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Using basis functions in iterative learning control: analysis and design theory

In this article, we discuss iterative learning control (ILC) for systems with input/output (i/o) basis functions. First, we show that various different ILC formulations in the literature can be captured by a common system representation involving i/o basis functions. Analysis of ILC control objectives in this framework yields ILC controller conditions which are required for convergence and optimal performance. Furthermore, analysis reveals how different ILC objectives (monotonic convergence, performance, minimisation of input amplitudes) can be reached by designing separate parts of the ILC controller. The analysis is subsequently expanded by studying the effects of trial-varying disturbances on performance, which results in suggestions for the compensation of these effects. Finally, we use these results to systematically design ILC controllers for the representation under study, and we show that the found results are applicable to existing ILC problem formulations with i/o basis functions, and problem formulations which can be interpreted as such.