Contents I. Introduction
In recent years, permanent magnet linear synchronous motor (PMLSM) has the advantages of simple structure, easy maintenance and fast response speed, therefore, they are widely used in the field of servo systems such as logistics and transport, rail transport, industrial robots and military [1]–[2]. However, PMLSM is a nonlinear, strongly coupled and multivariable controlled object [3]. Although PI control can be used in permanent magnet servo systems, the traditional PI control will have a large overshoot and is difficult to meet the control requirements of the servo system due to the fact that it will also be subject to external loads and other disturbance in practical applications [4]. With the rapid development of control theory and computer technology, in order to improve the response speed, anti-disturbance ability and control accuracy of the system, national and international scholars have carried out a lot of research, and put forward several nonlinear control methods applied in servo systems, such as predictive control [5], neural network control [6], fuzzy control [7] and sliding mode control. Among them, sliding mode control, as a variable structure control method, has the advantages of simple structure, corresponding rapidity and robustness to uncertainty and disturbance and has been widely used in practical systems. However, due to the use of convergence law control, the traditional linear sliding mode control is prone to large chattering, and no matter how the parameters are selected, the system error will only infinitely converge to the equilibrium state, which cannot be converged in a finite time, limiting its application in practical systems. An integral sliding mode structure is proposed, where a linear combination of the error integral over the speed and the speed error itself is selected as the sliding mode surface, which improves the robustness and stability of the system, but slows down the response time of the system due to its convergence law selection [8]. Terminal sliding mode control is put forward to ensure the convergence of finite time duration, but it suffers from slow convergence and singularity problems [9]. Repeated sliding mode control method is proposed, which introduces the error of its same moment in the previous week at the same moment from the current week, so as to achieve the purpose of eliminating the error, which is difficult to achieve in practical engineering applications, although it is good to improve the disturbance resistance and stability [10].
