Repetitive control of continuous systems: comparative study and application

A comparative study of two learning control schemes is presented for a class of linear continuous systems: one of them is the well known Arimoto´s algorithm, the other one is based on a closed loop controlled system using classical regulators. Both schemes are based on the particularity that the system has to refer to a periodically repeated predetermined trajectory, with the main objective of finally improving the system reactions principally with regard to the modeling errors and periodic disturbances. The stability studies are based on a frequency approach which is particularly well adapted to reveal the properties and limits of such algorithms according to the dynamic elements of the process transfer function. All the theorem proofs are given, and an example on the application of these theorems to a few process families with both algorithms outlining their differences and similarities is presented. Experimental results on an active magnetic bearing are included