Robust Direct Adaptive Regulation of Unknown Disturbances in the Vicinity of Low Damped Complex Zeros - Application to Active Vibration Control

Abstract : Adaptive feedback control approaches have been widely used to address the issue of rejecting multiple narrow band disturbances with unknown and time varying characteristics (frequency, phase and amplitude), in Active Vibration Control (AVC) and Active Noise Control (ANC). These approaches are based directly or indirectly on the use of the Internal Model Principle and the Youla-Kučera parametrization combined with an adaptive law. All the algorithms associated with these approaches make the assumption that the plant zeros are different from the poles of the disturbance model in order to achieve disturbance compensation. However in practice the problem is more intricate since it is not clear what happens if the plant has very low damped complex zeros (often encountered in mechanical structures) and the frequency of the disturbance is close to the anti-resonance frequency (the resonance frequency of the plant zeros). In this paper we evaluate comparatively in simulation and in real time on a benchmark test bed, two different approaches to deal with the low damped complex zeros of the plant. An evaluation of the combination of the two approaches is also presented.