Trajectory Tracking Control using Fourier Series based Learning Controller with Phase Compensation

W. Zuo, J. Jiang, and L. Cai (PRC)


Fourier series, nonlinear system, tracking, iterative learning control, phase compensation


In this paper, a Fourier series based learning controller (FLC) with a novel phase compensation method is proposed for the tracking control of a class of uncertain nonlinear systems. Without a priori knowledge of the system model, all the nonlinearities and uncertainties are lumped together and compensated for by FLC. The learning algorithm of FLC is designed in the Fourier space, which converts the tracking problem in the time domain into a number of regulation problems in the frequency domain. Due to the clear physical meaning of FLC, the influence of the phase lags between the system input and output can be reduced by the phase compensation method. Therefore, more frequency components can be employed in FLC and the control performance will be greatly improved. Experiments are conducted on a belt-driven positioning table to verify the effectiveness of the proposed control method.

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