Periodic disturbance restraint based on adaptive finite-dimensional repetitive control

An adaptive finite-dimensional repetitive control method that combines an adaptive control and finite-dimensional repetitive control is proposed to eliminate periodic disturbance with unknown frequency. The method identify the frequency of periodic disturbance by using an adaptive algorithm on line, and parameters of the finite-dimensional repetitive controller are adjusted to eliminate periodic disturbance. The convergence of this algorithm and stability of system are proved by the small signal input/outputted stable theory and the averaging method. Simulation results verified that the proposed scheme can identify quickly periodic disturbance frequency on line and eliminate periodic disturbance effectively.