磁浮系統本身為一個高度非線性且開迴路不穩定的系統。本論文希望先以相位領先控制器作為內迴路，讓系統處於穩定的狀態。再利用模糊PID控制器做為外迴路，克服系統的非線性及改善系統的響應特性。
因為傳統的模糊PID控制器參數設計是一件冗長的嘗試錯誤法，所以本論文用非二進位式適應型基因演算法來幫助我們找到最佳的參數值並應用至實務上。至於在實驗的部分則分為兩種測試: (1) 加入初始電壓的模糊PID控制器做定位、外來干擾等的磁浮系統測試 (2) 不加入初始電壓的模糊PID控制器做定位控制。
由實驗結果可知，使用非二進位的基因演算法所設計的模糊PID控制器不僅可以增加磁浮系統的操作範圍，且能迅速準確的定位，同時有抗外來干擾的能力。

Magnetic suspension systems are highly nonlinear and essentially unstable systems. In this thesis, we utilize a phase-lead controller operating in the inner loop to stabilize the magnetic suspension system at first. Furthermore, we design a fuzzy PID controller operating in the outer loop to overcome the nonlinearity and to improve the system’s performances.
Because of setting the parameters in traditional fuzzy PID is a long-winded trial and error, so we adopt non-binary modified adaptive genetic algorithms to help us finding the parameters of fuzzy PID controller. As to the experimental implementation, we set two situations in our experiment test: (1) we utilize fuzzy PID controller with initial voltage to test the positions control, and eliminate the extra disturbance. And, (2) we utilize fuzzy PID controller without initial voltage to control the position of suspension object.
For the experimental results, we obtain that the designed fuzzy PID controller not only increases the system’s operating range, but also positions accurately and rapidly, and it meanwhile can eliminate the extra disturbance.

Contents…………………………………………………………………..I
List of Symbols…………………………………………………………IV
List of Figures…………………………………………………………..VI
List of Tables………………………………………………………….VIII
Chinese Abstract ………………………………………………………..IX
English Abstract …………………………………………………………X

Chapter 1. Introduction 1
1.1 Research Motivation and Goal 1
1.2 Papers Review 2
1.3 Genetic Algorithms and Fuzzy Logic Controller 3
1.4 Research Results and Contributions 5
1.5 Thesis Structure 5

Chapter 2. Fuzzy System and Control 7
2.1 Introduction of Systems and Control 7
2.2 Fuzzy Sets and Membership Function 10
2.3 Simplified Fuzzy Reasoning Method 13
2.4 Hybrid Reduced Rule Fuzzy PID like controller 15

Chapter 3. Genetic Algorithms 20
3.1 Brief History of Genetic Algorithms 20
3.2 Foundations of Genetic Algorithms 22
3.3 Simple Genetic Algorithms(SGA) 23
3.4 Modifications to Simple Genetic Algorithms 26
3.4.1 Encoded and Decoded Processes 27
3.4.2 Fitness Function Definition 27
3.4.3 Mapping Objective Functions to Fitness Form 28
3.4.4 Fitness Scaling 28
3.4.5 Reproduction 30
3.4.6 Crossover Operator 31
3.4.7 Mutation 33
3.5 Adaptive Genetic Algorithm 33
3.5.1 Adaptive Probabilities of Crossover and Mutation 34
3.5.2 Elitist Strategy 38
3.5.3 Extinction and Immigration Strategy 39
3.5.4 The Structure of Modified Genetic Algorithm 41

Chapter 4. System Model Building 43
4.1 System Modeling and Linearization 43

Chapter 5. Fuzzy PID Controller Design 51
5.1 The Phase Lead Compensator 51
5.2 Design Steps of PIDFLC 54
5.3 Parameter Tuning of PIDFLC Using AGA 59
5.4 Flow Chart of Simulation 61
5.5 Compare the Simulation Results 62
Chapter 6. Experiments and Results 70
6.1 Experimental Apparatus 70
6.2 Experimental Steps 76
6.3 Experiment Results with Initial Voltage 77
6.3.1 Result of Simulation and Experiment 78
6.3.2 Operating Range Test 79
6.3.3 Different Initial Position Experiment 81
6.3.4 Extra Disturbance Elimination 83
6.4 Experiment Results with no Initial Voltage 85

Chapter 7. Conclusions and Recommendations 89

References 91

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