MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (2): 123-134.

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MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

钟万勰¹, 吴志刚¹, 高强¹, 梁以德², F. W. Williams²

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;Visiting City University of Hong Kong;
2. Department of Building and Construction, City University of Hong Kong, Hong Kong, P. R. China

收稿日期:2006-12-09 修回日期:2003-10-08 出版日期:2004-02-18 发布日期:2004-02-18
基金资助:
the National Key Basic Research Special Foundation of China (G1999032805);the National Natural Science Foundation of China (19732020, 10202004);the U K Engineering and Physical Sciences Research Council (GR/R05437/01)

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

ZHONG Wan-xie¹, WU Zhi-gang¹, GAO Qiang¹, A. Y. T. Leung², F. W. Williams²

1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;Visiting City University of Hong Kong;
2. Department of Building and Construction, City University of Hong Kong, Hong Kong, P. R. China

Received:2006-12-09 Revised:2003-10-08 Online:2004-02-18 Published:2004-02-18
Supported by:
the National Key Basic Research Special Foundation of China (G1999032805);the National Natural Science Foundation of China (19732020, 10202004);the U K Engineering and Physical Sciences Research Council (GR/R05437/01)

摘要/Abstract

摘要： When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).

Abstract: When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).

中图分类号:

钟万勰;吴志刚;高强;梁以德;F. W. Williams. MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(2): 123-134.

ZHONG Wan-xie;WU Zhi-gang;GAO Qiang;A. Y. T. Leung;F. W. Williams. MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(2): 123-134.

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MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (Ⅰ)

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