Design of a Noncausal FIR Model Inverse as a Compensator in Repetitive Control

Richard W. Longman () and Benjamas Panomruttanarug ()
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Richard W. Longman: Columbia University
Benjamas Panomruttanarug: Columbia University

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2005, pp 297-306 from Springer

Abstract: Summary A new method of designing compensators for repetitive controllers is presented. The ideal compensator is a filter that is the inverse of the plant, but this is usually unstable, and therefore cannot be used in practice. The approach used here works on a restricted class of transfer functions, and bypasses this difficulty by making a noncausal FIR model of the plant inverse. This model has poles only at the origin, and is therefore stable. Methods are presented to adjust the three parameters of the design for stability and good learning speed, i.e. the repetitive control gain, and the number of causal, and the number of noncausal gains chosen to compose the finite impulse response model. A third order system is studied, which models the closed loop behavior of one link of a commercial robot. One can produce a stable design with a number of gains ranging from 11 to 15 (this gives the number of real time computations for control update), and these numbers are not particularly sensitive to sample rate. Using 18, 20, or 30 gains can produce a quite reasonable plant inverse model that gives fast learning in repetitions at all frequencies.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27170-3_23

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DOI: 10.1007/3-540-27170-8_23

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