Abstract：Permanent magnet linear synchronous motor (PMLSM) has been increasingly used in many high-precision machining applications due to its high response, stiffness, and precision. However, the position tracking performance of PMLSM is susceptible to various uncertainties, such as load disturbance and mass change of actuator, because of the omission of the mechanical transmission. Recently, researchers have proposed terminal sliding mode control methods to improve the tracking performance of PMLSM. However, the design of the controller depends on the upper bound of system disturbances. Therefore, an adaptive fractional-order terminal sliding mode control strategy based on a positive semi-definite barrier function (PSB-AFTSMC) is proposed. Firstly, the dynamic model of PMLSM with uncertainties is established. Secondly, the fractional-order terminal sliding mode control method is used to suppress the influence of uncertain factors on the system, which ensures that the tracking error converges in finite time and reduces the steady-state error. To further improve the robust performance of the system, the upper bound of the uncertain disturbance is estimated in real time using the adaptive sliding mode control law. This method avoids the overestimation of the control gain, enhances the robustness of the system, and makes the system error converge to a predefined zero neighborhood. Finally, experimental results show that the strategy improves the tracking accuracy of the system and has strong robustness to load disturbance and payload variations. In order to highlight the superiority of the proposed method, the fractional-order terminal sliding mode control (FTSMC) method and the PSB-AFTSMC method are sequentially performed on a linear motor motion stage for position tracking experiments. When a 2 kg payload is added, the fluctuation frequency of the steady-state error curve of the PSB-AFTSMC is greater than that under nominal conditions, but the fluctuation amplitude remains relatively constant. Compared with the FTSMC, the PSB-AFTSMC has a smaller tracking error, and the tracking error is reduced by 60% around. Furthermore, in the nominal state, the sudden application of variable load disturbance to the linear motor system shows significant fluctuations in the error curve based on both control methods, but the fluctuation amplitude of the PSB-AFTSMC is small, which remains below 15 μm. However, the tracking error curve of the FTSMC method fluctuates with large amplitude, especially in 3~6 seconds, and fluctuates greatly twice with a maximum amplitude of approximately 40 μm. The superiority of the PSB-AFTSMC is reflected in the ability to adapt switching control to amplitude-varying disturbances without the constraint information of disturbances. In contrast, the FTSMC control method depends on the upper bound of uncertain disturbance. Finally, to verify that different orders have a specific impact on the control performance, additional experiments that only change order-value are done. The experimental results demonstrate that the fractional-order terminal sliding mode controller based on 0.5 order has superior control performance. The following conclusions can be drawn from the experimental analysis: (1) Regarding the permanent magnet linear synchronous motor motion platform under uncertain factors, the PSB-AFTSMC-based system demonstrates strong robustness, better tracking performance, and maintains accuracy within 15 μm. Furthermore, the tracking performance varies at different orders, and the fractional-order sliding mode control system near the 0.5 order has good steady-state performance. (2) The adaptive amplitude adjustment of the control input by the positive semi-definite barrier function solves the problem of sliding mode control relying on the bound information of the system disturbance, which is more suitable for practical applications.
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2023, Vol. 38 
