Design of norm-optimal iterative learning controllers: The effect of an iteration-domain Kalman filter for disturbance estimation

Iterative learning control (ILC) has proven to be an effective method for improving the performance of repetitive control tasks. This paper revisits two optimization-based ILC algorithms: (i) the widely used quadratic-criterion ILC law (QILC) and (ii) an estimation-based ILC law using an iteration-domain Kalman filter (K-ILC). The goal of this paper is to analytically compare both algorithms and to highlight the advantages of the Kalman-filter-enhanced algorithm. We first show that for an iteration-constant estimation gain and an appropriate choice of learning parameters both algorithms are identical. We then show that the estimation-enhanced algorithm with its iteration-varying optimal Kalman gains can achieve both fast initial convergence and good noise rejection by (optimally) adapting the learning update rule over the course of an experiment. We conclude that the clear separation of disturbance estimation and input update of the K-ILC algorithm provides an intuitive architecture to design learning schemes that achieve both low noise sensitivity and fast convergence. To benchmark the algorithms we use a simulation of a single-input, single-output mass-spring-damper system.