臺灣博碩士論文加值系統

時間延遲 (Time Delay) 效應經常發生在一般的動態系統當中。因此對於控制系統而言，發展一套針對時間延遲系統的穩定性分析以及控制器合成方法將是一個重要的課題。在此篇論文中，我們將提出一套針對複雜非線性時間延遲系統的Takagi-Sugeno模糊建模方法。根據模糊集合法則，此Takagi-Sugeno模糊系統能夠有效描述原始的複雜非線性時間延遲系統。與此同時，針對連續與離散時間延遲仿射 (Affine) 式Takagi-Sugeno模糊系統的穩定性以及穩定化問題也被陳述在本文中。基於Lyapunov穩定準則與Razumikhin定理，疊代線性矩陣不等式 (Iterative Linear Matrix Inequality) 演算法被使用於求解此一系統的穩定性條件。此種疊代線性矩陣不等式演算法被使用在連續與離散時間延遲仿射式Takagi-Sugeno模糊系統的模糊控制器設計，並提供可能的控制器解。更進一步，系統外界干擾 (Disturbance) 也同時被考慮在連續與離散時間延遲仿射式Takagi-Sugeno模糊系統的模糊控制器設計之中。 控制技巧將被運用去解決此一問題，以及當系統遭受外來干擾影響同時 的效能亦能被保證。本文最後，我們將展示一單擺系統 (Pendulum System) 與一聯結車式機械手臂 (Truck–Trailer Mobile Robot) 的數值模擬用以證明本篇論文所提方法的有效性。

Time delay effect often occurs in many dynamical systems. So that stability analysis and synthesis of time-delay systems is an important issue for the control systems. In this thesis, we will introduce the Takagi-Sugeno fuzzy modeling approach for the complex time-delay nonlinear systems. It can provide an effective representation of complex time-delay nonlinear systems in terms of fuzzy sets. Besides, the stability and stabilization issue to continuous and discrete time-delay affine Takagi-Sugeno fuzzy systems are presented. Based on Lyapunov stability criterion and Razumikhin theorem, an Iterative Linear Matrix Inequality algorithm is used to solve the stability conditions. The iterative linear matrix inequality algorithm is used to find the feasible solutions for the synthesis of the Takagi-Sugeno fuzzy controller design for continuous and discrete time-delay affine Takagi-Sugeno fuzzy systems. Moreover, the external disturbance is also considered into the controller design procedure for continuous and discrete time-delay affine Takagi-Sugeno fuzzy systems. The control technique is applied to deal with this problem and the performance is guaranteed for the worst case effect of disturbance on system states. Finally, the numerical simulations for the delayed pendulum system and nonlinear truck–trailer mobile robot system are given to show the applications of the present approach.

Abstract I
Nomenclature III
Acronyms V
List of Table and Figures VI
Table of Contents VIII

I.System Structure and Problem Formulations

1. Introduction 1
1.1 Motivation of This Thesis 1
1.2 Previous Works of the Investigate 2
1.3 Outline of This Thesis 6
1.4 Contributions 6

2. Structure of Takagi-Sugeno Fuzzy Systems
and Problem Formulations 8
2.1 Linearization for NonlinearSystems 9
2.2 Structural of Takagi-Sugeno Fuzzy Systems 11
2.2.1 Homogeneous Takagi-Sugeno Fuzzy Systems 11
2.2.2 Affine Takagi-Sugeno Fuzzy Systems 17
2.3 Parallel Distributed Compensation 23
2.4 Problem Formulations 26
2.5 Summary 28

II.Fuzzy Controller Design to the Nonlinear Time-Delay
Systems via Continuous and Discrete Time-Delay Affine
Takagi-Sugeno Fuzzy Systems

3. Fuzzy Controller Design for Takagi-Sugeno Fuzzy
Systems without Time Delay Effect 29
3.1 Useful Mathematic Tools 30
3.1.1 Linear Matrix Inequalities 30
3.1.2 Iterative Linear Matrix Inequality
Algorithm 34
3.1.3 S-Procedure 36
3.2 Controller Design for Takagi-Sugeno Fuzzy
Systems 37
3.2.1 Homogeneous Takagi-Sugeno Fuzzy Systems 37
3.2.2 Affine Takagi-Sugeno Fuzzy Systems 41
3.3 Summary 47

4. Fuzzy Controller Design for Time-Delay Affine
Takagi-Sugeno Fuzzy Systems 48
4.1 Time-Delay Systems 49
4.2 Fuzzy Controller Design for Continuous
Time-Delay Affine T-S Fuzzy Systems 50
4.2.1 Introduction of Continuous TD-ATSFS 50
4.2.2 Stability Condition for Continuous
TD-ATSFS 53
4.2.3 Fuzzy Controller Design for Continuous
TD-ATSFS via ILMI Algorithm 58
4.3 Controller Design for Discrete Time-Delay
Affine T-S Fuzzy Systems 65
4.3.1 Introduction of Discrete TD-ATSFS 65
4.3.2 Stability Condition for Discrete TD-ATSFS 67
4.3.3 Fuzzy Controller Design for Discrete
TD-ATSFS via ILMI Algorithm 71
4.4 Summary 76

5.Fuzzy Controller Design for Time-Delay Affine
Takagi-Sugeno Fuzzy Systems with Disturbance
Effect 77
5.1 Control Problems 78
5.2 Fuzzy Control of Continuous TD-ATSFS with
Disturbance Effect 79
5.2.1 Introduction of Continuous TD-ATSFSD 79
5.2.2 Stability Condition for Continuous
TD-ATSFSD 82
5.2.3 Fuzzy Controller Design for Continuous
TD-ATSFSD via ILMI Algorithm 89
5.3 Fuzzy Control of Discrete TD-ATSFS with
Disturbance Effect 94
5.3.1 Introduction of Discrete TD-ATSFSD 94
5.3.2 Stability Condition for Discrete
TD-ATSFSD 97
5.3.3 Fuzzy Controller Design for Discrete
TD-ATSFSD via ILMI Algorithm 102
5.4. Summary 107

III.Applications and Conclusions

6. Simulations of Fuzzy Controller Design for
Time-Delay Affine Takagi-Sugeno Fuzzy Systems 108
6.1 Continuous Time Case: Stabilization for a
Nonlinear Pendulum System 109
6.2 Discrete Time Case: Stabilization for a
Practical Nonlinear Truck–Trailer Mobile
Robot System 123
6.3. Summary 134

7. Conclusions and Future Works 135
7.1 Conclusions and Publications 135
7.2 Future Works 137

Appendix 138
Bibliography 147

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