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研究生： 陳家興
Chen, Chia-Hsing
論文名稱： 適用於資料取樣線性奇異系統等效模型之最佳化追蹤器與觀測器:數位重新設計與反覆學習控制方法
Optimal Tracker and Observer for the Equivalent Model of the Sampled-Data Linear Singular System: Digital Redesign and Iterative Learning Control Approach
指導教授： 蔡聖鴻
Tsai, Sheng-Hong Jason
學位類別： 博士
Doctor
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 112
中文關鍵詞： 追蹤器 、觀測器 、奇異系統 、數位重新設計 、反覆學習控制
外文關鍵詞： Tracker, observer, singular system, digital redesign, Iterative learning control
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    • 本論文主要的研究主題，敘述如下：首先，應用現有的一些技術，將線性奇異系統分解轉換可得到一具有直接傳輸項之線性等效正則模型。其次，針對此連續時間具有直接傳輸項之線性等效正則模型，開發出具有高增益特性及最佳化之線性二次型類比追蹤器與觀測器。然後，基於此線性二次型類比追蹤器與觀測器，分別使用具有預估特性與另一種方式之數位重新設計方法，各自發展出在相同的輸入與初值條件下，可使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可緊密貼近的相對應數位追蹤器，以及當模型之狀態變數不可測時之數位觀測器。最後，針對包含有直接傳輸項的連續時間線性非時變之正則模型，提出結合適用於此類模型之線性類比追蹤器之反覆學習控制的策略；此策略中，乃經由此線性類比追蹤器以得到學習控制律之適當控制輸入初值，如此，可有效地改善軌跡追蹤之性能；並藉由狀態初值學習法則，亦可解除典型反覆學習控制設計中初始條件設定之限制。在本論文中，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. First, via some existing techniques, the linear singular system can be decomposed into an equivalent regular system with a feedthrough term, from input to output. Second, the high-gain optimal linear quadratic analog tracker and observer for this equivalent model are developed. Third, based on this linear quadratic analog tracker (LQAT) and observer, the prediction-based digital redesign and alternative digital redesign methodologies are carried out, respectively, to derive the digital tracker for the state of the digitally controlled model closely matches the state of theoretically well-design continuous-time model with the same input and initial condition; and the digital observer while, as the states of both digitally controlled model and continuous-time model are unmeasured in turn. Finally, an iterative learning control (ILC) strategy, by combined with the LQAT, for the continuous-time linear time-variant (LTI) regular model with a singular feedthrough term is presented. The tracking performance improvement is achieved through the initial control input obtained by the LQAT, and the initial condition constraint, in typical ILC design, is removed by together with initial state learning law. 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 Figures vi List of Symbols and Abbreviations ix 1 Introduction 1 1.1 Literature Survey 2 1.1.1 Singular system tracking problems 2 1.1.2 Digital redesign 5 1.1.3 Iterative learning control 13 1.2 Dissertation Overview 15 2 The Equivalent Model of the Linear Singular System 17 2.1 Introduction to the Matrix Sign Function 18 2.2 The Regular Pencil and Standard Pencil 19 2.3 The Decomposition of Singular Systems 20 2.4 Summary 28 3 Optimal Tracker and Observer for the Equivalent Model of the Sampled-Data Linear Singular System: Digital Redesign 29 3.1 Introduction 30 3.2 Optimal Linear Quadratic Analog Tracker and Observer 30 3.3 Prediction-Based Quadratic Digital Tracker 34 3.4 Prediction-Based Quadratic Digital Observer 37 3.5 Illustrative Examples 42 3.6 Summary 54 4 An Alternative Digital Redesign for the Equivalent Model of the Sampled-Data Linear Singular System 55 4.1 Introduction 56 4.2 An Optimal Tracker for the Regular Model with a Feedthrough Term 56 4.3 Illustrative Examples 63 4.4 Summary 75 5 Iterative Learning Control for the LTI Regular Model with a Feedthrough Term Via LQAT 76 5.1 Introduction 77 5.2 ILC Scheme for LTI Regular Model with a Feedthrough Term 78 5.2.1 ILC scheme for a singular feedthrough term 78 5.2.2 ILC scheme for a nonsingular feedthrough term 83 5.3 New ILC Strategy for LTI Regular Model with a Feedthrough Term 84 5.4 Illustrative Examples 85 5.5 Summary 94 6 Conclusions 95 6.1 Conclusions 95 6.2 Future Research Directions 97 References 98 Appendix A The Principal th Root of a Matrix and the Associated Matrix Sector Function 107 Biography 111 Publication List 112

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