Abstract 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.
Fang Xin,Wang Limei,Zhang Kang. High Order Nonsingular Fast Terminal Sliding Mode Control of Permanent Magnet Linear Motor Based on Disturbance Observer[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 409-421.
[1] 凌志健, 赵文祥, 吉敬华. 高推力永磁直线作动器及其关键技术综述[J]. 电工技术学报, 2020, 35(5): 1022-1035. Ling Zhijian, Zhao Wenxiang, Ji Jinghua.Overview of high force density permanent magnet linear actuator and its key technology[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1022-1035. [2] Zhang Kang, Wang Limei, Fang Xin.High-order fast nonsingular terminal sliding mode control of per-manent magnet linear motor based on double dis-turbance observer[J]. IEEE Transactions on Industry Applications, 2022, 58(3): 3696-3705. [3] 李争, 安金峰, 肖宇, 等. 基于自适应观测器的永磁同步直线电机模型预测控制系统设计[J]. 电工技术学报, 2021, 36(6): 1190-1200. Li Zheng, An Jinfeng, Xiao Yu, et al.Design of model predictive control system for permanent magnet synchronous linear motor based on adaptive observer[J]. Transactions of China Electrotechnical Society, 2021, 36(6): 1190-1200. [4] 王立俊, 赵吉文, 董菲, 等. 基于自适应内模观测器的永磁同步直线电机高带宽强鲁棒预测电流控制策略研究[J]. 中国电机工程学报, 2019, 39(10): 3098-3107. Wang Lijun, Zhao Jiwen, Dong Fei, et al.High-bandwidth and strong robust predictive current control strategy research for permanent-magnet synchronous linear motor based on adaptive internal model observer[J]. Proceedings of the CSEE, 2019, 39(10): 3098-3107. [5] Sun Guanghui, Ma Zhiqiang, Yu Jinyong.Discrete-time fractional order terminal sliding mode tracking control for linear motor[J]. IEEE Transactions on Industrial Electronics, 2018, 65(4): 3386-3394. [6] 付东学, 赵希梅. 永磁直线同步电机自适应反推全局快速终端滑模控制[J]. 电工技术学报, 2020, 35(8): 1634-1641. Fu Dongxue, Zhao Ximei.Adaptive backstepping global fast terminal sliding mode control for per-manent magnet linear synchronous motor[J]. Transa-ctions of China Electrotechnical Society, 2020, 35(8): 1634-1641. [7] 曹荣敏, 郑鑫鑫, 侯忠生. 基于改进多入多出无模型自适应控制的二维直线电机迭代学习控制[J]. 电工技术学报, 2021, 36(19): 4025-4034. Cao Rongmin, Zheng Xinxin, Hou Zhongsheng.An iterative learning control based on improved multiple input and multiple output model free adaptive control for two-dimensional linear motor[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4025-4034. [8] 刘川, 朱非甲, 马伟, 等. 直线电机的线性自抗扰控制[J]. 电机与控制学报, 2013, 17(1): 71-76. Liu Chuan, Zhu Feijia, Ma Wei, et al.Research on linear active disturbance rejection control over linear motor[J]. Electric Machines and Control, 2013, 17(1): 71-76. [9] Shao Ke, Zheng Jinchuan, Huang Kang, et al.Finite-time control of a linear motor positioner using adaptive recursive terminal sliding mode[J]. IEEE Transactions on Industrial Electronics, 2020, 67(8): 6659-6668. [10] 余洋, 田夏, 从乐瑶, 等. 基于反推控制和模态估计的永磁同步电机驱动柔性涡簧储能控制方法[J]. 电工技术学报, 2019, 34(24): 5084-5094. Yu Yang, Tian Xia, Cong Leyao, et al.Energy storage control method of flexible spiral springs driven by permanent magnet synchronous motor based on back-stepping control and modal estimation[J]. Transa-ctions of China Electrotechnical Society, 2019, 34(24): 5084-5094. [11] Butcher M, Karimi A.Linear parameter-varying iterative learning control with application to a linear motor system[J]. IEEE/ASME Transactions on Mechatronics, 2010, 15(3): 412-420. [12] Junejo A K, Xu Wei, Mu Chaoxu, et al.Adaptive speed control of PMSM drive system based a new sliding-mode reaching law[J]. IEEE Transactions on Power Electronics, 2020, 35(11): 12110-12121. [13] Chen S Y, Chiang H H, Liu T S, et al.Precision motion control of permanent magnet linear syn-chronous motors using adaptive fuzzy fractional-order sliding-mode control[J]. IEEE/ASME Transactions on Mechatronics, 2019, 24(2): 741-752. [14] 成瑀, 赵文祥, 吉敬华, 等. 直线永磁游标电机的开绕组单位功率因数直接推力控制[J]. 中国电机工程学报, 2019, 39(7): 1870-1878. Cheng Yu, Zhao Wenxiang, Ji Jinghua, et al.Unity power factor direct thrust force control of linear permanent-magnet vernier motor fed by dual inverter[J]. Proceedings of the CSEE, 2019, 39(7): 1870-1878. [15] Chaudhari S, Shendge P D, Phadke S B.Disturbance observer based controller under noisy measurement for tracking of nDOF uncertain mismatched nonlinear interconnected systems[J]. IEEE/ASME Transactions on Mechatronics, 2020, 25(3): 1600-1611. [16] Aghababa M P.Sliding-mode control composite with disturbance observer for tracking control of misma-tched uncertain nDoF nonlinear systems[J]. IEEE/ASME Transactions on Mechatronics, 2018, 23(1): 482-490. [17] 张康, 王丽梅. 基于反馈线性化的永磁直线同步电机自适应动态滑模控制[J]. 电工技术学报, 2021, 36(19): 4016-4024. Zhang Kang, Wang Limei.Adaptive dynamic sliding mode control of permanent magnet linear syn-chronous motor based on feedback linearization[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4016-4024. [18] 周华伟, 于晓东, 高猛虎, 等. 基于不匹配干扰观测器的圆筒型永磁直线电机新型滑模速度控制[J]. 中国电机工程学报, 2018, 38(7): 2163-2170, 2231. Zhou Huawei, Yu Xiaodong, Gao Menghu, et al.Novel sliding mode speed control for tubular permanent magnet linear motors based on mismatched disturbance observers[J]. Proceedings of the CSEE, 2018, 38(7): 2163-2170, 2231. [19] Sun Guanghui, Ma Zhiqiang.Practical tracking control of linear motor with adaptive fractional order terminal sliding mode control[J]. IEEE/ASME Transa-ctions on Mechatronics, 2017, 22(6): 2643-2653. [20] Qiao Jianzhong, Li Zhenxing, Xu Jianwei, et al.Composite nonsingular terminal sliding mode attitude controller for spacecraft with actuator dynamics under matched and mismatched disturbances[J]. IEEE Transactions on Industrial Informatics, 2020, 16(2): 1153-1162. [21] Boldea I.Linear electric machines, drives, and MAGLEVs handbook[M]. Boca Raton: CRC, 2013. [22] 刘旭东, 李珂, 张奇, 等. 基于非线性扰动观测器的永磁同步电机单环预测控制[J]. 中国电机工程学报, 2018, 38(7): 2153-2162, 2230. Liu Xudong, Li Ke, Zhang Qi, et al.Single-loop predictive control of PMSM based on nonlinear disturbance observers[J]. Proceedings of the CSEE, 2018, 38(7): 2153-2162, 2230. [23] Zheng Jinchuan, Wang Hai, Man Zhihong, et al.Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode[J]. IEEE/ASME Transactions on Mechatronics, 2015, 20(4): 1743-1752. [24] Li Shihua, Tian Yuping.Finite-time stability of cascaded time-varying systems[J]. International Journal of Control, 2007, 80(4): 646-657.
2023, Vol. 38 
