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Research Papers

Polynomial Chaos Based Design of Robust Input Shapers

[+] Author and Article Information
Tarunraj Singh

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

Puneet Singla

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260psingla@buffalo.edu

Umamaheswara Konda

Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY 14260venkatar@buffalo.edu

J. Dyn. Sys., Meas., Control 132(5), 051010 (Aug 24, 2010) (13 pages) doi:10.1115/1.4001793 History: Received May 05, 2009; Revised March 21, 2010; Published August 24, 2010; Online August 24, 2010

A probabilistic approach, which exploits the domain and distribution of the uncertain model parameters, has been developed for the design of robust input shapers. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. Residual energy of the system is used as the cost function to design robust input shapers for precise rest-to-rest maneuvers. An optimization problem, which minimizes any moment or combination of moments of the distribution function of the residual energy is formulated. Numerical examples are used to illustrate the benefit of using the polynomial chaos based probabilistic approach for the determination of robust input shapers for uncertain linear systems. The solution of polynomial chaos based approach is compared with the minimax optimization based robust input shaper design approach, which emulates a Monte Carlo process.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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PC uniform distribution (two delays filter)

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PC uniform distribution (three delays filter)

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Polynomial chaos based estimate of mean and variance

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PC gaussian distribution (two delays filter)

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PC Gaussian distribution (three delays filter)

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Compact support distributions

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PC compact polynomial distribution (two delays filter)

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PC compact polynomial distribution (three delays filter)

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Three mass-spring systems

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Two-dimensional orthogonal basis functions

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Residual energy distribution

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Residual energy distribution

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Computational cost comparison

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