Research Papers

Perturbation Theory Based Robust Design Under Model Uncertainty

[+] Author and Article Information
XinJiang Lu

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong

Han-Xiong Li1

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong


Corresponding author.

J. Mech. Des 131(11), 111006 (Oct 07, 2009) (9 pages) doi:10.1115/1.3213529 History: Received February 19, 2009; Revised July 28, 2009; Published October 07, 2009

In real-world applications, a nominal model is usually used to approximate the practical system for design and control. This approximation may make the traditional robust design less effective because the model uncertainty still affects the system performance. In this paper, a novel robust design approach is proposed to improve the system robustness to the variations in design variables as well as the model uncertainty. The proposed robust design consists of two separate optimizations. One is to minimize the variation effects of the design variables to the performance based on the nominal model just as what the traditional deterministic robust design methods do. The other is to minimize the effect of the model uncertainty using the matrix perturbation theory. Through solving a multi-objective optimization problem, the proposed design can improve the system robustness to the uncertainty. Simulation examples have demonstrated the effectiveness of the proposed design method.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Influence of the model uncertainty to singular value σ

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Figure 2

The new robust design methodology

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Figure 3

Design details of the proposed approach

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Figure 4

Maximal singular values of J0 and J versus the design variable d1 (a) σmax0 and σmax and (b) the difference Δσmax

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Figure 5

|Δλ| and the bound S1

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Figure 6

Lower and upper bounds of σmax

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Figure 7

Comparison of the proposed robust design (β=0.95) with the traditional robust design (β=1)

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Figure 8

A low-pass filter

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Figure 9

Performance comparison under Δd, Δp, and the model uncertainty: (a) comparison with the Euclidean norm method and (b) comparison with the condition number method

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Figure 11

Comparison under Δd, Δp, and the model uncertainty: (a) the Euclidean norm method versus proposed method and (b) the condition number method versus proposed method



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