Ph.D. Thesis Defense by Courtney D. James

(Dr. Nader Sadegh, advisor)

"The Design of Robust Multi-rate Repetitive Learning
(Control with Applications to the Regulation of Practical Systems with Harmonic Disturbances)"

Abstract

Repetitive learning control (RLC) is the term given to a class of controllers that are based in some form on the internal model principle (Francis and Wonham, 1975). It is appli-cable to the control of systems whose task and [significant] disturbances are periodic. RLC exploits the cyclic nature of such systems by using the measured output error(s) to repeatedly update the feedforward plant input so as to theoretically drive the error to zero. In this way, tracking errors can be reduced below that which would be attainable using more conventional control techniques; e.g., proportional-plus-derivative (PD), proportional-integral-derivative (PID), etc...

Convergence and asymptotic stability of a single repetitive controller can be readily assessed for a linear closed-loop system in the absence of noise and transients and subject to only strictly time dependent periodic disturbances. This research, extends the convergence and performance criteria to include more practical cases such as: (a) systems whose periodic disturbance are a function of some state, instead of time; (b) systems in which more than one controller is used in parallel; (c) systems in which the [digital] repetitive controller must sample at a slower rate than the plant (i.e., multi-rate RLC); and (d) systems where non-harmonic errors are also present. Tests were performed both in simulation and empirically on a custom designed test fixture to verify the predicted results and phenomena. It is proven theoretically and experimentally that an upper bound exists on the amplitude of the a sys-tem's disturbances, above which, RLC will no longer converge. In addition, two somewhat novel repetitive controller formulations were developed: (1) a hybrid repetitive controller and (2) an adaptive external model repetitive controller (A-EMRC).