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Hard disk drives (HDDs) encounter a challenge of large storage capacity demand. A particular problem a HDD faces is that a periodic disturbances caused by different sources. These disturbances which do not change drastically will degrade the performance of voice coil motor actuator based servo system so that significant repeatable run-out is formed in position error signal. This paper shows a method which can cancel most of the components in it. In this method, we suppose to rebuild a signal which can approximately represent the disturbances thus cancel the disturbances by adding the opposite value of this signal. When rebuilding this signal, internal model principle and magnitude/phase adaptive estimation algorithm is used to recreate the disturbance signal. Moreover, a polynomial adaptive fitting method which does not need frequency estimation is proposed to deal with time delay problem which exists in the signal recreation stage. It turns out that the adaptive fitting method is much more effective to deal with multiple frequency disturbances. Simulation results show the cancellation effectiveness for single frequency and multiple frequency disturbances even when the disturbance is time-varying in both frequency and amplitude/phase.