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Research Papers

Mixed Additive/Multiplicative H Model Reduction

[+] Author and Article Information
Yin-Lam Chow

e-mail: yldick.chow@gmail.com

Yue-Bing Hu

e-mail: yuebinghu@gmail.com
Department of Mechanical Engineering,
The University of Hong Kong,
Hong Kong, China

Xianwei Li

Research Institute of Intelligent Control and Systems,
Harbin Institute of Technology,
Heilongjiang, Harbin 150080, China
e-mail: lixianwei1985@gmail.com

Andreas Kominek

Institute of Control Systems,
Hamburg University of Technology,
Hamburg 21073, Germany
e-mail: andreas.kominek@tu-harburg.de

James Lam

Department of Mechanical Engineering,
The University of Hong Kong,
Hong Kong, China
e-mail: james.lam@hku.hk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 22, 2012; final manuscript received March 22, 2013; published online May 23, 2013. Assoc. Editor: Won-jong Kim.

J. Dyn. Sys., Meas., Control 135(5), 051005 (May 23, 2013) (10 pages) Paper No: DS-12-1233; doi: 10.1115/1.4024111 History: Received July 22, 2012; Revised March 22, 2013

In this paper, the problem of mixed additive/multiplicative model reduction for stable linear continuous-time systems is studied. To deal with nonsquare or nonminimum phase systems, the multiplicative error bound is constructed using spectral factorization technique. By virtue of the bounded real lemma and the projection lemma, a linear matrix inequality approach is proposed for mixed additive/multiplicative H model reduction, which can be implemented by the well-known cone complementary linearization method. Finally, two numerical examples are provided to demonstrate the effectiveness and advantages of the obtained results.

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References

Figures

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Fig. 1

Block-diagram representation of mixed model reduction scheme

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Fig. 3

Comparison of additive errors in Example 1

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Fig. 4

Comparison of multiplicative errors in Example 1

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Fig. 2

Comparison of maximum singular values of the original system and the reduced-order systems in Example 1

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Fig. 5

The Pareto curve between 1/αadd and 1/αmul of Theorem 1 in Example 1

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Fig. 6

Comparison of magnitude responses of the original system and the reduced-order systems in Example 2

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Fig. 7

Comparison of phase responses of the original system and the reduced-order systems in Example 2

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Fig. 8

Comparison of multiplicative error magnitude responses in Example 2

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