Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part I: Theory

[+] Author and Article Information
Foued Ben Amara, A. Galip Ulsoy

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109

Pierre T. Kabamba

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109

J. Dyn. Sys., Meas., Control 121(4), 648-654 (Dec 01, 1999) (7 pages) doi:10.1115/1.2802530 History: Received March 14, 1997; Online December 03, 2007


An adaptive regulation approach against disturbances consisting of linear combinations of sinusoids with unknown and/or time varying amplitudes, frequencies, and phases for SISO LTI discrete-time systems is considered. The new regulation approach proposed is based on constructing a set of stabilizing controllers using the Youla parametrization of stabilizing controllers and adjusting the Youla parameter to achieve asymptotic disturbance rejection. Three adaptive regulator design algorithms are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time varying are given. In the case of error feedback, the on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance of the adaptation algorithms is illustrated through a simulation example. A companion paper [4] describes the implementation and evaluation of the algorithms for the problem of noise cancellation in an acoustic duct.

Copyright © 1999 by The American Society of Mechanical Engineers
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