Direct adaptive regulation in the vicinity of low damped complex zeros — Application to active vibration control

The adaptive feedback approach is now widely used for the rejection of multiple narrow band disturbances with unknown and time varying frequencies in Active Vibration Control (AVC) and Active Noise Control (ANC). The approach is 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 the approach 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 have 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). A recent international investigation on adaptive regulation in the presence of unknown time varying disturbances [16] has considered such a situation for a benchmark example. Several solutions have been proposed and the most successful has been based on the appropriate choice of the desired closed loop poles to be achieved by the Youla-Kučera central controller [5] using a Q FIR filter with the minimum number of parameters. Recently in [12] it was suggested that over parametrization of the Q (FIR) filter can enhance the robustness of the linear and adaptive scheme in the vicinity of plant complex zeros. The present paper compares these two approaches using the same benchmark example as in [16]. The results from simulations and real time experiments used to evaluate the two approaches are presented.