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研究生:廖聰魁
研究生(外文):Tsung-Kuei Liao
論文名稱:單輸入單輸出T-S模糊系統的控制器與估測器設計演算法
論文名稱(外文):The algorithm of designing controllers and observers for SISO T-S fuzzy systems
指導教授:鍾 鴻 源張 文 哲
指導教授(外文):Hung-Yuan ChungWen-Jer Chang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:70
中文關鍵詞:模糊控制Takagi-Sugeno 模糊模型控制典型式估測典型式李亞普諾夫漸近穩定理論
外文關鍵詞:fuzzy controlTakagi-Sugeno fuzzy modelcontrollable canonical formobservable canonical formLyapunov asymptotic stability theorem
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在本篇論文中針對Takagi-Sugeno (T-S) 模糊模型[1]的系統架構提出了控制器以及估測器的設計方式,並對系統中考慮收斂速度影響時作探討與設計。在控制器部分,我們利用平行分配補償(Parallel Distributed Compensation; PDC)[2]的設計觀念對以T-S 模糊模型描述的非線性受控體作控制器設計,在每一個子系統屬於可控標準式時,我們引用李亞普諾夫(Lyapunov)漸近穩定理論並以李亞普諾夫等式取代李亞普諾夫不等式後,我們可直接獲得李亞普諾夫方程式的解,透過此解便可進一步求到最終的控制器對受控體做控制並達到系統穩定的要求。對於估測器的部分,針對T-S 模糊模型描述的非線性受控體,當每一個子系統的狀態矩陣用可估測標準式描述時,我們同樣利用李亞普諾夫漸近穩定理論分析估測誤差與系統輸出的收斂情形,推導並求解李亞普諾夫方程式後,我們能夠直接設計此系統的狀態估測器。除此之外,本論文尚且針對T-S模糊系統在考慮系統輸出收斂速度的要求下,進行控制器的設計與解決,並使系統輸出的響應收斂情形有大幅度的改善。
In the past, LMI(Linear Matrix Inequalities) technique is used to solve the fuzzy controller, observer and to analyze the stability of Lyapunov inequalities of the T-S (Takagi-Sugeno) fuzzy systems. However, there are still many difficulties in systematically designing the T-S fuzzy controller and the observer. In this thesis, we provide a fuzzy controller and observer design method for the nonlinear plant whose structure is represented by T-S fuzzy model. The model-based fuzzy controller and observer are designed by the concept of the so-called “PDC (Parallel Distributed Compensation)” [2]. Applying the Lyapunov asymptotic stability theorem instead of Lyapunov inequality, we can solve the Lyapunov equation via the algorithm provided in this work. The final stable controller and observer of the nonlinear plant can be obtained directly. This method is mainly based on the fact that each subsystem of T-S fuzzy model can be represented by the controllable and the observable canonical form. Besides, the decay rate of system state can also be improved.
Table of content
Page
Abstract Ⅰ
Table of contentⅡ
List of figuresⅤ
Chapter 1: Introduction 1
1-1. Research background 1
1-2. Motivation 1
1-3. Organization 2
Chapter 2: An algorithm of designing controllers for SISO T-S fuzzy
systems 3
2-1. Introduction 3
2-2. T-S fuzzy model and the stability conditions 5
2-3. Fuzzy controller design 6
2-4. T-S fuzzy controller design algorithm 9
2-5. Simulation 11
2-6. Discussion13
Chapter 3: Fuzzy controller design with decay rate for SISO T-S fuzzy
systems 18
3-1. Introduction18
3-2. T-S fuzzy model and the PDC concept18
3-2-1. T-S fuzzy model 18
3-2-2. Parallel distributed compensation (PDC)19
3-3. Decay rate and the stability conditions20
3-4. T-S fuzzy controller design with decay rate22
3-5. Fuzzy controller design algorithm with decay rate23
3-6. Simulation 26
3-7. Discussion 27
Chapter 4: Output feedback gain design with decay rate for SISO T-S fuzzy systems32
4-1. Introduction 32
4-2. T-S fuzzy model and the PDC concept32
4-3. Stability conditions and the output feedback gain design with decay
rate 34
4-3-1. Stability conditions of system34
4-3-2. Output feedback gain design36
4-4. T-S fuzzy output feedback gain design algorithm37
4-5. Simulation40
4-6. Discussion42
Chapter 5: Observer design for SISO T-S fuzzy system46
5-1. Introduction 46
5-2. T-S fuzzy model and the T-S fuzzy observer47
5-3. The stability conditions of the fuzzy system with the observer
feedback 49
5-4. Fuzzy controller and the observer design algorithm 53
5-5. Simulation 59
5-6. Discussion 61
Chapter 6: Conclusions 65
6-1. The fuzzy controller design 65
6-2. The analysis of fuzzy observer feedback control 65
6-3. Future direction66
References 67
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