Optimal Adaptive Feedback Disturbance Rejection

Discrete-time adaptive disturbance rejection has broad engineering and scientific applications. It is most relevant in active noise and vibration control. Disturbance rejection algorithms can be of two types, feed-forward or feedback. The latter generally exhibit superior performance since they take into account the effect of the feedback path from control to measurement. In this paper we propose an optimal adaptive feedback disturbance rejection algorithm. The main result is based on a controller parameter update law derived from a retrospective cost function. The proposed algorithm requires minimal plant information and does not require a measurement of the disturbance. This work extends earlier work on ARMARKOV adaptive controllers in several ways. First, we employ an ARMA model stucture for both plant and the controller instead of a μ-MARKOV parameterization thus reducing the number of tunable parameters. Next, the step size function is replaced by an optimal gain matrix. Finally, the proposed algorithm is reformulated in a way that online computations are reduced. The effectiveness of the algorithm in rejecting tonal disturbances with unknown frequency and phase is demonstrated via simulation.