Adaptive compensation of disturbances formed as sums of sinusoidal signals with application to an active vibration control benchmark

An intuitive solution for the problem of adaptive attenuation of a disturbance formed as a finite sum of unknown sinusoidal signals is proposed for an internally stable discrete-time plant. The compensator is formed as a weighted sum of stable filters. An identification-based procedure for adaptive tuning of the coefficients is proposed for the case of unknown disturbance. We also propose a time-invariant compensator that provides perfect attenuation of a disturbance for the case when a model identification error is sufficiently small and disturbance frequencies are known. The technique is applied to a case study on a challenging benchmark example in the field of active vibration control. Attenuation of a disturbance formed as a sum of up to three sinusoidal signals with unknown/time-varying frequencies is demonstrated via simulation and experimental studies.