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Research Papers

Minimax State/Residual-Energy Constrained Shapers for Flexible Structures: Linear Programming Approach

[+] Author and Article Information
Matthew Vossler

Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260mvossler@buffalo.edu

Tarunraj Singh

Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, NY 14260tsingh@buffalo.edu

J. Dyn. Sys., Meas., Control 132(3), 031010 (Apr 28, 2010) (8 pages) doi:10.1115/1.4001275 History: Received October 15, 2008; Revised November 13, 2009; Published April 28, 2010; Online April 28, 2010

The focus of this paper is on the design of shaped profiles subject to transient state constraints and terminal energy limits. The issue of robustness to modeling errors is addressed by formulating a minimax optimization problem in a linear programming framework, permitting the generation of near-globally optimal shaped profiles. To illustrate the proposed technique, a deflection-limited/residual energy constrained, controller design for flexible structures undergoing rest-to-rest maneuvers will be presented. Techniques for improving robustness by the addition of state sensitivity equations, which increases the robustness in the vicinity of the nominal model, are explored. Results for the benchmark oscillator illustrate the benefit of the proposed approach over traditional designs.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Undamped floating oscillator

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Figure 2

Linearly approximated residual energy constraints

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Figure 3

Nonrobust deflection-limited control profile for δ=0.15

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Figure 4

Deflection profile

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Figure 5

Post-processed control strategy

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Figure 6

Robust deflection-limited control profile for δ=0.15

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Figure 9

Maximum deflection distribution

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Figure 8

Residual energy distribution

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Figure 7

3-Plant deflection-minimized energy-limited control profile

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