AAS 98-119

BRIDGING LEARNING CONTROL AND REPETITIVE CONTROL USING BASIS FUNCTIONS

Hao-Ping Wen - Columbia Universtiy; M. Q. Phan - Princeton Universtiy; R. W. Longman - Columbia University

Abstract

The field of repetitive control develops control algorithms that learn to eliminate repetitive errors in a feedback controller's response to a periodic command or in its response to a constant command with a periodic disturbance. The typical objective is to attempt to eliminate all tracking error as time progresses for each time step of the period. It is often difficult to obtain this convergence based on the nominal system model, and even when convergence is guaranteed based on the nominal model, phase errors at high frequencies, for example due to unmodeled low amplitude high frequency dynamics, can destroy the convergence. This paper studies the use of projections of the error histories on chosen basis functions sets as a means to obtain improved robustness of repetitive control. The first set of basis function addressed comes from Fourier series, and has the advantage that the understanding of the stability boundary based on frequency response can be applied. Then other sets of basis functions including the use of wavelets are considered, and the potential advantages and disadvantages are investigated.

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