Designing Iterative Learning and Repetitive Controllers

Abstract

This chapter discusses results in learning and repetitive control presented in a series of 60 publications. Emphasis in the summary is on the most practical approaches, with 8 learning laws discussed in detail, together with experimental demonstrations of their effectiveness. The distinction between learning control and repetitive control is discussed, and for linear systems it is suggested that in practical applications there is very little distinction, with most of the learning laws being ones that could be applied to either class of problems. Methods of long term stabilization are introduced, including use of zero-phase low-pass filtering of the error or the accumulated learning signal, and quantization based stabilization. Long term stabilization is demonstrated in experiments up to 10,000 repetitions. Learning laws are presented that require tuning only 2, 3 or 4 parameters. The methods of tuning them are clear, and can be done experimentally without needing a mathematical model. Demonstrations on a commercial robot performing a high speed maneuver, resulted in decreases in the RMS tracking error by factors of 100 to nearly 1,000 in a small number of repetitions. Such improvements can be obtained by simply tuning the learning controller in a manner similar to how one might tune a PD controller.