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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (2): 135-142.

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

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

  1. 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 (II)

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

  1. 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)

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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).

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