Fourier series based learning control and application to positioning table

A new Fourier series based learning control scheme is presented in this paper. The proposed controller consists of two parts: a time domain feedback controller that is designed to stabilize the system and improve the robustness to random disturbance, and a Fourier series based learning controller that is used to generate the best feedforward in the face of deterministic modeling uncertainties. The learning controller is essentially a feedback controller in frequency domain. A new iterative algorithm based on the Fourier series approximation generates the optimal feedforward to force the state trajectory converge to a stable sliding surface. Only the historical input and output information of the closed-loop system is used. There is no requirement for knowledge about the system structure and parameters. The stability analysis of the closed-loop system with the learning controller is also provided. The effectiveness of the proposed controller is experimentally verified on a positioning table.