Recursive sliding mode control with adaptive disturbance observer for a linear motor positioner

The control performance of linear motor (LM) is deteriorated by payload variations, friction, and external disturbances. In this paper, a robust recursive sliding mode controller combined with an adaptive disturbance observer (RSM-ADO) is proposed for the high-speed and high-precision control of an LM positioner. The benefits of the proposed ADO lie in that it can be designed without the need for the upper bound information of the disturbance and its derivative. Hence, the ADO is ideally capable of rejecting any time-varying disturbances. Furthermore, a recursive integral sliding surface is constructed for the RSM controller such that the reaching phase is eliminated. Benefiting from the proposed recursive structure, the tracking error can converge to zero in finite time. Besides, system chattering is eliminated in the reaching control input due to the integral element. Lyapunov analysis is investigated to prove the finite time convergence of the tracking error under the proposed RSM-ADO control scheme. Experiments demonstrate the superior property of stronger robustness and fewer chattering effects of the proposed method compared to existing disturbance observers and adaptive recursive terminal sliding mode (ARTSM) controller.