Adaptive feedforward compensation algorithms for AVC systems in the presence of a feedback controller

In Jacobson, Johnson, Mc Cormick, and Sethares (2001) and Landau, Alma, and Airimitoaie (2011) adaptation algorithms taking into account the ''positive'' feedback coupling arising in most of the active noise and vibration control systems have been proposed and analyzed. The stability of the system requires satisfaction of a positive real condition through an appropriate filtering of the regressor vector. It is shown in this note that the presence in addition of a feedback controller on one hand strongly influences the positive real conditions for stability and the structure of the filter to be used in the algorithm and on the other hand improves significantly the performance of the system. Experimental results obtained on an active vibration control (AVC) system clearly illustrate the benefit of using a hybrid adaptive feedforward + feedback approach.