13 xiii LISTS OF TABLES NO TITLE PAGE 5.1 Categories of MATLAB Works Simulink Description Simulink Product Peak-to-Peak and Sway Angle for Bang-Bang Input Settling Time and Trolley Position for Bang-Bang Input Peak-to-Peak and Sway Angle for Inverse Dynamic with Pole / Zero Cancellation Input Settling Time and Trolley Position for Inverse Dynamic with Pole / Zero Cancellation Input Peak-to-Peak and Sway Angle for Closed-Loop and Open-Loop Control System Settling Time and Trolley Position for Closed-Loop and Open-Loop Control System 78
14 xiv LIST OF FIGURES NO TITLE PAGE 1.1 Project Flow Chart Difference between Crane and Hoist Bridge Crane Gantry Crane Tower / Jib Crane Block Diagram of a Control System Open-Loop Control System Close-Loop Control System Manually Control for Gantry Crane Automatic Control for Gantry Crane Destructive Interference Input Shaping Process Posicast Control Multi Pulse Shaped Input Input Shaper Position in a System Model of a Gantry Crane MATLAB Software Design Flow Chart Default Appearance of the Desktop SIMULINK Library SIMULINK Library Browser for Real-Time Workshop Function Block for the System 49
15 xv 5.6 Function Block Parameter Parameters Labelling in Block Mask Editor Simulation Model using MATLAB with Step Input Function Output Response of the System with Step Input Function Subsystem 1 for Transfer Function P -1 (s) Function Block for M(s) Pole/Zero Cancellation Input Shaper Gantry Crane System with Pole/Zero Cancellation Input Shaper Output Response of the System with Step Input Function and Pole/Zero Cancellation Function Block for C(s) Block Parameter for Delayed Input Gantry Crane System with Delayed Input Input Shaper Output Response of the System with Step Input Function and Delayed Input Method Generation of Bang-bang Input Force Parameters of Bang-bang Input General Model (a) Sway Motion when Input Force is Positive (b) Sway Motion when Input Force is Negative Input Plot Sway Angle Arc Length and Chord Length Trolley Position General Model for Inverse Dynamic Analysis with Pole / Zero Cancellation Input 68
16 xvi 5.28 Look under Mask for Input Shaping Function Block Parameter for Input Shaping Sway Angle for Inverse Dynamic Analysis with Pole / Zero Cancellation Input Trolley Position for Inverse Dynamic Analysis with Pole / Zero Cancellation Input General Model of Closed Loop System Sway Angle for Closed Loop and Open Loop System Trolley Position for Closed Loop and Open Loop System 77
17 xvii LIST OF SYMBOLS ω n - Natural frequency ξ - Damping ratio K - Stiffness u - Normalized time α - Speed motion β - Relationship between α and ω n M - Trolley mass m - Payload mass l - Length of the hoisting rope F x - Input force g - Gravitational acceleration = 9.81ms -2 G - Centre point S - Point of suspension x - Trolley position x - Velocity x - Acceleration θ - Sway angle - Angular velocity - Angular acceleration
18 1 CHAPTER I PROJECT INTRODUCTION This chapter will discuss about the adaptive algorithm for the tuning of two input shaping methods. The project introduction, project objective, problem statement and scopes of work, methodology and thesis outline will also be presented. 1.1 Introduction This project attempts to design the controller for the gantry crane system and interface it with MATLAB in Real-Time Workshop. The input of the system is using step function. The problem of controlling systems with resonant modes is considered. For simplicity, second-order systems are considered. Two feed-forward control methods are discussed. In the first method, the control signal is a linear combination of two signals: the reference input signal and the signal delayed by a certain time period. In the second method, the control signal is obtained by filtering the reference signal using a transfer function such that the plant poles are cancelled by the compensator zeros.
19 2 The first method is referred to as the delayed input method, and the second method as the pole/zero cancellation method. The two methods are compared and an algorithm is proposed for the tuning of the pole/zero cancellation method. This project includes the previous work in three ways. First, the tuning algorithm is made adaptive by replacing the batch least squares algorithm by the recursive least-square algorithm recommended. Second, it is shown that the adaptive algorithm can be used to tune the delayed input method as well as the pole/zero cancellation method. Finally, the adaptive algorithm is shown to be effective for the tuning of the input shaping methods with double zeros placed at the locations of the plant poles instead of single zeros. The results are all demonstrated experimentally using a simulation of MATLAB software. The algorithm has major interest because of its simplicity, thus it is easily implemented in real-time. 1.2 Objective The objective of this project is to specify a controller function by using an adaptive algorithm for the tuning of two input shaping methods for gantry crane that can move as robustness, quickly, accurately, and safely as possible without vibration from an initial position to target position. 1.3 Problem Statement Gantry cranes are widely used for factories, transportation, nuclear installation and also construction. The crane has to move the load 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 experienced 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
20 3 movement the load. Vibration is a serious problem in a mechanical system. The problem can be solved by placing an appropriate controller with input shaping methods to the gantry crane system. 1.4 Scope of Work While doing the project, the scope of work plays very important role, which is a guidelines for student should attain to fulfil the requirement of the project. For this project, the scopes of work are such as listed below: i. Study the basic concept of the gantry crane system, input shaping methods and design, and adaptation. ii. Study the mathematical modelling, nonlinear feedback control of a gantry crane, desired motion, modelling of the gantry crane, derivation of the equations of motion, and linearization. iii. Understand theoretically about input shaping methods involved. iv. Analysis and make the comparison between the two input shaping methods.
21 1.5 Methodology (Flow Chart) 4
22 Figure 1.1: Project Flow Chart 5
23 6 The flow of this project can be represented by Figure 1.1: Project Flow Chart. The project started with literature review of the project such as review about adaptive algorithm, input shaping methods, mathematical modelling, and gantry crane. The literature review is usually a theoretical understanding about the project being developed. Next, proceeds with mathematical modelling by which it is an understanding process of the mathematical modelling of input shaper, for this project the input shapers are pole / zero cancellation method, and input delayed method. Then, the flow is to design the pole / zero methods equations and analysis in MATLAB, where the nonlinear input shaping model is develop using MATLAB and Simulink, and apply the adaptive algorithm into the nonlinear crane for open loop. If the response does not satisfy, the operation will reverse back to the mathematical modelling. The analysis is made based from the simulation results. Two parameters to be analysed position of the trolley and sway angle of the hoisting rope. Next, proceeds with mathematical modelling by which it is an understanding process of the mathematical modelling of input shaper - input delayed method. Then, the flow is to design the input shaper methods equations and analysis in MATLAB, where the nonlinear input shaping model is develop using MATLAB and Simulink, and apply the adaptive algorithm into the nonlinear crane for open loop. If the response does not satisfy, the operation will reverse back to the mathematical modelling. The analysis is made based from the simulation results. Two parameters to be analysed position of the trolley and sway angle of the hoisting rope. Based from all simulation results, data is analysed for both input shaper and compare which methods produce better performance in terms of position of the trolley and sway angle of the hoisting rope.
24 7 1.6 Report Structure This thesis is a documentary to deliver the generated idea, the concepts applied, the activities done, and the final year project product produced. The thesis consists of six chapters. This paper is organized as follows. Chapter I is regarding of the background studies of the project including introduction of the project, objective, problem statement, scopes of work and methodology. Chapter II enclose literature review about gantry crane including history, applications, and working principle. Furthermore, the standard techniques of input shaping that will reduced the vibration for the gantry crane is also covered in this chapter. Chapter III will introduce the derivation of equations of adaptive version of input shaping techniques explaining the purpose of this study. On the other hand, this chapter will explain how to get equations for the input shaping in s-domain. Chapter IV will illustrates more on the input shaping analysis. This method will review the process by specifying the system input function. Chapter V contain the utilized methodology for software. The design flow and construction of the project is introduced. It gives brief description about each procedure in completing the project. It also covered the experimental result, analysis and discussion, for both input shaping methods. Furthermore, the comparison between both techniques is also scrutinized. Chapter VI is the conclusion of the initial progress of the project and recommendation that can be implemented in the future.
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