Tracking analysis of an adaptive vibration controller

The problem of rejection of a sinusoidal disturbance of known frequency, acting at the output of a discrete-time complex-valued linear stable plant with unknown dynamics, is considered. It is assumed that output signal is contaminated with wideband measurement noise. The paper presents convergence and tracking analysis of a new narrow-band disturbance elimination scheme described recently. It is shown that the proposed adaptive feedback regulator converges locally in the mean to the optimal (minimum-variance) regulator. It is also shown that it has very good robustness properties.