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When performing periodic tasks, the modeling uncertainties will also present some periodicity. In this paper, by appropriately applying Fourier series approximation, a practical nonlinear adaptive repetitive controller is proposed for motion control of hydraulic servomechanisms to learn and compensate the periodic modeling uncertainties. Robust control term is also constructed to effectively attenuate the effect of approximation errors, and thus asymptotic tracking performance is achieved. In addition, robustness is also discussed with respect to other nonperiodic disturbances, which reveals a guaranteed transient performance and steady-state tracking accuracy can be achieved by the proposed controller with a practical assumption. Compared to the traditional repetitive controllers, the major advantage of this controller is that it not only requires little exact knowledge of the system dynamic structure or its parameters, but also greatly reduces the noise sensitivity and heavy memory requirements. Comparative experimental results are obtained to verify the high accuracy tracking performance of the proposed control strategy.
Yao et al. (Wed,) studied this question.