Adaptive attenuation of disturbance formed as a sum of sinusoidal signals applied to a benchmark problem

The problem of adaptive attenuation of a disturbance formed as a finite sum of unknown sinusoidal signals is solved for a discrete-time plant with unstable zeros. It is assumed that a reliable model of the plant is known and the system is internally stable. We propose to construct a control signal as a linear combination of outputs of carefully chosen filters. The coefficients of the combination are tuned via an on-line identification based on the plant model. However, our approach avoids constructing an inverse of the plant model. 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 unknown/time-varying sinusoidal signals is demonstrated via simulation and experimental studies.