Super-twisting sliding mode control with defined boundary layer for chattering reduction of permanent magnet linear synchronous motor

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.