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.
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December 1999
Technical Papers
Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part I: Theory
Foued Ben Amara,
Foued Ben Amara
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109
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Pierre T. Kabamba,
Pierre T. Kabamba
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109
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A. Galip Ulsoy
A. Galip Ulsoy
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109
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Foued Ben Amara
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
A. Galip Ulsoy
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109
J. Dyn. Sys., Meas., Control. Dec 1999, 121(4): 648-654 (7 pages)
Published Online: December 1, 1999
Article history
Received:
March 14, 1997
Online:
December 3, 2007
Connected Content
A companion article has been published:
Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part II: Experiments
Citation
Ben Amara, F., Kabamba, P. T., and Ulsoy, A. G. (December 1, 1999). "Adaptive Sinusoidal Disturbance Rejection in Linear Discrete-Time Systems—Part I: Theory." ASME. J. Dyn. Sys., Meas., Control. December 1999; 121(4): 648–654. https://doi.org/10.1115/1.2802530
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