Time Domain Prediction of Final Error Due to Noise in Learning and Repetitive Control

Abstract

Repetitive control is a field that creates controllers to eliminate the effects of periodic disturbances on a feedback control system. The methods have applications in spacecraft problems, to isolate fine pointing equipment from periodic vibration disturbances such as slight imbalances in momentum wheels or cryo pumps. A closely related field of control design is iterative learning control (ILC) which aims to eliminate tracking error in a task that repeats, each time starting from the same initial condition. Experiments done on a robot at NASA Langley Research Center showed that the final error levels produced by different candidate repetitive and learning controllers can be very different, even when each controller is analytically proven to converge to zero error in the deterministic case. The difference in final error level can be an important criterion for deciding which controller one wants to implement in practice. A time domain approach to predicting final error was previously developed for ILC which handles a certain class of ILC methods. Here we create methods to include zero phase filtering that is very important in creating practical designs, and we also develop methods for higher order ILC and for repetitive control.