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研究生:黃志成
研究生(外文):Chih-ChengHuang
論文名稱:具有奇異的系統矩陣之系統的模型轉換及控制
論文名稱(外文):Model Conversion and Control for the System with a Singular System Matrix
指導教授:蔡聖鴻
指導教授(外文):Jason Sheng-Hong Tsai
學位類別:博士
校院名稱:國立成功大學
系所名稱:電機工程學系碩博士班
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:2013
畢業學年度:101
語文別:英文
論文頁數:131
中文關鍵詞:模型轉變黎卡迪方程式矩陣符號函數奇異系統數位重新設計
外文關鍵詞:Model conversionRiccati equationmatrix sign functionsingular systemsdigital redesignrobust control
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本論文主要研究主題,敘述如下:首先以矩陣符號函數運算技術與模型轉換演算法,針對具有奇異的系統矩陣之多重輸入及狀況延遲系統,提出新的連續系統及離散系統模型相互轉換演算法。其次,再針對可穩定之奇異系統,藉由有效且適當設定廣義的黎卡迪方程式權重矩陣方法,提出保證可解之演算法,且藉由矩陣符號函數運算求出黎卡迪方程式之解。進一步,藉由第一項研究主題所提出的模型相互轉換演算法,針對具有奇異的系統矩陣之奇異系統,設計具有預測特性數位重新設計之資料採樣追蹤控制器。在相同的輸入與初值條件下,可使數位追蹤器之數位化控制模型與理論上設計良好的連續模型之狀態變數緊密貼近。最後,使用強健控制方法,探討一類內含確定範圍邊界的扇形或量化致動器及未知但有界的雜訊之非線性奇異系統,提出保證全域指數穩定控制器設計方法。此外,在此研究主題中,可估算上述穩定化後之系統的穩定收斂速度。在本論文中,更以多個例題來說明所提方法之有效性。
The research objectives of this dissertation are stated as follows. Firstly, based on matrix sign function techniques, conversion algorithms, translating bilaterally discrete models between continuous ones, are newly presented for multiple input-state-delay systems with a singular continuous-time system matrix. Secondly, for stabilizable singular systems, a constructive methodology for assign the appropriate weighting matrices of the generalized Riccati equation, is proposed to guarantee the solvability of the equation and to solve it via the matrix sign function. Thirdly, to design the sampled-data tracker for the singular system with a singular continuous-time system matrix, a prediction-based digital redesign is derived by using the proposed modeling conversion shown in the first research topic. As a result, the state of the digitally controlled model closely matches the state of theoretically well-design continuous-time one with the same input and initial condition. Finally, a robust control scheme is proposed to guarantee the globally exponential stability for a class of nonlinear singular systems with the actuator in a certain range and unknown-but-bounded disturbance. Moreover, the corresponding convergence rate of such stabilizable systems is estimated in this research topic. Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies.
中文摘要 i
Abstract ii
Acknowledgement iii
Contents iv
List of Tables vii
List of Figures viii
Symbols and Abbreviations x
Chapter 1 Introduction 1
1.1 Literature Survey 2
1.1.1 The matrix sign function and discrete-continuous model conversion 2
1.1.2 Algebraic Riccati equation 3
1.1.3 The singular system control problems 4
1.1.4 Digital redesign 8
1.2 Dissertation Overview 12
Chapter 2 Continuous to Discrete Model Conversion for the Multiple Input-State-Delay System with a Singular System Matrix 15
2.1 Introduction 16
2.2 Continuous to Discrete Model Conversion for the System with a Singular System Matrix 17
2.3 Continuous to Discrete Model Conversion for the System with Multiple Input-State Time Delay 22
2.4 Illustrative Examples 26
2.5 Summary 32


Chapter 3 Discrete to Continuous Model Conversion for Multiple Input -State-Delay System with a Singular Continuous-Time System Matrix 34
3.1 Introduction 35
3.2 Discrete to Continuous Model Conversion for the System with a Singular Continuous-Time System Matrix 35
3.3 Discrete to Continuous Model Conversion for the System with Multiple Input-State Time Delay 39
3.4 Illustrative Examples 43
3.5 Summary 53
Chapter 4 Solving Algebraic Riccati Equation for Singular System 54
4.1 Introduction 55
4.2 Solving the Generalized Algebraic Riccati Equation 58
4.3 Illustrative Examples 65
4.4 Summary 73
Chapter 5 An Alternative Digital Redesign for the Equivalent Model of the Sampled-Data Linear Singular System with a Singular System Matrix 74
5.1 Introduction 75
5.2 An Optimal Tracker for the Regular Model with a Feedthrough Term 75
5.3 An Illustrative Example 82
5.4 Summary 87
Chapter 6 Constraint Actuator for a Class of Nonlinear Singular Systems with a Singular System Matrix and Disturbance 88
6.1 Introduction 89
6.2 Globally Exponential Stabilization for a Class of Nonlinear Singular System 89
6.3 An Illustrative Example 95
6.4 Summary 97


Chapter 7 Conclusions 99
7.1 Conclusions 99
7.2 Future Research Directions 100
Appendix A The Principal th Root of a Matrix and the Associated Matrix Sector Function 102
Appendix B The Singular System Descriptions 106
Appendix C Solving Riccati Equation via Matrix Sign Function 115
References 117
Biography 130
Publication List 131

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