Robustness analysis of an adjoint optimal iterative learning controller with experimental verification

Abstract

A new modification to the steepest-descent algorithm for discrete-time iterative learning control is developed for plant models with multiplicative uncertainty. A theoretical analysis of the algorithm shows that if a tuning parameter is selected to be sufficiently large, the algorithm will result in monotonic convergence provided the plant uncertainty satisfies a positivity condition. This is a major improvement when compared to the standard version of this algorithm, which lacks a mechanism for finding a balance between convergence speed and robustness. The proposed algorithm has been investigated experimentally on an industrial gantry robot and found to display a high degree of robustness to both plant modelling error and initial state error. The algorithm also exhibits both long-term performance and excellent tracking performance, as demonstrated by experimental tests of up to 4000 iterations. To further examine robustness, the plant has been approximated by simple models including one consisting of an integrator and a gain. A simple tuning rule for this reduced model is proposed, which generates a stable system with a good rate of convergence. The robustness properties of the steepest descent algorithm have then been experimentally verified.

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Identifiers

ORCID for P L Lewin: orcid.org/0000-0002-3299-2556

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

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