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Research Papers

Control Design and Robustness Analysis of Linear Time-Periodic Systems

[+] Author and Article Information
S. Kalender

 University of Southern California, Los Angeles, CA 90089kalender@usc.edu

H. Flashner

 University of Southern California, Los Angeles, CA 90089hflashne@usc.edu

J. Comput. Nonlinear Dynam 3(4), 041003 (Aug 19, 2008) (10 pages) doi:10.1115/1.2960481 History: Received June 19, 2007; Revised January 05, 2008; Published August 19, 2008

This paper proposes a new design approach for control of periodically time-varying systems. The approach is based on the point-mapping technique to obtain an equivalent linear time-invariant sampled-data system for the linear periodically time-varying system with a piecewise parametrization of the control vector. This allows the known control design techniques for sampled-data systems to be applied. The proposed approach is then extended for analysis of robustness of the control design with respect to plant parametric uncertainties. This is achieved by computation of approximate discrete-time dynamics of the perturbed system by truncated point-mappings. By computing an upper norm bound on the error due to the truncated approximations, the robustness analysis of the system with respect to the parametric uncertainties is then formulated as a discrete-time structured singular value problem. Two numerical examples are considered to illustrate the approach and the extension of the approach for robust stability analysis.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Continuous control design problem

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Figure 2

Closed-loop control of an interpolated system

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Figure 3

Discrete-time formulation of the closed-loop system

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Figure 4

General control configuration

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Figure 7

Inverted double pendulum subjected to periodic forcing

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Figure 8

Closed-loop state trajectories

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Figure 9

Closed-loop control forces

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Figure 10

Closed-loop state trajectories with the quadratic function parametrized steady-state optimal controller for different parameter values

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