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

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 and active noise control. These approaches are directly or indirectly based on the use of the internal model principle and the Youla–Kucera 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 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 antiresonance frequency (the resonance frequency of the plant zeros). In this brief, we comparatively evaluate 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.