Iterative learning control and repetitive control for engineering practice

TLDR

Linear iterative learning and repetitive control are introduced as general‑purpose control laws that require only a few tunable parameters, analogous to PID controllers in classical control. The study seeks to present these linear iterative learning and repetitive control laws that need only a few tunable parameters. The authors show that tuning is straightforward: by adjusting the command to an existing feedback controller and enforcing a suitable transient condition, the method yields large reductions in tracking error. Experiments on a commercial robot reduced RMS tracking error by 100–1000× within 8–12 learning trials, and the same design criteria apply to both learning and repetitive control.

Abstract

This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune. The method of tuning them is straightforward, making tuning easy for the practicing control engineer. The approach can then serve the same function for learning/repetitive control, as PID controllers do in classical control. Anytime one has a controller that is to perform the same tacking command repeatedly, one simply uses such a law to adjust the command given to an existing feedback controller and achieves a substantial decrease in tracking error. Experiments with the method show that decreases by a factor between 100 and 1000 in the RMS tracking error on a commercial robot, performing a high speed trajectory can easily be obtained in 8 to 12 trials for learning. It is shown that in engineering practice, the same design criteria apply to learning control as apply to repetitive control. Although the conditions for stability are very different for the two problems, one must impose a good transient condition, and once such a condition is formulated, it is likely to be the same for both learning and repetitive control.