不確定性Takagi-Sugeno模糊系統之觀察器與控制器合成設計

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葉善茹(Shan-ju Yeh) 查詢紙本館藏

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電機工程學系

論文名稱

不確定性Takagi-Sugeno模糊系統之觀察器與控制器合成設計
(Observer and controller synthesis for uncertain T-S fuzzy systems)

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摘要(中)

本論文對不確定性模糊系統討論了觀察器與基於觀察器下的強健控制器合成設計，文章中所討論的觀察器與基於觀察器下的強健控制器設計方法都是基於Takagi-Sugeno (T-S) 模糊系統。首先，在第二章我們引用了未知輸入設計概念與選擇設計動態觀察器模型而不是古典的觀察器模型，同時，藉由廣義反矩陣的輔助求出系統設計參數，並且由李亞普諾夫函數(Lyapunov function)推導出能使估測誤差收斂到零的條件，上述條件最後是線性矩陣不等式的型態，可由軟體工具快速有效的找出最佳解，最後，數値範例證實了文章中所提出的模糊觀察器設計方法，在有擾動環境下仍然有很好的表現。
另一個在論文中被討論的問題是對於不確定性T-S模糊系統做基於觀察器下的強健控制。在很多真實實驗中並不是所有狀態都可以量測得到，因此，在第三章中提出了基於觀察器下的強健性控制器合成方法。根據文獻指出，對於不確定性模糊系統所做的觀察器與控制器設計普遍會遇到兩個問題。第一個問題是所得到的穩定條件是雙線性矩陣不等式(Bilinear Matrix Inequalities: BMIs)，其型態無法運用現有的MATLAB Linear Matrix Inequality (LMI) 工具求最佳解，第二個問題是穩定條件有交叉偶合(cross-coupled)項，其需要用兩步驟求解法，上述的求解方法將會增加解的保守性。第三章提出的設計方法解決了以上兩個問題，達到狀態估測並回授控制器完成系統穩定之目的。最後，模擬結果展現了我們設計的觀察器與控制器是有效的。

摘要(英)

The thesis proposes the observer and robust observer-based controller synthesis for uncertain Takagi-Sugeno (T-S) fuzzy systems. At first, in Chapter 2, we introduce unknown input concept and choose to design dynamic observer instead of classical observer. In the meantime, designed system parameters are found with the aid of generalized inverse. Moreover, based on the Lyapunov theory, sufficient conditions making estimated errors converge to zero are derived in the form of linear matrix inequalities (LMIs). Feasible solutions can be found by MATLAB LMI tool box efficiently. Finally, a numerical example is given to substantiate the performance of fuzzy observer under the environment with uncertainties as expected.
The other problem discussed in this thesis is the robust observer-based control for the uncertain T-S fuzzy system. It is known that, in many practical experiments, not all of the system states can be measured. Hence, in Chapter 3, we develop a design method of robust observer-based controller for T-S fuzzy systems. According to the survey of related papers, there are two common problems we will face when designing observer and controller for uncertain fuzzy systems. The first problem is that sufficient conditions we obtain are in the form of bilinear matrix inequalities (BMIs) which could not be solved easily. The second problem is that there are cross-coupled terms in the sufficient conditions having to be solved by two-stage procedure which will enhance the conservatism of the result. In Chapter 3, the proposed method is capable of overcoming previous mentioned two problems. Estimated system states feedback to the controller so that the stability of the system is achieved. Consequently, the results of simulation show that synthesized fuzzy observer and robust observer-based controller work effectively.

關鍵字(中)

★ T-S 模糊系統
★ 觀察器
★ 控制器

關鍵字(英)

★ T-S fuzzy systems
★ observer
★ controller

論文目次

Contents
Page
Abstract II
List of Figures IV

Chapter 1 1
Introduction 1
1.1 Review of previous researches 1
1.2 Motivation of the thesis 5

Chapter 2 6
Unknown Input Based Observer Synthesis for Uncertain T-S Fuzzy Systems 6
2.1 Introduction 6
2.2 System description and problem formulation 6
2.3 Observer synthesis 8
2.4 Numerical example 15
2.5 Summary 23

Chapter 3 24
A Synthesis of Observer-based Controller for Stabilizing Uncertain T-S Fuzzy Systems 24
3.1 Introduction 24
3.2 System description and problem formulation 24
3.3 Fuzzy observer and fuzzy robust observer-based controller synthesis 27
3.4 Numerical example 37
3.5 Summary 44

Chapter 4 45
Conclusion and future works 45

Reference 47

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指導教授

王文俊(Wen-june Wang)

審核日期

2014-7-30

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