使用BMI最佳化方法之新型強健控制器設計

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Title:	使用BMI最佳化方法之新型強健控制器設計
Other Titles:	A novel robust controller synthesis : bmi optimization approach
Authors:	林俊辰;Lin, Chun-chen
Contributors:	淡江大學電機工程學系碩士班周永山;Chou, Yung-shan
Date:	2005
Issue Date:	2010-01-11 06:57:23 (UTC+8)
Abstract:	強健穩定控制器設計是控制領域的重要問題之一，該問題主要討論在有模式誤差(例如:元件之參數擾動或未建模之動態成分)或外界干擾的情形下，如何設計控制器使系統保持穩定。過去參數擾動情形的研究，大都是利用(D,G)-K疊代交替的計算方法來設計控制器。在這架構中，控制器與乘數運算子之求解是固定其中一個求解另一個，然後交替進行。為了提高系統對擾動的容忍範圍，常需增加它們的階數，因此所得到的控制器階數經常高，增加了硬體實現的困難度，這是(D,G)-K疊代交替設計的一大缺點。近年來，有其他的學者嘗試以雙線性矩陣不等式(bilinear matrix inequality，BMI)的方式來設計控制器，但仍未脫離控制器與乘數運算各自求解的窠臼。有別於以往的(D,G)-K疊代交替設計方法，本論文提出一套新型BMI架構的設計方法，不僅能同時求解控制器與乘數運算子，而且在交替式求解的過程中控制器與乘數運算子的階數都不會增加。從模擬結果中得知我們所提出的μ合成方法的確比過去的方法有更好的效果。 The design of robustly stabilizing controllers is an important issue in the control area, which focuses on synthesizing a controller to keep the closed-loop system stable in the face of possibly various types of modeling errors (such as mismatched system parameters or un-modeled dynamics) and external disturbances. For the real parametric uncertainty cases, the so called (D,G)-K iteration controller synthesis method or named real μ synthesis, had been developed. This method proceeds by designing an optimal controller K with the (D,G)-scalings fixed and computing the (D,G)-scalings with K fixed, and then continues iteratively. In order to enlarge the stability margin of the system, the orders of the controller and the scalings/multipliers are often increased, which makes the hardware implementation of the controller difficult. This is a serious drawback of this method which has its origin at the separate design framework. Recently, some researchers proposed a BMI approach to the robust controller design problem. Nevertheless, the separate design framework of the controller and the multiplier remains. In this thesis, we present a novel robust controller design method in BMI formulation. Quite different from the conventional (D,G)-K iteration method, the proposed method can perform simultaneous search for the controller and the multiplier. In addition, the orders of the controllers and the multipliers are kept fixed during the whole design procedure. Simulation results demonstrate that our method indeed performs better than many other methods.
Appears in Collections:	[Graduate Institute & Department of Electrical Engineering] Thesis

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