Small gain robustness issues in the p-integrator repetitive controller

Abstract

The basic theory of the digital p-integrator controller is utilized to modify the command to a stable analog feedback control system in order to produce zero tracking error of a repetitive command. Mapping of continuous time poles and zeros to the images in the discrete time domain is performed. It is shown that for a pole excess of one, with p odd, the p-integrator learning controller will often produce a stable learning process, even for relatively large sample times. For a pole excess of two, a stable learning process can often be achieved for any p as long as the sample time is kept sufficiently short. Therefore, when the pole excess is zero and one utilizes the proper p-integrator controller with p odd, stable performance is often produced, even for relatively large sample times.