臺灣博碩士論文加值系統

二節機械手臂為一個複雜且難以分析的系統。我們使用Takagi-Sugeno ( T-S ) 模糊模型建構出與系統近似的狀態方程式，並設計以平行分佈補償為理念的模糊控制器。我們使用Lyapunov stability approach 推導出使系統穩定的線性矩陣不等式。但滿足線性矩陣不等式的解無法確保系統的效能，因此，我們使用基因演算法來演化取得滿足線性矩陣不等式的最佳解。除此之外，針對傳統T-S模糊理論的歸屬函數設計過於保守的問題，使用階級式基因演算法來求取最佳控制性能的歸屬函數，同時可以獲得平行分佈補償模糊控制器增益。最後給定一組參考訊號並使用電腦模擬驗證控制性能。

The object of this thesis is to design an LMI-based fuzzy controller for an MIMO two-link robot arm using hierarchical genetic algorithm. The Takagi-Sugeno (T-S) fuzzy model is utilized to represent the equation of motion of the two-link robot arm. After the design of a nonlinear function matrix R, the dynamic equation of the robot arm is built with only four fuzzy rules. The stability of the system is guaranteed by linear matrix inequalities (LMIs) from Lyapunov approach. Genetic algorithms (GAs) are applied to find the best parameter matrix of LMIs. Hierarchical genetic algorithm (HGA) is used to seek both the best membership functions and parameter of LMIs. According to HGAs and LMIs, the parallel distributed compensation (PDC) controller is designed to track the state trajectory of a reference model.

致謝…………………………………………………………………………………………….I
摘要…………………………………….……………………………………………………..II
Abstract………………………………………..……………………………………………III
目錄…………………………………………………………………………………………..IV
圖目錄………………………………………………………………………………………VI
表目錄……………………………………………….……………………………………VIII
第一章 緒論……………………………………………………………………………...……1
1-1 研究背景……………………………………….…………………………………1
1-2 研究動機…………………………………………………………………………1
1-3 論文架構………………………………………………………………………….2
第二章 T-S模糊控制…………………………………………………………………………3
2-1 模糊邏輯理論…………………………………………………………………….3
2-2 T-S模糊模型.........................................................................................................10
2-3 平行分佈補償和穩定分析……………………………………………………...10
第三章 二節機械手臂系統………………………………………………………………….17
3-1 機械手臂之數學模型…………………………………………………………...17
3-2 機械手臂之T-S模糊模型………………………………………………………20
3-3 基於LMI之模糊控制器設計…………………………………………………..22
3-4 電腦模擬……………………………………………………………………...…23
第四章 智慧型機械手臂控制………………………………………………………………29
4-1 基因演算法……………………………………………………………………...29
4-2 LMI結合GA之模糊控制器設計………………………………………………35
4-3 LMI結合GA之電腦模擬………………………………………………………35
4-4 LMI結合HGA之模糊控制器設計…………………………………………….39
4-5 LMI結合HGA之電腦模擬…………………………………………………….41
第五章 結論………………………………………………………………………………….47
參考文獻……………………………………………………………………………………...48

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