Robust adaptive repetitive control for unknown linear systems with odd-harmonic periodic disturbances

This article presents a novel tracking control strategy for unknown linear systems perturbed by odd-harmonic periodic disturbances that combine adaptive and repetitive control methods. The proposed control strategy results in a robust adaptive odd-harmonic repetitive controller (RA-OHRC). Direct adaptive control with a robust adaptation law is utilized to accurately track the desired trajectory, ensuring the boundedness and convergence of the tracking error. An internal-model-based repetitive controller is added to compensate for periodic disturbances with odd-harmonic components. The boundedness and the convergence of the tracking error are verified through the Lyapunov-based stability analysis. The effectiveness of the proposed RA-OHRC scheme can be demonstrated using the simulation studies involving a servomotor model, which achieves accurate reference tracking, excellent disturbance rejection capability, and robustness against uncertainties.