Practical tracking control of linear motor via fractional-order sliding mode

In this work, a novel discrete-time fractional-order sliding mode control (SMC) scheme is proposed, which guarantees the desired tracking performance of a linear motor control system. By using Euler's discretization method, a discrete-time model is firstly established for the linear motor, which includes the nonlinear friction and the uncertainties. Considering the practicability of the engineering application, a new discrete-time fractional-order sliding surface is constructed by taking the Grünwald–Letnikov definition based fractional-order difference of the tracking error into account. Compared to the classical integer-order sliding surface, by the proposed fractional-order sliding surface in this work, a better performance can be achieved due to the memory effect of the fractional calculus. To drive the system trajectories to the predefined sliding surface in finite sampling steps, a novel equivalent control is then designed, which can adjust the switching control input adaptively. Meanwhile, the theoretical analysis for the tracking error of the linear motor system is presented, and the practical reachability of the sliding surface is validated by numerical simulations. Finally, the effectiveness of the proposed control strategy is verified by a group of tracking experiments on a linear motor platform.