A learning variable structure controller of a flexible one-link manipulator

Abstract

In this paper, tip regulation of a flexible one-link manipulator by Learning Variable Structure Control (LVSC) is investigated. Switching surface is designed according to a selected reference model which relocates system poles to be negative real ones, hence link vibration is eliminated. The proposed LVSC incorporates a learning mechanism to improve regulation accuracy. Rigorous proof shows: the tracking error sequence converges uniformly to zero; the uniformly bounded learning control sequence converges to the equivalent control almost everywhere. For practical considerations, the learning mechanism is further conducted in frequency domain by means of Fourier series expansion, hence achieves better regulation performance. Numerical simulations confirm the effectiveness and robustness of the proposed approach.