面向永磁同步电机无位置传感器驱动的新型 K_∞ 等效滑模控制

A Novel K∞-Function-Based Equivalent Sliding Mode Control for Position-Sensorless Drives of Permanent Magnet Synchronous Motors

摘要

针对永磁同步电机（PMSM）无位置传感器驱动中，磁链观测器存在谐波干扰及对电气参数失配和负载变化的鲁棒性差等问题，提出了一种基于新型 K_∞ 等效滑模控制（K_∞-ESMC）的无位置传感器驱动策略。首先，在系统干扰及其导数未知的情况下，为实现系统状态的有限时间收敛，结合超螺旋算法、等效控制理论与 K_∞ 函数，设计了一种新型 K_∞-ESMC 方法，并根据李雅普诺夫稳定性理论证明了其收敛性；然后，为分别提高转子位置信息的观测性能和对电气参数失配及负载变化等干扰的鲁棒性，采用提出的 K_∞-ESMC 方法，分别设计了自适应混合有效磁链观测器（HAFO）和自适应转速观测器。实验结果表明：相比基于经典 HAFO 的驱动方法，提出的驱动策略提高了电机的动态性能和对电气参数失配及负载变化的鲁棒性，在宽速域变速测试中，最大转速观测误差减少了约 34 r/min，最大位置观测误差减少约 0.4 rad；在 1.5 N·m 阶跃负载测试中，电机可在约 1.93 s 内恢复至 500 r/min 运行；除此之外，在定子电阻的 50%与 200%失配测试中呈现了良好的鲁棒性。

Abstract

To address harmonic interference in flux observers and poor robustness to electrical parameter mismatches and load variations in position-sensorless drives of permanent magnet synchronous motors (PMSMs),a position-sensorless drive strategy based on a novel K∞-function-based equivalent sliding mode control (K∞-ESMC) is proposed.First,to achieve finite-time convergence of the system states when system disturbances and their derivatives are unknown,a novel K∞-ESMC method is designed by combining the super-twisting algorithm,equivalent control theory,and the K∞-ESMC function,and its convergence is proved based on Lyapunov stability theory.Then,to improve rotor-position observation performance and robustness to disturbances such as electrical parameter mismatches and load variations,an adaptive hybrid active flux observer (HAFO) and an adaptive speed observer are designed using the proposed K∞-ESMC method.It is shown by experimental results that,compared with the drive method based on the conventional HAFO,the dynamic performance of the motor and its robustness to electrical parameter mismatches and load variations are improved by the proposed strategy.In wide-speed-range variable-speed tests,the maximum speed observation error is reduced by approximately 34 r/min,and the maximum position observation error is reduced by approximately 0.4 rad.In the 1.5 N·m step-load test,operation at 500 r/min is restored within approximately 1.93 s.In addition,good robustness is demonstrated under stator-resistance mismatch conditions of 50% and 200%.

关键词

永磁同步电机 / 无位置传感器驱动 / 混合有效磁链观测器 / K_∞ 等效滑模控制

Key words

permanent magnet synchronous motor / position-sensorless drive / hybrid active flux observer / K∞-function-based equivalent sliding mode control

参考文献

[1] 侯利民,赵世杰,兰骁儒,等. 基于多智能体系统一致性的多永磁同步电机转速协同控制方法[J]. 中国电机工程学报, 2025,45（10）：4034-4045.

[2] Hou Limin,Zhao Shijie,Lan Xiaoru,et al. Speed cooperative control for multi—PMSMs based on multi—agent systems consensus[J]. Proceedings of the CSEE, 2025,45（10）：4034-4045.

[3] 许观达,肖飞,连传强,等. 考虑 VSI 非线性影响的内置式永磁同步电机无电流传感器 MTPA 控制策略[J]. 电工技术学报, 2025,40（10）：3131-3142.

[4] Xu Guanda,Xiao Fei,Lian Chuanqiang,et al. Current sensorless MTPA operation of interior permanent magnet synchronous motor drives considering VSI nonlinearity[J]. Transactions of China Electrotechnical Society, 2025,40（10）：3131-3142.

[5] 张航,梁文睿,陈哲,等. 基于定子磁链间接计算的内置式永磁同步电机无位置传感器鲁棒性提升控制[J]. 中国电机工程学报, 2022,42（7）：2723-2732.

[6] Zhang Hang,Liang Wenrui,Chen Zhe,et al. Sensorless robustness improvement control for IPMSM drive based on stator flux indirect calculation[J]. Proceedings of the CSEE, 2022,42（7）：2723-2732.

[7] 刘计龙,肖飞,沈洋,等. 永磁同步电机无位置传感器控制技术研究综述[J]. 电工技术学报, 2017,32（16）：76-88.

[8] Liu Jilong,Xiao Fei,Shen Yang,et al. Position—sensorless control technology of permanent—magnet synchronous motor—a review[J]. Transactions of China Electrotechnical Society, 2017,32（16）：76-88.

[9] 王菁,颜建虎,季国东,等. 一种基于双位置观测器的永磁同步电机低速无位置传感器控制方法[J]. 电工技术学报, 2023,38（2）：375-386.

[10] Wang Jing,Yan Jianhu,Ji Guodong,et al. A sensorless control method for permanent magnet synchronous machine based on dual position observers at low speed[J]. Transactions of China Electrotechnical Society, 2023,38（2）：375-386.

[11] 张国强,项润华,王高林,等. 基于静止轴系脉冲信号注入的永磁同步电机无传感器控制策略[J]. 中国电机工程学报, 2021,41（12）：4297-4305.

[12] Zhang Guoqiang,Xiang Runhua,Wang Gaolin,et al. Pulse signal injection in stationary reference frame for sensorless PMSM drives[J]. Proceedings of the CSEE, 2021,41（12）：4297-4305.

[13] 林起联,刘凌,刘思源. 面向永磁同步电机无传感器控制的新型已知回归项有效磁链全阶模型[J]. 西安交通大学学报, 2024,58（11）：147-155.

[14] Lin Qilian,Liu Ling,Liu Siyuan. Novel known regressor active flux full—order model for sensorless control of permanent magnet synchronous motors[J]. Journal of Xi’an Jiaotong University, 2024,58（11）：147-155.

[15] 孙庆国,朱晓磊,牛峰,等. 基于改进型积分滑模观测器的 PMSM 无位置传感器控制[J]. 中国电机工程学报, 2024,44（8）：3269-3277.

[16] Sun Qingguo,Zhu Xiaolei,Niu Feng,et al. Sensorless control of permanent magnet synchronous motor based on improved integral sliding mode observer[J]. Proceedings of the CSEE, 2024,44（8）：3269-3277.

[17] 刘思源,刘凌. 面向永磁同步电机无传感器控制的二阶改进扩展状态观测器[J]. 西安交通大学学报, 2024,58（8）：1-8.

[18] Liu Siyuan,Liu Ling. A second—order improved extended states observer for permanent magnet synchronous motor sensorless control[J]. Journal of Xi’an Jiaotong University, 2024,58（8）：1-8.

[19] Jin Dongsong,Liu Ling,Liang Deliang.A flux observer based on a dual—layer adaptive algorithm for SPMSMs position sensorless drive[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2025,13（2）：2358-2371.

[20] 张彦平,尹忠刚,苏明,等. 基于共振扩张状态观测器的内置式永磁同步电机统一全速域无位置传感器控制[J]. 电工技术学报, 2023,38（22）：6070-6081.

[21] Zhang Yanping,Yin Zhonggang,Su Ming,et al. Unified full speed sensorless control of interior permanent magnet synchronous motor based on resonance extended state observer[J]. Transactions of China Electrotechnical Society, 2023,38（22）：6070-6081.

[22] Kshirsagar P,Burgos R P,Jang J,et al. Implementation and sensorless vector—control design and tuning strategy for SMPM machines in fan—type applications[J]. IEEE Transactions on Industry Applications, 2012,48（6）：2402-2413.

[23] Jin Dongsong,Liu Ling,Lin Qilian,et al. Sensorless control strategy of PMSM with disturbance rejection based on adaptive sliding mode control law[J]. IEEE Transactions on Transportation Electrification, 2024,10（3）：5424-5438.

[24] Jin Dongsong,Liu Ling. Adaptive second—order disturbance observer—based position sensorless drive strategy for PMSM[J]. IEEE Transactions on Power Electronics, 2024,39（12）：16415-16428.

[25] Xu Wei,Jiang Yajie,Mu Chaoxu,et al. Improved nonlinear flux observer—based second—order SOIFO for PMSM sensorless control[J]. IEEE Transactions on Power Electronics, 2019,34（1）：565-579.

[26] 骆正红,胡亚山. 基于巴特沃斯结构的改进磁链观测器的永磁同步电机无位置传感器控制[J]. 电机与控制学报, 2024,28（9）：60-69.

[27] Luo Zhenghong,Hu Yashan. Improved flux observer based on Butterworth filter for sensorless control of permanent magnet synchronous motor[J]. Electric Machines and Control, 2024,28（9）：60-69.

[28] Park Y,Sul S K. Sensorless control method for PMSM based on frequency—adaptive disturbance observer[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2014,2（2）：143-151.

[29] Liu Jiali,Zhang Yongchang. Performance improvement of nonlinear flux observer for sensorless control of PMSM[J]. IEEE Transactions on Industrial Electronics, 2023,70（12）：12014-12023.

[30] Liu Yang,Li Hongyi,Lu Renquan,et al. An overview of finite/fixed—time control and its application in engineering systems[J]. IEEE/CAA Journal of Automatica Sinica, 2022,9（12）：2106-2120.

[31] Shen Xiaoning,Liu Guangxin,Lin Xinpo,et al. Robust fixed—time sliding mode control for DC/DC converters with varying exponential coefficient[J]. IEEE Transactions on Power Electronics, 2026,41（5）：8054-8064.

[32] 刘思源,刘凌,靳东松. 永磁同步电机新型有效磁链固定时滑模扰动辨识策略[J]. 西安交通大学学报, 2023,57（9）：144-151.

[33] Liu Siyuan,Liu Ling,Jin Dongsong. A novel active flux fixed—time sliding mode disturbance identification method for permanent magnet synchronous motor[J]. Journal of Xi’an Jiaotong University, 2023,57（9）：144-151.

[34] Yu Xiang,Li Peng,Zhang Youmin. The design of fixed—time observer and finite—time fault—tolerant control for hypersonic gliding vehicles[J]. IEEE Transactions on Industrial Electronics, 2018,65（5）：4135-4144.

[35] 方馨,王丽梅,张康. 基于扰动观测器的永磁直线电机高阶非奇异快速终端滑模控制[J]. 电工技术学报, 2023,38（2）：409-421.

[36] 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.

[37] Moreno J A,Osorio M. Strict Lyapunov functions for the super—twisting algorithm[J]. IEEE Transactions on Automatic Control, 2012,57（4）：1035-1040.

[38] Song Jiawei,Zuo Zongyu,Basin M. New class K_∞ function—based adaptive sliding mode control[J]. IEEE Transactions on Automatic Control, 2023,68（12）：7840-7847.

[39] Huang Xianqing,Lin Wei,Yang Bo. Global finite—time stabilization of a class of uncertain nonlinear systems[J]. Automatica, 2005,41（5）：881-888.

基金资助

国家自然科学基金资助项目(51977173)

国家自然科学基金资助项目(52277065)