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研究生:呂政緯
研究生(外文):Cheng-Wei Lu
論文名稱:模糊控制之全域穩定分析與追蹤控制
論文名稱(外文):Global Stability Analysis for Fuzzy Systems and Tracking Control
指導教授:練光祐
指導教授(外文):Kuang-Yow Lian
學位類別:碩士
校院名稱:中原大學
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
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:75
中文關鍵詞:強健性追蹤控制T-S模糊模式穩定性分析模糊估測器線性矩陣不等式平行分布補償
外文關鍵詞:Tracking ControlT-S fuzzy modelParallel Distributed CompensationRobust PerformanceFuzzy ObserverStability AnalysisLinear Matrix Inequalities
相關次數:
  • 被引用被引用:1
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  • 收藏至我的研究室書目清單書目收藏:0
T-S 模糊模式(T-S fuzzy model),是近幾年來廣泛使用於處理非線性系統的控制方法之一。此種模糊模式可將非線性系統以模糊理論中的IF-THEN規則庫來取代且其推論部為線性方程式的型式為他的主要特色,而且此模式化方式可近似或完整的表示原非線性系統。在設計控制器上使
用所謂平行分布補償(PDC)的概念並利用線性系統的方法,最後將穩定性分析的問題轉換為線性矩陣不等式(LMIs)的型式並用Matlab 去求解。在討論T-S 模糊模式時,我們所探討的大都僅僅限於區域穩定,在討論區
域穩定時,首先提出線性矩陣不等式(LMIs) 有解並不代表整個模式區域皆穩定,隨後提出如何找出這個穩定的區域,最後並提出全域穩定的條件。在追蹤控制上,我們藉由一些技巧可將原本複雜的追蹤系統轉換成比較簡單的型式。在此追蹤控制上,我們知道要量測所有的狀態在實際
的系統中是不太可能,所以在此我們使用估測器來量測這些不可量測的狀態。在現實的情況中,系統的內部部分狀態如果不可得知,可能會造成控制器或估測器的前件部的變數狀態跟著無法得知,而這變數狀態必須取決於估測器,這是我們最後探討的課題。
Recently, there has been a rapid growing interesting in using T-S fuzzy model to approximate nonlinear system. The T-S fuzzy model which originates from Takagi and Sugeno mainly deals with the nonlinear systems. With using this model, the nonlinear system is represented by several fuzzy subsystems in fuzzy IF-THEN rules where the con-sequent part is linear dynamical equation. Blending these IF-THEN rules, we can exactly represent the original nonlinear system. When consider the controller and observer design, we use the conception of parallel distributed compensation (PDC) to carry out these designs. We discuss the stability analysis of T-S fuzzy systems by using the Lyapunov's direct method. The sufficient conditions are formulated into linear matrix inequalities (LMIs). Typically, the stability analysis is investigated in local region due to the local sector nonlinearity. We introduce the concept of region of model and region of stability to characterize the stability property. The stability region can be obtained by using the level set of Lyapunov function. In addition, a global stability condition is addressed. As a second part of thesis, we discuss the tracking control of nonlinear systems by using T-S fuzzy model. To cope with the problem of immeasurable states, the observer-based fuzzy controller is our main concern. An H 1 performance criterion is proposed to attenuate the disturbance due to immeasurable premise variables. Furthermore, an asymptotical tracking can be achieved when the disturbance is with a Lischitz-type property. All the stability conditions and the derivation of control gains are converted into LMIs problems which can be solving by Matlab’s toolbox.
Contents
1IntroductoryChapter1
1.1Background...................................1
1.2 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Takagi-Sugeno Fuzzy System 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Construction of T-S Fuzzy Model . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Sector Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 T-S Fuzzy Model [27] . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Parallel Distributed Compensation . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Linear Matrix Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Calculation of Summation Index . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 T-S Fuzzy Model with Local Sector Nonlinearity 18
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 T-S Fuzzy Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Stability Region of T-S Fuzzy Model . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Determined by Vector Field on the Boundary . . . . . . . . . . . . 23
3.3.2 Determined By the Level Set of Lyapunov Function . . . . . . . . . 26
3.3.3 Extended to State-Feedback Systems . . . . . . . . . . . . . . . . . 26
3.4 Application on a Boost Converter . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Global Stability Analysis of T-S Fuzzy Model . . . . . . . . . . . . . . . . 36
3.6 Example for Global Stability . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 Tracking Control Design with Fuzzy Observer 43
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Basic Fuzzy Tracking Control . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.1 Tracking Control Design . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.2 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Measurable Premise Variables . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.1 Fuzzy Observer Design . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.2 Stability Conditions for Tracking Control . . . . . . . . . . . . . . . 48
4.4 Immeasurable Premise Variables . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4.1 Tracking Control Based on Robust Performance . . . . . . . . . . . 51
4.4.2 Disturbance Satisfying Lipschitz Condition . . . . . . . . . . . . . . 54
4.5 Global Tracking Control Design with Observer . . . . . . . . . . . . . . . . 55
4.5.1 All Measurable States . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.2 Measurable Premise Variables . . . . . . . . . . . . . . . . . . . . . 56
4.6 Simulation Results for Chua’s Circuit System . . . . . . . . . . . . . . . . 57
4.6.1 Simulation Result for Section 4.2 . . . . . . . . . . . . . . . . . . . 59
4.6.2 Simulation Result for Section 4.3 . . . . . . . . . . . . . . . . . . . 59
4.6.3 Simulation Result for Section 4.4 . . . . . . . . . . . . . . . . . . . 60
4.7 Example for Global Tracking Control . . . . . . . . . . . . . . . . . . . . . 60
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5 Conclusions 71
References 72

List of Figures
2.1 Global sector nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 For global sector nonlinearity, Á(x) is bounded by d1 and d2 . . . . . . . . 8
2.3 Local sector nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 For local sector nonlinearity, Á(x) is bounded by d1 and d2 only in the
region [ ¡ d; d] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 The concept of parallel distributed compensation . . . . . . . . . . . . . . 13
3.1 The vector field on boundary x1 = 2 . . . . . . . . . . . . . . . . . . . . . 23
3.2 The vector field on boundary x2 = 1 . . . . . . . . . . . . . . . . . . . . . 24
3.3 The state trajectory starting from initial state (0,5.3) . . . . . . . . . . . . 25
3.4 The stable region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 The Boost Converter Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 The state ˜ x response for the boost converter . . . . . . . . . . . . . . . . . 33
3.7 The state ˜ x response only for T-S fuzzy controller . . . . . . . . . . . . . . 34
3.8 The state ˜ x response for boost converter with initial state(-150,-50) . . . . 35
3.9 The state trajectory, membership function and controller with D = 1, d = 0:1 41
3.10 The state trajectory and controller with D = 1, d = 0:1 and D = 50, d = ¡ 50 42
4.1 Chua’s circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Tracking control of x1(t) and x2(t) with measurable states . . . . . . . . . 62
4.3 Tracking control of x3(t) and controller input with measurable states . . . 63
4.4 Tracking and observer for x1(t) and x2(t) with known premise variables . . 64
4.5 Tracking and observer for x3(t) and controller input with known premise
variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6 Tracking and estimation error for x(t) with known premise variables . . . . 66
4.7 Tracking and observer for x1(t) and x2(t) with unknown premise variables . 67
4.8 Tracking and observer for x3(t) and controller input with unknown premise
variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.9 Tracking and estimation error for x(t) with unknown premise variables . . 69
4.10 Global Tracking control with measurable states . . . . . . . . . . . . . . . 70
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