Repetitive Control (RC) normally adjusts the command to a feedback control system that is performing a periodic command, or is trying to cancel a periodic disturbance, with the aim of converging to zero error. Iterative Learning Control (ILC) is similar but aims for zero error tracking a repeating finite time command. This thesis develops a series of methods to enhance the performance of such systems or to assist in analyzing their performance. The organization of the thesis is outlined below.

Chapter I introduces the basic concepts of RC/ILC and gives a short overview of their histories. Chapter 2 addresses the problem of cancelling multiple unrelated periodic disturbances in RC systems. The research generalizes RC to cancel multiple unrelated periodic disturbances using an FIR compensator, a zero phase low pass filter for robustness, and an interpolator that helps one handle drifting periods. Chapter 3 studies the way in which the RC objectives of canceling periodic errors of a specific period, and the possible feedback control objective of tracking more general commands, interact in the usual RC configurations. It is shown that placing the repetitive controller inside the feedback control system loop, or putting it outside but with a feedforward command introduced, can allow both objectives to be addressed simultaneously. Chapter 4 investigates how fast an RC system converges to zero tracking error as a settling time and as a function of frequency. It is shown that the heuristic frequency response based estimate of the time for decay can be a good indicator of settling time and also shown that the FIR compensator designed to mimic the inverse of the system frequency response can give particularly fast settling times. Chapter 5 is devoted to studying the relationships between the proofs of convergence using the two formulations. It is seen that many of the issues that must be handled in the continuous time formulation become much simpler in discrete time. It is also shown what is required to make the simplest form of ILC converge in a well behaved monotonic manner. Chapter 6 presents the conclusions.