永磁直线同步电机自适应分数阶终端滑模控制

doi:10.19595/j.cnki.1000-6753.tces.221489

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摘要针对永磁直线同步电机的位置跟踪性能易受负载扰动、动子质量变化等不确定性的影响,提出一种基于半正定屏障函数的自适应分数阶终端滑模控制策略。首先,采用分数阶终端滑模控制方法来抑制不确定性对系统的影响,保证了跟踪误差在有限时间收敛,且能够有效的减小系统稳态误差。然后,为了进一步改善系统鲁棒跟踪性能,设计基于半正定屏障函数的自适应控制对不确定扰动的上界进行估计,避免了控制增益的过高估计且削弱了系统抖振。此外,该自适应策略在不需要外界扰动先验信息的情况下,可以使得系统误差收敛到一个预定的零邻域内。最后,实验结果表明该策略提高了系统的跟踪精度,对负载扰动和附加有效载荷具有较强鲁棒性。

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关键词 ：永磁直线同步电机, 自适应分数阶终端滑模控制, 半正定屏障函数, 鲁棒性

Abstract：Permanent magnet linear synchronous motor (PMLSM) has been increasingly used in many high precision machining applications due to its advantages of high response, high stiffness and high 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, terminal sliding mode control methods have been proposed to improve the tracking performance of PMLSM. However, the design of the controller is dependent on the upper bound of system disturbances. To address this problem, 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. Then, 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 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, which 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 2kg payload is added, the fluctuation frequency of steady-state error curve of the PSB-AFTSMC is greater than that of steady-state error curve under nominal conditions, but the fluctuation amplitude does not change much. Compared with the FTSMC, the PSB-AFTSMC has a smaller tracking error, and the tracking error is reduced by about 60%. Furthermore, in the nominal state, 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 within 15μm. However, the tracking error curve of the FTSMC method fluctuates with large amplitude, especially in the period of 3~6 seconds, and fluctuates greatly twice with the maximum amplitude reaching about 40μm. 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, while the FTSMC control method depends on the upper bound of uncertain disturbance. Finally, to verify that different orders have a certain impact on the control performance, an additional set of experiment that only change order-value is done. The experimental result shows that the fractional-order terminal sliding mode controller based 0.5 order has better control performance.
The following conclusions can be drawn from the experimental analysis: 1) Aiming at the permanent magnet linear synchronous motor motion platform under the influence of uncertain factors, the PSB-AFTSMC-based system has strong robustness, better tracking performance, and the accuracy is maintained within 15μm. Moreover, the tracking performance varies at different orders and the fractional-order sliding mode control system near the 0.5 order has better steady-state performance. 2) The adaptive adjustment of the amplitude of the control input by using 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.

Key words： Permanent magnet linear synchronous Motor adaptive fractional-order terminal sliding mode control positive semi-definite barrier function robustness

PACS:

TM36

基金资助:国家自然科学基金项目（51875366）资助项目

通讯作者: 王丽梅女,1969年生,教授,博士生导师,研究方向为交流伺服驱动技术。E-mail：wanglm@sut.edu.cn

作者简介: 赵鑫宇男,1996年生,博士研究生,研究方向为永磁直驱伺服系统及其控制。E-mail：zhaoxy_sut@163.com

引用本文:

赵鑫宇, 王丽梅. 永磁直线同步电机自适应分数阶终端滑模控制[J]. 电工技术学报, 0, (): 67-67. Zhao Xinyu, Wang Limei. Adaptive Fractional-Order Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor. Transactions of China Electrotechnical Society, 0, (): 67-67.

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