結合參數估測及模型簡化之系統判別法則

Abstract

在本篇論文中，我們針對某些多輸入、單輸出的線性數位動態系統，藉由引入model reduction技術作為系統判別法則中之一輔助步驟。然而，對於多輸入、多輸出的系統，在特定的情形下，可將其視為多個多輸入、單輸出的系統，相同的技術一樣能套用上。而我們所用的估測法則仍是承接Gauss (1809) 提出的Least-squares Theory來做最佳的參數估測。Model reduction部分，採用balanced realization的方式。經由Matlab電腦模擬的結果，說明了我們所提出的這項方法是正確的，同時也是可行的。這篇論文的研究成果對於適應控制、系統監控都有相當之重要性。

In this thesis, we focus on system identification of some digital multi-input single-output systems, by combining parameter estimation and model reduction techniques. However, the same techniques could be also applied to multi-input multi-output system. In parameter estimation, we still apply least-squares theory (Gauss, 1809) to perform optimal estimation. In model reduction, we employ balanced realization methods. Finally, the results via computer software simulation conform to our algorithm. This search is important in adaptive control, system monitoring, etc. English Abstract ……………………………………………………………… ii Acknowledgement …………..………………………………………………….. iii Contents ……..……………………………………………………….. iv List of Tables ……………………………………………………………… vi List of Figures ……………………………………………………………… vii Chapter 1 Introduction ……………………………………………..…….. 1 1.1 General description …………………………..…………….. 1 1.2 Literature review ………………………………………… 2 1.3 The purpose of this thesis and propose approach ………… 2 1.4 Organization of this thesis ……………..……………….. 3 Chapter 2 Materials and Methods ………………………………………… 5 2.1 Representation of dynamic system …………………..…….. 5 2.2 Parameter estimation methods ………………………… 6 2.2.1 Least-squares theory ……………………………… 7 2.2.2 Sequential least-squares estimation ……………… 8 2.3 Model reduction methods ……………………………… 10 2.3.1 Balanced realization ……………………………… 10 Chapter 3 Main results …………………………………………………… 13 3.1 Formulation of A LTI MISO system …….…….…………….. 13 3.1.1 1st order example …………………………..……….. 16 3.1.2 2nd order example ………………………..………….. 22 3.1.3 Mixed order example ……………………………… 28 3.2 A System subject to modal type disturbance …………………… 34 3.2.1 1st order example …………………………..……….. 36 3.2.2 2nd order example …………………………..……….. 41 3.2.3 3rd order example ………..……………………..…… 46 3.3 A cascade LTI MISO system ……………..…………………….. 51 3.3.1 1st order example ………………………………..….. 53 3.3.2 2nd order example ……………………………..…….. 58 3.3.3 Mixed order example ……………………………… 63 3.4 A feedback LTI MISO system ………………………..…….. 68 3.4.1 1st order example ………………………..………….. 71 3.4.2 2nd order example …………………………..……….. 76 3.4.3 Mixed order example ……………………………… 81 3.5 Discussion …………………………………………………… 86 Chapter 4 Conclusion ………………………………………………..….. 87 References …………………………………………………………………… 89