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Research Papers

Robust Stochastic Design of Linear Controlled Systems for Performance Optimization

[+] Author and Article Information
Alexandros A. Taflanidis1

Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556a.taflanidis@nd.edu

Jeffrey T. Scruggs

Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708jeff.scruggs@duke.edu

James L. Beck

Engineering and Applied Science Division, California Institute of Technology, Pasadena, CA 91125jimbeck@caltech.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(5), 051008 (Aug 19, 2010) (15 pages) doi:10.1115/1.4001849 History: Received November 05, 2009; Revised May 03, 2010; Published August 19, 2010; Online August 19, 2010

This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for H2 and multi-objective H2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional “worst-case” notions of robust optimal control.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three-dimensional example of failure surfaces

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Figure 2

Illustration of some key steps in SSO. The x in the plots corresponds to the optimal solution

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Figure 3

Structural model

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Figure 4

Comparison between optimal first-passage reliability (labeled F), H2 and mH2 designs based on nominal model

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Figure 5

Optimal first-passage reliability-based controllers

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Figure 6

Failure probability under optimal robust first-passage reliability design

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Figure 7

Optimal controllers for mH2 synthesis

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Figure 8

Probability of unacceptable performance for (a) optimal design (black curves) and (b) nominal design (grey curves) for different probability models

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