Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency

Two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency. The rst is an indirect algorithm where the frequency of the disturbance is estimated, and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the eeect of the disturbance. A direct algorithm that uses the concept of a phase-locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously. Approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters. Simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency. The indirect algorithm is found to have a larger capture region for the parameter estimates, whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates. The content of the paper does not necessarily reeect the position or the policy of the federal government, and no oocial endorsement should be inferred.