本論文旨在研究使用基因演算法於含壓電材料之可撓性曲柄滑塊連桿機構的主動式強健控制器設計。由於連桿機構在高速運轉下會產生慣性力的干擾，且撓性機構在模態截斷、線性時變參數擾動、殘餘模態所引起之過溢效應等種種因素下，皆會導致系統不穩定。
在機械結構控制的應用上，本文以有限元素法將含壓電材料之連桿機構進行模式化工作，並取低頻模態做為控制器與觀測器的設計。在系統的強健性方面，利用基因演算法找出符合強健穩定性條件的最佳值，使系統在受到時變參數擾動及過溢效應下仍能維持系統的穩定性。
由數值模擬結果顯示，利用基因演算法找出來的各項參數，均能有效抑制連桿在高速運動下產生的變形，並避開時變參數擾動及過溢效應所造成的不穩定。

The purpose of this thesis is to study the active robust control for the flexible slider-crank linkage mechanism with piezoelectric films using genetic algorithms. The instability caused by the inertia force that is induced by the high-speed rotation flexible slider-crank linkage, mode truncation, parameter uncertainties, and spillover effect due to the residual modes of structure.
For the application of the mechanical structure system, a mathematical model for a slider-crank linkage mechanism with piezoelectric films is developed in conjunction with finite element method (FEM), and the lower frequency modes are separated into controlled modes and residual modes. For the robustness of the system, a robust stability condition and genetic algorithms are employed to ensure the stability of the system under the parameter uncertainties and spillover effect simultaneously.
Numerical simulation is performed to the control methodology with genetic algorithms can suppress deform of flexible slider-crank linkage mechanism operating at high speeds, and the instability caused by the parameter uncertainties and spillover effect can be avoided.

Contents
Contents…………………………………………………………i
List of Figures……………………………………………………iv
List of Tables……………………………………………………v
List of Symbols…………………………………………………vi
Chinese Abstract………………………………………………viii
English Abstract…………………………………………………ix

Chapter 1 Introduction……………………………………………1
1.1 Research Motivation and Goal…………………………………..1
1.2 Papers Review………………………………………………2
1.2.1 Robust Control of Flexible Linkage Mechanisms………………2
1.2.2 Genetic Algorithms……………………………………4
1.3 Overview…………………………………………………5

Chapter 2 System Description……………………………………6
2.1 Physical Description and Assumptions……………………………6
2.2 Kinematics Analysis by Complex Number…………………………6
2.3 Mathematical Modeling of Control Actuator and Sensor………………8
2.3.1 Control Actuator………………………………………8
2.3.2 Control Sensor………………………………………….9
2.4 Structure Modeling…………………………………………10
2.4.1 Equation of Motion…………………………………….10
2.4.2 Finite Element Method (FEM)............................................11
2.4.3 Transformation into State Space Form……………………13

Chapter 3 Genetic Algorithms……………………………………18
3.1 Introduction………………………………………………..18
3.2 General Structure of Genetic Algorithms…………………………19
3.3 Genetic Algorithms Terminology………………………………19
3.3.1 Chromosome Representation……………………………19
3.3.2 Fitness Function……………………………………….20
3.3.3 Reproduction…………………………………………20
3.3.4 Crossover……………………………………………21
3.3.5 Mutation……………………………………………22
3.3.6 Elitist Strategy………………………………………22
3.4 The Structure of Genetic Algorithms with Elitist Strategy…………….22

Chapter 4 Robust Control System Design………………………......28
4.1 System Description…………………………………………29
4.2 Illustrative Example………………………………………….35
Chapter 5 Conclusions and Recommendations……………………47
5.1 Conclusions………………………………………………..47
5.2 Future Works……………………………………………….48
Appendix：Proof of the Theorem…………………………………..49
References………………………………………………………50

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