臺灣博碩士論文加值系統

自然界，大部分的系統都是用連續時間系統的狀態方程式來描述。由於在數位技術及微電子學方面的快速進步，使得原本以類比設計的控制方法可以用數位控制器去實現，並且得到吾人所希望的提高可靠度、降低設計成本、更具設計上的彈性以及高性能的控制法則的設計目標。許多有關數位控制器的設計方法發表在文獻上，無論如何，保證控制系統的穩定度才是最重要的課題。
本文提出以線性矩陣不等式(linear matrix inequalities, LMIs)及李亞波諾夫穩定準則(Lyapunov stability criterion)為基礎，針對線性非時變離散時間系統而提出一些有關穩定度分析及控制法則的設計方法，所設計的數位系統，在設計程序中即已將穩定度考慮進去，並且予以有效的檢查。吾人考慮三個數位設計的問題，包括數位重新設計、狀態回授及基於觀測器的數位強健穩定控制與數位順滑模態控制器的設計，吾人將所有穩定的充份條件利用Schur complement轉換成線性矩陣不等式的表示方式，並且以套裝軟體的工具箱予以有效的求解。最後，吾人以數值範例來說明所提設計方法確屬有效。

Most physical control systems are described by continuous-time state equations for which many well-established analog control design methods are available. With the rapid and revolutionary advances in digital technology and microelectronics, it has made possible to implement such analog controllers using a digital controller for the sake of better reliability, more flexibility, low cost and high-performance control. There are many digital controller design methods reported in the literature. However, to guarantee the stabilizability of the control systems is the most important issue.
This thesis presents some stability analyses and controller design method for a class of linear uncertain discrete-time systems based on linear matrix inequalities (LMIs) techniques and Lyapunov stability criterion. With the developed LMI-based stability condition, the stability of the designed digital systems is effectively checked during the design procedure. Digital redesign approach, state feedback observer-based robust stabilization control and sliding mode control cases are considered; some sufficient stability and stabilization conditions are represented in terms of LMIs, which can be solved efficiently by using existing LMI software packages. Finally, numerical examples are given to illustrate the effectiveness of the proposed design methods.

Chinese Abstract i
English Abstract ii
Contents iii
List of Tables v
List of Figures vi
Chapter 1 Introduction
1.1 Introduction 1
1.2 Literature Review 3
1.3 Motivations and Objectives 7
1.4 Mathematical Preliminaries 8
1.4.1 Definition of Linear Matrix Inequalities 8
1.4.2 Schur’s Complement 9
1.4.3 S-procedure 10
1.4.4 Congruence Transformation 11
1.4.5 Generalized eigenvalue problems 11
1.5 Contributions of the Thesis 12
1.6 Thesis Organization 13

Chapter 2 Digital redesign using LMI techniques
2.1 Introduction 14
2.2 Problem Statement 18
2.3 Main Results 21
2.4 Numerical Verifications 26
2.5 Concluding Remarks 34

Chapter 3 State feedback and observer-based robust
stabilization Design using LMI
3.1 Introduction 35
3.2 State Feedback Design Using LMI 36
3.3 Observer-Based Robust Stabilization Design Using LMI 42
3.4 Simulation Results 51
3.5 Concluding Remarks 59

Chapter 4 LMI –based sliding mode controller design
method
4.1 Introduction 60
4.2 Nominal Discrete-Time System Sliding Mode Controller
Design 61
4.3 Discrete-Time System with State Uncertainty and
Matched Disturbance Sliding Mode Controller Design 66
4.4 Discrete-Time System With State Uncertainty and
Mismatched Disturbance Sliding Mode Controller
Design 73
4.5 Numerical example 75
4.6 Concluding Remarks 80

Chapter 5 Conclusions and future work
5.1 Conclusions 81
5.2 Future Work 82

References 84

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