Rejection of Sinusoidal Disturbances With Unknown Slowly Time-Varying Frequencies for Linear Time-Invariant Systems

In recent years, adaptive schemes have been developed to reject sinusoidal disturbances with unknown frequencies, phases, and amplitudes. However, the analysis methods typically used are only suitable for sinusoidal disturbances with piecewise constant frequencies, ignoring smooth continuous variations. This note proposes a robust adaptive scheme to reject output disturbances dominated by sinusoidal terms with unknown time-varying frequencies. The performance is first analyzed in the ideal case where all the frequencies and their derivatives are known exactly to establish a performance baseline. Then a computationally tractable adaptive algorithm is proposed and analyzed for the more realistic unknown frequency case, and simulations are used to demonstrate the performance of the adaptive scheme.