臺灣博碩士論文加值系統

本篇論文提出一個基於觀測器/卡爾曼濾波器鑑別方法並具有適應性的機制來調整具有多目標權重矩陣的代價函數，因此重新推導出一個用在具有直接傳輸項和輸入、狀態、輸出飽和限制之未知系統的新型軌跡追蹤器。首先，用觀測器/卡爾曼濾波器鑑別方法鑑別出含有直接傳輸項之未知線性或非線性系統的數學等效模型。再藉由等效的數學模型來分析和設計控制器。修改線性二次效能指標使之具有輸入、狀態、輸出飽和限制的概念，並將之離散化，因此透過離散化後的線性二次效能指標還能夠保有連續的線性二次效能指標的表現。為了精
確的限制輸入、輸出、狀態，利用OKID 型調整機制來找出能有效限制輸入、輸出、狀態的權重值。最後，我們可以提出，適用於含直接傳輸項並具有輸入、狀態、輸出飽和限制之未知系統的軌跡追蹤器，基於觀測器/卡爾曼濾波器鑑別方法的權重調整機制。

An observer/Kalman filter identification (OKID) method-based adaptive mechanism for tuning weighting matrices of multi-objective cost function is newly proposed in this thesis. An efficient algorithm is newly derived for the new tracker-design for the unknown system with an input-output feed-through term and input/state/output constraints. First, the unknown linear/nonlinear system containing an input-output feed-through term is identified by the observer/Kalman filter identification (OKID) method to have the equivalent mathematical model, then the controller is analyzed and designed by the equivalent mathematical model. The linear analogue quadratic performance index is modified to contain the term of input, state, and output constraints. The linear analogue quadratic performance index with input, state, and output constraints can be directly discretized into an equivalent discrete function, so that the obtained quadratic sub-optimal digital tracker can preserve the performance of the linear analogue quadratic performance index. In order
to make the exceeding input, state and output update quickly and accurately, an OKID-based adaptive mechanism for tuning the weighting matrices is constructed. Finally, an OKID-based adaptive mechanism for tuning weighting matrices of the new tracker-design for the unknown system with an input-output feed-through term and input, state, and output constraints is proposed.Examples show the usefulness of the proposed design.

中文摘要 ....................... I
Abstract ......................II
Acknowledgments............... IV
List of Contents............... V
List of Tables............... VII
List of Figures............. VIII
Chapter
1. Introduction ..................................... 1
2. Observer/Kalman Filter Identification............. 3
2.1 Basic observer equation.......................... 3
2.2 Computation of Markov parameters................. 5
2.2.1 System Markov parameters ...................... 5
2.2.2 Observer gain Markov parameters ............... 5
2.3 Eigensystem realization algorithm ............... 6
3. A New Tracker for the Equivalent Mathematical Model with a Feed-through Term ..................... 9
3.1 Continuous-time quadratic performance index with input, state, and output constraints .................. 9
3.2 A new optimal digital tracker under input, state, and output constraints for the regular model with a feed-through term ......................................... 11
3.3 An extension for the newly proposed tracker from a given linear system to the unknown nonlinear stochastic system.......18
4. OKID-based Tuning Mechanism ................. 20
4.1 Define calculating parameters............... 20
4.2 Off-line virtual OKID-based tuning systems...... 21
4.3 Tuning weighting matrix......................... 24
4.4 The procedure of performing weighting matrix..... 25
5. Illustrative Examples........................ 28
5.1 Example 5.1 ................................ 28
5.2 Example 5.2 ................................ 29
5.2.1 Without input and state constraints....... 30
5.2.2 With input and state constraints.......... 32
5.3 Example 5.3 ................................ 36
5.3.1 Without input and output constraints...... 38
5.3.2 With input and output constraints......... 40
5.4 Example 5.4 ................................ 44
5.4.1 Without input and output constraints...... 47
5.4.2 With input and output constraints......... 49
5.5 Example 5.5................................. 52
6.Conclusion.................................... 54
References...................................... 55
Appendix A Derivation of Linear Quadratic Discrete-time Performance Index with Input, Output, and State Constraints (3.15).......................................... 58

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