A common setting for the design of iterative learning and repetitive controllers with experimental verification

Abstract

SUMMARYPrevious work has shown that the structure of repetitive control (RC) and that of iterative learning control (ILC) differ only in the location of an internal model of the disturbance. In this paper, it is shown how this common setting permits derivation of controllers in one domain based on an existing controller in the other. This is illustrated using the following case studies: 1) an RC scheme using a state feedback structure is derived based on an existing ILC scheme, which also uses state feedback (the underlying structure is first extended to comprise both current‐error feedback and previous‐error feedforward implementations); and 2) an ILC scheme using an output injection structure is developed based on an existing RC scheme, which uses state feedback, but differs from 1) by containing only a single internal model representation. All controllers are shown to have similar equivalent representations, with parameters derived by using linear quadratic regulator analysis. This correspondence enables comparison of the effect of the structure (ILC or RC, state feedback or output injection), number of internal models, and use of error (feedback or feedforward) on subsequent performance. This is undertaken using experimental results obtained using a gantry robot. Copyright © 2012 John Wiley & Sons, Ltd.