The super-twisting algorithm (STA, a class of second-order sliding mode control (SOSMC)) is widely used in permanent magnet linear synchronous motor (PMLSM) systems for its least amount of information and simplest calculations among the SOSMC algorithms. Due to the discretization and sign function of the STA, the chattering problem may be induced. In this paper, we propose an STA method with a defined boundary layer (called δSTA) to further reduce chattering in high-precision positioning system. With the δSTA method, when the sliding variable crosses the zero point, the speed is adjusted via two different saturation functions, instead of discontinuous sign functions of the STA. The proposed control law was proven to be stable, ensuring the establishment of a second-order sliding mode. Both the simulation and experimental results showed that the proposed control scheme, with a defined boundary layer width, can improve the steady-state positioning accuracy and significantly reduce system chattering.

超扭曲算法（STA，一类二阶滑模控制（SOSMC））由于其信息量最少且在SOSMC算法中计算最简单而广泛用于永磁直线同步电动机（PMLSM）系统中。由于STA的离散化和符号功能，可能会引起颤动问题。在本文中，我们提出了一种具有定义边界层的STA方法（称为δSTA），以进一步减少高精度定位系统中的抖动。使用δSTA方法时，当滑动变量越过零点时，可通过两个不同的饱和度函数（而不是STA的不连续符号函数）来调节速度。实践证明，所提出的控制律是稳定的，可以确保建立二阶滑模。