We propose an adaptive feedforward cancellation (AFC) scheme based on multirate discretization for compensation of periodic disturbance in hard disk drive servo systems. By discretizing the plant by a multirate scheme, we obtain the inverse of the closed-loop transfer function. Our scheme cancels selected repeatable runout (RRO) components more rapidly even when the disturbance signal is time-varying in both frequency and amplitude. We also show by simulation and experiment that the scheme can attenuate selected RRO harmonics effectively in a wide frequency range without amplifying other frequency harmonics, which cannot be achieved by conventional AFC. Our scheme is robust against time-varying periodic disturbances and actuator resonance frequency shifting.