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Design of an iterative learning control for a servo system using multi-dictionary matching pursuit

Many motion systems repeatedly follow the same trajectory. However, in many cases, the motion system does not learn from tracking errors obtained in a previous cycle. Iterative Learning Control (ILC) resolves this issue by compensating for previous tracking errors, but it suffers from not being able to distinguish between tracking errors caused by machine dynamics versus errors caused by noise, and by trying to ’learn’ the noise, additional errors are introduced. In this paper we address this issue by using the servo error signal by identifying the time-varying nonlinear effects, which can be learned and therefore improve the position accuracy, versus the stochastic effects, which cannot be learned. The identification of these effects is performed by means of time-frequency analysis of the servo error and therefore our goal is to obtain a high-resolution time-frequency energy distribution of the analyzed signal. Here we compare the servo error energy distribution by three means: (1) Wigner distribution; (2) adaptive signal decomposition over one dictionary of modulated versions of wavelets (simple atomic dictionary); (3) and by means of combining several simple atomic dictionaries into a complex atomic dictionary. We show that the latter approach leads to the highest-resolution energy distribution and tracking performance.