Realtime Controller Tuning for Periodic Disturbance Rejection: with Application to Active Noise Control

Incomplete knowledge of plant or disturbance dynamics complicates the design of a feedback control system. Uncertainty in plant dynamics can cause feedback instabilities, and uncertainty in disturbance dynamics may deteriorate feedback performance. In this monograph, we develop and analyze methods that can be used tune feedback controllers to overcome these two difficulties. Several algorithms are presented that deal with uncertainty in the disturbance model alone. Time- varying internal models are used to reject time- varying disturbances, and the stability and performance of the feedback system is carefully analyzed. The situation where the disturbance and the plant models are both uncertain is also considered, and a new algorithm is developed to cancel the uncertain disturbances while maintaining robust stability. The algorithm is developed by considering simultaneous perturbations to the plant and controller. The plant perturbation is used to represent the uncertainty in the plant model and the controller perturbation is identified with the algorithm to achieve the performance goals in the presence of the robustness constraints.