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Research Papers

# A Survey/Review of Frequency-Weighted Balanced Model Reduction Techniques

[+] Author and Article Information
Abdul Ghafoor2

School of Electrical, Electronic and Computer Engineering, University of Western Australia, Western Australia 6009, Australiaaghafoor@ee.uwa.edu.au

Victor Sreeram

School of Electrical, Electronic and Computer Engineering, University of Western Australia, Western Australia 6009, Australiasreeram@ee.uwa.edu.au

$SΣ=ΣS$, where $S$ is a diagonal matrix with the diagonal elements $±1$.

A transfer function $X(s)$ is called co-inner(38) if $X(s)XT(−s)=I$. A transfer function $X(s)$ is called inner if $XT(−s)X(s)=I$. Note that $X(s)$ need not be square. A matrix function is called all-pass if $X(s)$ is square and $XT(−s)X(s)=I$.

2

Present address: National University of Science and Technology, Pakistan.

J. Dyn. Sys., Meas., Control 130(6), 061004 (Sep 24, 2008) (16 pages) doi:10.1115/1.2977468 History: Received August 31, 2006; Revised June 05, 2008; Published September 24, 2008

## Abstract

In this paper, a survey/review of frequency-weighted balanced model reduction techniques is presented. Several comments regarding their properties are given. A modified frequency interval Gramian based method is also presented. The computational issues are also discussed. The techniques are illustrated and compared using practical numerical examples.

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## Figures

Figure 1

Closed-loop system diagram: P(s) is the plant and K(s) is the full order controller

Figure 2

Closed-loop system diagram: P(s) is the plant, K(s) is the full order controller, and Kr(s) is the reduced-order controller

Figure 3

Integration limits for various frequency ranges

Figure 4

Four disk system

Figure 5

Singular value comparison of the error functions σ[W(s)(K(s)−Kr(s))V(s)], where Kr(s) is the sixth order controller

Figure 6

Singular value comparison of the error functions σ[W(s)(K(s)−Kr(s))V(s)], where Kr(s) is the seventh order controller

Figure 7

Simple mechanical system

Figure 8

Singular value comparison of the error functions σ[G(s)−Gr(s)] in the desired frequency range [ω1,ω2]=[3,10]rad∕s.

Figure 9

Singular value comparison of the error functions σ[G(s)−Gr(s)] in the desired frequency range [ω1,ω2]=[3,10]rad∕s. A close up view.

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