High Order Nonsingular Fast Terminal Sliding Mode Control of Permanent Magnet Linear Motor Based on Disturbance Observer

Permanent magnet linear synchronous motor (PMLSM) has higher thrust density and lower heat loss. There are no mechanical coupling and ball screw problems, so it is widely used in the field of high-speed, high-precision CNC machining. Because the motor works in complex and changeable working environment such as model uncertainty, load disturbance, parameter perturbation. PMLSM system usually has a variety of matched/mismatched disturbances, and the problems of the rapidity and accuracy deterioration of position tracking are shown. To address these issues, a high order nonsingular fast terminal sliding mode control strategy based on disturbance observer is proposed in this paper. Firstly, a PMLSM dynamic model including matched/unmatched disturbances is established. The dynamic model takes position error, velocity error and feedback current as state variables. Then, a nonlinear disturbance observer (NDO) is designed to observe matched/unmatched disturbances, thus reducing the conservatism of the system to multiple disturbances. Then, based on the PMLSM system model and observation disturbance, a high-order nonsingular fast terminal sliding mode controller (HNFTSMC) is designed. Its characteristic is that the acceleration error term is added to the sliding mode surface of the traditional nonsingular fast terminal to establish the connection between the sliding mode surface and the control voltage. Realize the overall control of motor position, speed and current, and improve the dynamic and stable performance of the position tracking system. On the one hand, nonlinear disturbance observer is used to weaken chattering of sliding mode control and enhance the ability to suppress mismatched disturbances. On the other hand, sliding mode control can effectively improve the robustness of the system to the disturbance observation error. The introduction of current and observation disturbances into the sliding mode surface can improve the dynamic performance of the system. Finally, the correctness and effectiveness of the proposed control strategy are verified by experiments. Under no load condition, the tracking error of HNFTSMC-NDO method under cosine command is −5.09～5.54μm, the tracking error of HNFTSMC is −10.29～11.38μm, and the tracking error of NFTSMC is −16.08～18.65μm. Under load conditions, the tracking error of HNFTSMC-NDO method is −6.28～6.85μm, the error of HNFTSMC is −13.38～14.08μm, and the error of NFTSMC is −21.89～22.88μm. The tracking errors of the three methods under the triangle wave command at no load are respectively within 4.43～4.53μm, 6.97～10.25μm, and 14.35～14.16μm. The tracking error range of the three methods under load is 5.62～5.03μm, 10.44～14.35μm and 16.45～16.80μm respectively. When the command is a step signal, the sudden change of load makes the positions of the three control systems change suddenly, but in terms of fluctuation amplitude and recovery time, HNFTSMC-NDO (0.11mm, 0.013s), HNFTSMC (0.2mm, 0.014s) and NFTSMC (0.31mm, 0.021s). The above results show that HNFTSMC-NDO achieves better control accuracy and robustness in the tracking process. The following conclusions can be drawn from the above analysis: ① In this paper, the position error, velocity error and feedback current are taken as state variables, and the influence of matched/mismatched disturbance is considered to construct the PMLSM mathematical model. ② A nonlinear disturbance observer is used to estimate the matched/mismatched disturbances, which provides an idea to reduce the conservatism of the system to multiple disturbances and weaken the chattering problem in sliding mode control. ③ By adding system disturbance value and feedback q axis current to the sliding mode surface, HNFTSMC-NDO is designed to achieve the overall control of position, speed and acceleration, which can effectively improve the dynamic and stable performance of the linear motor servo system and the performance of restraining disturbance. © 2023 Chinese Machine Press. All rights reserved.