Discrete-time Adaptive Feedback Disturbance Rejection using a Retrospective Performance Measure

ABSTRACT A discrete-time adaptive feedback disturbance rejection algorithm is developed for applications where the disturbance spectrum is unknown. Feedforward control methods are frequently used to reject disturbances with a known spectrum, but a feedback controller is required when the disturbance is unknown. Multi-input multi-output (MIMO) disturbance rejection algorithms are developed for controllers represented by both state-space models and time-series models. The controller parameters are updated using a gradient algorithm. Adaptive step size functions are developed, which guarantee that the controller matrices asymptotically approach their optimal value. We define a retrospective performance as the performance of the system at the current time assuming the current controller had been used over a previous window of time. The retrospective performance is minimized as a surrogate measure of the true performance. Using the retrospective performance allows us to remove dependence on unknown plant and disturbance information. The algorithm requires knowledge of some Markov parameters of the system from the control signal inputs to the performance variables. No information is required of the disturbance spectrum. We demonstrate feedback disturbance rejection on constant, tonal, and broadband disturbances.