Modal Synthesis Method for Norm Computation of <em>H</em><sub>∞</sub> Decentralized Control Systems (Ⅰ)

ZHONG Wan-xie; WU Zhi-gang; GAO Qiang; A. Y. T. Leung; F. W. Williams

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(2): 111-120

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, 2004, 25(2): 111-120.

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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, 2004, 25(2): 111-120.

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Modal Synthesis Method for Norm Computation of H_∞ Decentralized Control Systems (Ⅰ)

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;

Received Date: 2002-12-09
Rev Recd Date: 2003-10-08
Publish Date: 2004-02-15

Abstract

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).
- H_∞ control,
- decentralized control,
- modal synthesis,
- generalized Rayleigh quotient,
- extended Wittrick-Williams algorithm

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References(22)

References

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