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Research Papers

Discrete-Time Control 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. Dyn. Sys., Meas., Control 130(4), 041009 (Jun 09, 2008) (9 pages) doi:10.1115/1.2936871 History: Received March 23, 2007; Revised January 05, 2008; Published June 09, 2008

A discrete-time control design approach for periodically time-varying systems is introduced. The method employs a period-to-period (point-mapping) formulation of the system’s dynamics and a parametrization of the control input to obtain an equivalent time-invariant discrete-time representation of the system. The representation is generalized to include sampling within the period and varying sampling rates in different feedback loops. The proposed formulation allows for the design of feedback control laws using established discrete-time control methodologies. In this paper, dead-beat and optimal control laws with state- or output-feedback control are presented. An example of a multivariable control design for double inverted pendulum with periodic forcing is used to illustrate the proposed approach.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Closed-loop control problem formulation

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Figure 2

Discrete-time formulation of the closed loop system with fast sampling

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Figure 3

Controller-observer configuration

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Figure 4

Inverted double pendulum subjected to periodic forcing

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Figure 5

Closed loop state trajectories and control forces

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Figure 6

Closed loop state trajectories and control forces for fast-sampling configuration (Ts=T∕2)

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Figure 7

Performance comparison: (a) L-F based controller and (b) proposed controllers

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Figure 8

Closed loop state trajectories for output-feedback controllers

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Figure 9

Output-feedback control forces

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