Algorithms for iterative learning control of nonlinear plants employing time-variant system descriptions

Abstract

This paper deals with the design of iterative learning controllers (ILC) based on extended state space models for non-linear cyclic process control. In order to design a suitable learning operator, knowledge about the plant's dynamical behaviour is needed which implies that a system model has to be set up. It is expedient to acquire a state space model of the plant using identification methods. Here we deal especially with the case, that a linear model represents system dynamics inadequately. We start with a non-linear model and linearize the system along the current trajectory, thus obtaining a linear time variant model. Using this as basis, we develop methods for identification and control of the nonlinear process. Experimental results show that a good system model is also useful to perform a pre-training for the ILC; this is especially interesting in case large deviations from a desired system output trajectory must be avoided. The presented algorithms have been implemented and tested experimentally with a real-life nonlinear processing plant. Iterative learning Controllers with reduced sampling rateWe use the techniques developed in [2] to design stable linear ILC by choosing an appropriate sampling time (for the ILC). In principle the generic time invariant state space model is represented by:In the course of this paper modifications to this model are added to take the nonlinear dynamics into account.

Entwurf zeitvarianter Filter für iterativ lernende Regelungen auf Basis der Wavelet-Transformation (Design of Time variant Filters for Iterative Learning Controllers based on Wavelet Transforms)

“…Die neben der Beseitigung der Störung noch auftretende Verschlechterung der Konvergenz des ILR durch die Filterung kann man im Vergleich zum ungefilterten ILR zeigen, indem in Gleichung (6) = I gesetzt wird. Da die im Folgenden betrachteten zeitvarianten Filter hauptsächlich in den tatsächlich von der Störung betroffenen Bereichen wirken, ist der Einfluss auf das Konvergenzverhalten des ILR in der Praxis relativ gering.…”