State-space solution to weight optimization problem in loop-shaping control

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• 作者：M. Osinuga^a ; ¹ ; ^{mobolaji.osinuga-2@postgrad.manchester.ac.uk}  ; [Author Vitae] ; S. Patra^b ; ^{sourav@ee.iitkgp.ernet.in}  ; [Author Vitae] ; A. Lanzon^a ; ^{alexander.lanzon@manchester.ac.uk}  ; [Author Vitae]
• 关键词：鈩?/em>&infin ; loop-shaping ; Robust stability margin ; Weight optimization ; Convex optimization
• 刊名：Automatica
• 出版年：2012
• 期刊代码：13_00051098
• 类别：cp
• 出版时间：March, 2012
• 卷：48
• 期：3
• 页码：505-513
• 文件大小：728 K

摘要

This paper proposes a state-space solution to weight optimization problem in loop-shaping control. A pointwise-in-frequency weight optimization framework is transformed into convex optimization searches that are independent of frequency. The introduced optimization problem therefore avoids gridding of the frequency space and consequently, the inaccuracies attributed to fitting transfer functions to magnitude data. In this optimization problem, the order of the weight is specified 鈥榓 priori鈥? thus facilitating the synthesis of low-order controllers, which is desirable from an implementation perspective. The proposed solution algorithm simultaneously synthesizes a robust stabilizing controller and a loop-shaping weight (pre-compensator) that maximize the robust stability margin subject to constraints on the performance and the singular values of the weight. Three numerical examples are given to illustrate the effectiveness of the technique.