Tuning to stabilize adaptive internal model controller for periodic disturbance cancellation

This paper presents an application of adaptive internal model principle controller to an active noise cancellation problem. The algorithm is extended to handling the large phase delays that arise in active noise control problems because of the inherent transport delays. Internal model principle controllers, such as the integral action in a PI controller, require, as a necessary condition of stability, that gains are chosen to ensure negative feedback. Previously the algorithm had fixed gains which resulted in negative feedback, and stability, only for plants whose phase did not vary by more than 180 degrees. By adaptively tuning the two control gains in the feedback loop, this implicit phase requirement is eliminated. The new algorithm now requires, at a minimum, that no more than 100% uncertainty exists in the plant model. Simulations on Ben Amara's model of an acoustic duct show the effectiveness of the proposed approach.