Reduced-order ILC: The Internal Model Principle reconsidered

When iterative learning control (ILC) is applied to improve a system's tracking performance, the trial-invariant reference input is typically known or contained in a prescribed set of signals. Current ILC algorithms, however, neglect this information and only exploit the trial-invariance of the input signal. In this paper we propose a novel ILC design that explicitly incorporates the additional knowledge on the trial invariant input. The proposed design approach results in a reduced-order ILC, in the sense that the order of its trial domain description equals the number of given trial-invariant input signals that are to be tracked. In contrast, current ILC algorithms yield a trial-domain controller of order N, the ILC trial length in discrete time. We discuss the advantages and disadvantages of reduced-order ILC when it is designed to minimize a 2-norm based objective.