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

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

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(2): 121-127

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 (Ⅱ)[J]. Applied Mathematics and Mechanics, 2004, 25(2): 121-127.

Citation:

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 (Ⅱ)[J]. Applied Mathematics and Mechanics, 2004, 25(2): 121-127.

Citation:

PDF( 290 KB)

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

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

FullText(HTML)

References(6)

References

[1]	钟万勰, 吴志刚, 高强，等.H∞分散控制系统范数计算的模态综合法(Ⅰ)[J]. 应用数学和力学, 2004,25(2):111—120.
[2]	Leung A Y T.Dynamic Stiffness & Sub-Structures[M].London: Springer,1993.
[3]	王文亮, 杜作润.结构振动与动力子结构分析[M].上海: 复旦大学出版社, 1985.
[4]	ZHONG Wan-xie, Williams F W, Bennett P N. Extension of the Wittrick-Williams algorithm to mixed variable systems[J].Journal of Vibration and Acoustics,Transactions of the ASME,1997,119(3): 334—340. doi: 10.1115/1.2889728
[5]	ZHONG Wan-xie, Howson W P, Williams F W. H∞ control state feedback and Rayleigh quotient[J].Computer Methods in Applied Mechanics and Engineering,2001,191(3-5): 489—501. doi: 10.1016/S0045-7825(01)00286-9
[6]	Jamshidi M. Large-Scale Systems—Modeling, Control and Fuzzy Logic[M].New Jersey: Prentice-Hall, 1997.