A Speed-Constrained Sliding Mode Position Controller for PMLSM Based on Control Barrier Function

Sliding mode control (SMC) is widely used in the servo system of permanent magnet linear synchronous motor (PMLSM) and the problem of speed constraint exists in conventional sliding mode position controller (SMPC). The position speed integrated sliding mode controller (PSISMC) is an effective method to constrain speed for SMC due to its advantages of fast response and safety. However, the cascaded sliding mode surface structure of PSISMC makes the sliding mode surface design more complicated, and the low-speed crawling phenomenon in servo system of PMLSM may also affect the positioning accuracy. To handle these issues, a speed-constrained SMPC based on the control barrier function (CBF) is proposed in this manuscript. By introducing CBF, the speed constraint is transformed into a constrained quadratic programming (QP) problem of q-axis current, achieving speed constraint while avoiding the use of cascaded sliding mode surfaces. A good speed constraining effect can be achieved by appropriately selecting the parameters of CBF. In addition, a new sliding mode reaching law consisting of the double power reaching law (DPRL) and a super-twisting-like integral term is proposed. Compared with the exponential reaching law (ERL) in PSISMC, DPRL can alleviate the contradiction between sliding mode chattering and convergence speed. The super-twisting-like term is proposed and designed to alleviate the low-speed crawling phenomenon. Finally, experiments have demonstrated the advantages of CBF-SMC in positioning and tracking performance, as well as the effectiveness of its speed constraint capability.