Case studies of filtering techniques in multirate iterative learning control

Iterative learning control (ILC) is a simple and efficient solution to improve tracking accuracy for systems that execute repetitively the same tracing operation. For engineering applications of ILC, the main concern is the monotonic decay of tracking errors, in the sense of infinity norm or peak error, along the trials. Low cost in implementation and robustness in performance are also critical factors. To achieve these important but sometimes contradicting goals, several multirate ILC schemes have been developed, in which different data sampling rates are used for feedback online loop and feedforward ILC offline loop. That is, multirate ILC uses a different (often lower) rate from the sampling rate of a feedback system to update input. Before the input signal is applied to the system for the next trial, it is upsampled to reach the original sampling rate. Since downsampling will cause distortion of frequency spectra, anti-aliasing and anti-imaging filters and signal extension are used together with downsampling and upsampling operations. In this paper, these technologies are integrated with three different multirate ILC schemes, pseudo-downsampled ILC, two-mode ILC, and cyclic pseudo-downsampled ILC, to achieve better performance. A series of experimental results on an industrial robot are presented to demonstrate the efficiency of multirate ILC schemes and compare the performance. The results demonstrate that multirate ILC schemes are able to achieve not only monotonic learning transient, but also much better tracking accuracy than conventional one-step-ahead ILC schemes.