線性系統與T-S模糊系統的強健控制器設計

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詹勝仲(Sheng-Chung Chan) 查詢紙本館藏

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論文名稱

線性系統與T-S模糊系統的強健控制器設計
(Design of Robust Controller for Linear Systems and T-S Fuzzy Systems)

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摘要(中)

本論文主要在探討線性系統和模糊系統的強健控制器的設計，其中包含了系統參數的不確定性以及相關性能的討論。大部分學者對於強健控制的設計都使用李亞普諾夫(Lyapunov)穩定準則作為依據，對於線性系統的狀態回授設計混合 / 的條件下使用線性矩陣不等式(Linear Matrix Inequality - LMI)求解強健的控制器增益，通常都會得到不錯的結果。但對於輸出回授的的設計，會產生非凸集合(non-convex)問題，使得LMI的求解必須做更多的假設。於是本論文的第二章，利用基因演算法(Genetic Algorithm-GA)搜尋最佳的控制器增益應用於輸出回授系統以及混合 / 性能的最小化問題，這個建議的方法並不需要做任何的假設，所以基於GA的強健控制器的增益設計優於LMI演算法。
為了擴展強健控制設計的觀念，本論文也探討非線性系統控制的問題，而非線性系統又可透過Takagi-Sugeno (T-S) 模糊模組的型式來近似非線性系統，進而利用LMI演算法探討其穩定性和控制器的設計。而T-S模糊系統的設計主要採用平行分配補償 (Parallel Distributed Compensation - PDC) 之設計觀念，若複雜的系統將導致T-S模糊的規則數太多，進而造成LMI無法求得共同的正定矩陣P的窘境。因此在第三章建議使用強健控制的觀念，使得PDC的設計少了交叉項的影響，大大的降低LMI演算法的規則數，但是此強健控制器的觀念不容易求得共同的正定矩陣P，因此提出以族群型多項式 (Family of Polynomials) 的穩定理論取代李亞普諾夫的穩定法則，利用混合型的特徵值 (eigenvalues) 來取代混合型的權重，最後透過根軌跡 (Root Locus) 的作圖觀念來判斷T-S模糊系統的穩定度。此方法的優點為不需求得共同正定矩陣P，但缺點為T-S模糊模型必須具備一定的形式和限制。於是本論文在第四章提出模糊區域觀念的設計，來改善上述的問題。
當模糊模型的規則數變多時，此時LMI演算法的規則數也相對的增加，為了降低規則且增加求解的機率，於是提出T-S模糊區域概念，設計強健性的模糊控制器。基於上述模糊區域設計的觀念，將T-S模糊系統擴展至時間延遲的非線性系統。

摘要(英)

The motivation of this dissertation attempts to apply the robust control technologies to nonlinear controller design, for which the nonlinear system can be approximated as a T-S fuzzy system. First, a novel idea is introduced to solve the robust controller which has to satisfy performance requirements. Next, we deal with the T-S fuzzy model with the robust controller design technologies. The fuzzy region concept is used to discuss the complex nonlinear system.
In order to extend the application of robust controller, this study also explores the nonlinear systems as well as their T-S fuzzy models. In addition, we will manage to reduce the rules of the controller such that the interference effect in PDC-based controller can be cancelled. But the robust controller is not easy to find the common positive-definite matrix P. This systematic method is developed by root locus technique to check the stability. The advantage of this method doesn’t need to find the common positive-definite matrix P to satisfy Lyapunov stability criterion, yet the methodology has some restrictions. Therefore, a region-based concept is presented to improve the problem.
The control approach is proposed incorporating fuzzy region concept and robust control techniques to stabilize the general T-S fuzzy models with simple design processes. It was emphasized that the proposed idea can eliminate the interaction between the subsystems. Also, this approach is able to reduce the control rules and the total number of LMIs. At last, we will extend it to the time-delay problem for T-S fuzzy systems.

關鍵字(中)

★ 強健控制
★ T-S模糊系統
★ 線性系統
★ 基因演算法

關鍵字(英)

★ linear systems
★ GA
★ robust control
★ T-S fuzzy systems

論文目次

Abstract
Contents i
Nomenclature iii
Acronyms v
List of Figures vi
List of Tables viii
Chapter 1 INTRODUCTION 1
1.1 Historical Background 1
1.2 Literature Reviews 7
1.3 Motivations and Purposes 12
1.4 Contributions 14
1.5 Organization 14
Chapter 2 DESIGN OF ROBUST CONTROLLER WITH GA-BASED FOR LTI SYSTEMS 16
2.1 Introduction 16
2.2 Preliminaries and Problem Descriptions 17
2.2.1 Descriptions and Performances for Polytopic Model 17
2.2.2 Stable Controller Design via Linear Matrix Inequalities 19
2.3 Design Concept and Preliminaries 21
2.3.1 Generalized edge theorem and Hurwitz testing matrix 21
2.3.2 Average Performance Concept 24
2.4 Main Results 25
2.4.1 Hierarchical Robust Stability Conditions for 25
2.4.2 GA-based Robust Controller Seeking Algorithm 27
2.5 A Numerical Example 32
2.6 Summary 39
Chapter 3 DESIG OF ROBUST CONTROLLER FOR T-S FUZZY MODELS 40
3.1 Introduction 40
3.2 Typical T-S Fuzzy Systems and Its Stability Conditions 41
3.2.1 Descriptions of Typical T-S Fuzzy Models 41
3.2.2 PDC-based State Feedback Fuzzy Controller Design 43
3.2.3 Stable Controller Design via Linear Matrix Inequalities 46
3.3 Design Concept and Preliminaries 49
3.4 Main Results 49
3.4.1 Robust Control Gain of T-S Fuzzy Models 49
3.4.2 The Stability Problem of Robust Controller 51
3.4.3 Check of Stability with Polynomial Method 52
3.5 A Numerical Example 55
3.6 Summary 60
Chapter 4 DESIGN OF ROBUST CONTROLLER WITH FUZZY REGION Concept 61
4.1 Introduction 61
4.2 Regional-based T-S Fuzzy System and Its Stability Conditions 62
4.2.1 Descriptions of Regional-based T-S Fuzzy Model 62
4.2.2 Regional-based Fuzzy Controller Design 65
4.3 Problem Descriptions 69
4.3.1 Extending the Region Concept 69
4.3.2 Regional-based T-S Fuzzy System with Delay-Time 72
4.4 Main Results 73
4.4.1 Stability Analysis of Open-loop Fuzzy System with Time-Delay 73
4.4.2 Stability Analysis of Closed-loop Fuzzy System with Time-Delay 75
4.4.3 Synthesis of Regional-based State Feedback Fuzzy Control via LMI/GA Algorithms 79
4.5 A Numerical Example 82
4.6 Summary 89
Chapter 5 CONCLUSIONS AND RECOMMENDATIONS 89
References 92
Publication List 101

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指導教授

鍾鴻源(Hung-Yuan Chung)

審核日期

2011-8-22

推文