Repetitive process based higher-order iterative learning control law design

Abstract

Iterative learning control has been developed for processes or systems that complete the same finite duration task over and over again. The mode of operation is that after each execution is complete the system resets to the starting location, the next execution is completed and so on. Each execution is known as a trial and its duration is termed the trial length. Once each trial is complete the information generated is available for use in computing the control input for next trial.

This thesis uses the repetitive process setting to develop new results on the design of higher-order ILC control laws. The basic idea of higher-order ILC is to use information from a finite number of previous trials, as opposed to just the previous trial, to update the control input to be applied on next trial, with the basic objective of improving the error convergence performance. The first set of new results in this thesis develops theory that shows how this improvement can be achieved together with a measure of the improvement available over a non-higher order law.

The repetitive process setting for analysis is known to require attenuation of the frequency content of the previous trial error from trial-to-trial over the complete spectrum. However, in many cases performance specifications will only be required over finite frequency ranges. Hence the possibility that the performance specifications could be too stringent. The second set of new results in this thesis develop design algorithms that allow different frequency specifications over finite frequency ranges.

As in other areas, model uncertainties arise in applications. This motivates the development of a robust control theory and associated design algorithms. These constitute the third set of new results. Unlike alternatives, the repetitive process setting avoids the appearance of product terms between matrices of the nominal system dynamics statespace model and those used to describe the uncertainty set. Finally, detailed simulation results support the new designs, based on one axis of a gantry robot executing a pick and place operation to which iterative learning control is especially suited.

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Identifiers

ORCID for Eric Rogers: orcid.org/0000-0003-0179-9398

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