Unified Analysis of Iterative Learning and Repetitive Controllers in Trial Domain

While iterative learning control (ILC) and repetitive control (RC) have much ground in common, they fundamentally differ in the initial conditions at each repetition. This difference has lead to distinct analysis techniques, hereby clouding the interrelations between both control strategies. To facilitate the transfer of results, this paper presents a unified approach to ILC and RC. Both control problems are formulated in the trial domain using so-called system lifting. For a given system, the corresponding ILC and RC trial-domain models differ, and a thorough system theoretic analysis and comparison of these models is performed. To illustrate the value of a unified formulation of ILC and RC, the analysis of the most commonly used ILC and RC structures is harmonized. This analysis reveals central differences and similarities between various stability, monotonic convergence and steady-state performance conditions.