Rejection of sinusoidal disturbance of unknown frequency for linear system with input delay

We present a new approach for rejection of a sinusoidal disturbance of unknown frequency, bias, amplitude, and phase for a linear unstable plant with a delay in the control channel. To solve the problem, we combine the well-known predictor feedback approach with the adaptive scheme that identifies the frequency of the disturbance. Compared to the existing results, the dynamic order of our adaptive scheme is low (equal to three) and the approach applies to plants that are unstable and have an arbitrary relative degree. The results are illustrated by the numerical example.