摘要
本論文研究應用適應性基因演算法於混合式模糊PID控制器設計與線性直流馬達的定位控制。由於具有高速及精密的定位能力，線性直流馬達被廣泛地應用在許多領域中。然而，隨著定位精度要求的增加，在精密定位中，非線性摩擦力的影響會變的很顯著。由於巨觀範圍內的動摩擦力及微觀範圍內的靜摩擦力差異極大，我們將針對巨觀與微觀兩個階段分別設計控制器。在巨觀階段，我們採用混合式模糊PID控制器，並利用適應性基因演算法來搜尋最佳的控制器參數，以改善系統的性能。本文並提出一項新的適應性突變及交配率計算方法。在微觀階段，由於不易求得精密的摩擦力模型，故採用繼電器迴授的方法來設計PID控制器。最後經由電腦模擬及實驗，證明本論文所使用的控制方法可獲得令人滿意的成果。

Abstract
This thesis studies on the design of hybrid fuzzy PID controller via genetic algorithms and the position control of linear DC motors. Due to the high precision and high speed positioning ability, linear DC motors have been widely used in many fields. However, with the higher requirements of positioning accuracy, the effect of nonlinear friction becomes very significant. Because of the large difference between dynamic friction in macrodynamic region and static friction in microdynamic region, we design the two-stage controller for positioning in macrodynamic and microdynamic stage individually. In the macrodynamic stage, we use the hybrid fuzzy PID controller and finding the optimal membership functions and scaling factors of the controller via adaptive genetic algorithms to enhance performance of the system. A novel formula for calculating adaptive crossover and mutation rate is also presented. Since it is not easy to establish a precise static friction model in the microdynamic region, the relay feedback method is adopted to design PID controllers. Finally, through computer simulations and experiments, it is obviously that the performance of the proposed controllers is satisfactor

Contents
Contents i
List of Symbols iv
List of Figures vii
List of Tables ix
Chinese Abstract x
English Abstract xi

Chapter 1. Introduction 1
1.1 Research Motivations and Goal 1
1.2 Papers Review 2
1.2.1 Position Control of Linear DC Motors 2
1.2.2 Friction Models 3
1.2.3 Genetic Algorithms and Fuzzy Logic Controller 7
1.2.4 Tuning Methods of PID Controllers 8
1.3 Thesis Overview 9

Chapter 2. Model Building 10
2.1 Equations of Linear DC Motors 10
2.2 Macrodynamic Model Identification 12
2.3 Analysis of Microdynamic Behaviors 14

Chapter 3. Genetic Algorithms 19
3.1 Introduction to Genetic Algorithms 19
3.2 Fundamentals of Genetic Algorithms 22
3.2.1 Encoded and Decoded Processes 22
3.2.2 Fitness Function 23
3.2.3 Reproduction 25
3.2.4 Crossover 26
3.2.5 Mutation 27
3.3 Adaptive Genetic Algorithms 28
3.3.1 Adaptive Probabilities of Crossover and Mutation 29
3.3.2 Elitist Strategy 32
3.3.3 Extinction and Immigration Strategy 33
3.3.4 The Structure of Adaptive Genetic Algorithms with Elitist,
Extinction and Immigration Strategy 35

Chapter 4. Fuzzy Systems and Control 37
4.1 Introduction of Fuzzy Systems 37
4.2 Simplified Fuzzy Reasoning Method 40
4.3 Hybrid Reduced Rule Fuzzy PID Like Controller 42

Chapter 5. Controller Design 45
5.1 Hybrid Reduced Rule Fuzzy PID Controller Design 46
5.1.1 Design Steps of PIDFLC 46
5.1.2 Parameters Tuning of PIDFLC Using AGA and the
Simulation Results 51
5.2 Relay Feedback Tuning of PID Controllers 55
5.3 Dynamics Transition Condition 57

Chapter 6. Experiments and Results 59
6.1 Experimental Setup 59
6.2 Experimental Results 61
6.2.1 Position Control with Macrodynamic Controller 61
6.2.2 Position Control with Microdynamic Controller 64
6.2.3 Position Control with Two-stage Controller 66

Chapter 7. Conclusions and Recommendations 71

References 73

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