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In this paper, a new adaptive method is proposed for online frequency estimation of a periodic disturbance by the output measurement based on the fast Fourier transform algorithm. The performance of the proposed algorithm is evaluated in the face of time varying frequency, time varying amplitude, non-sinusoidal periodic disturbance, and different plants. Also, the convergence rate of the method is compared by other estimation methods. Then, the online estimation is used in the repetitive controller structure for eliminating periodic disturbances with unknown frequencies. A new analysis is performed on RC and the stability conditions are determined in a theorem. These are illustrated in simulation results. The effectiveness of this method is shown on the application of ϕ -shaped PZT active suspension and it is compared by existing results. [ABSTRACT FROM AUTHOR]