Notch Anti-Stagnation Based Model-Free Predictive Current Sliding Mode Control of Permanent Magnet Synchronous Motor Drives
Wei Yao1, Fu Junrong2, Wang Gaolin3, Wang Fengxiang1
1. National and Local Joint Engineering Research Center for Electrical Drives and Power Electronics Quanzhou Institute of Equipment Manufacturing Haixi Institutes Chinese Academy of Sciences Jinjiang 362216 China; 2. College of Electrical Engineering and Automation Fuzhou University Fuzhou 350100 China; 3. School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China
Abstract：Model-free predictive sliding mode control (SMC) achieves complete independence from physical models and parameters by constructing a data-driven model. However, its modeling and updating processes demand high-quality sampled data. Stagnation and its adverse effects have emerged as a significant challenge. This paper proposes a notch anti-stagnation-based model-free predictive current SMC method for permanent magnet synchronous motor (PMSM) drives. A notch term is designed to extract specific frequency band harmonics generated by the control strategy. These harmonics are inversely injected into the sampled data to force the generation of data gradients. This paper aims to mitigate the risk of stagnation and provide an effective method for high-performance control of PMSMs in complex environments. The proposed method consists of the following key steps. Firstly, a notch term is designed by adjusting the notch width and depth. The harmonics produced by the control strategy do not contribute to model updates. This process generates data gradients, reducing the likelihood of stagnation. Secondly, a universal model is established based on the data gradients, and all model coefficients are estimated using the recursive least squares (RLS) algorithm. The prediction process incorporates time-shift considerations, and the model is ultra-localized to implement an intelligent proportional function as the predictive component in the control function. Thirdly, a non-singular fast sliding mode surface is designed. The sliding mode component of the control function integrates both equivalent and switching control laws. Then, the state variables converge onto the sliding mode surface, forming the complete control function of the system. Finally, the system's stability, robustness, and reachability of the sliding mode component, as well as the convergence and stability of the estimation, are discussed under theoretical conditions. Experimental results on the PMSM platform demonstrate the effectiveness of the proposed method. During steady-states with different load torques and speed references, the proposed method reduces the number of stagnation occurrences from the compared method’s 382 and 339 to 8. In terms of phase current quality, 5th and 7th harmonic contents are reduced, as evidenced by the total harmonic distortion (THD) of single sample points. Under a load torque of 11.5 N·m, continuous Fourier analysis of 1000 sample points shows that the average THD value and THD covering range are reduced from 7.588% and 1.980% to 6.69% and 1.203%, respectively. Similar improvements are observed under a load torque of 4.6 N·m. The proposed method decreases the speed’s integrated time and absolute error (ITAE) from 0.02276 to 0.02129. Finally, guidelines for selecting the main parameters of the proposed method are provided. The following conclusions can be drawn. (1) Compared with the model-free SMC method without anti-stagnation, the proposed method significantly reduces the possibility of stagnation by generating data gradients, effectively addressing stagnation and its adverse effects. (2) The adaptability of the universal model in the predictive component is improved, and the current quality and prediction accuracy are both enhanced by combining with the non-singular fast sliding mode surface in the sliding mode component. (3) The proposed method is independent of physical models and parameters, exhibiting enhanced robustness.
魏尧, 付俊荣, 王高林, 汪凤翔. 基于陷波抗停滞的永磁同步电机无模型预测电流滑模控制[J]. 电工技术学报, 2026, 41(2): 475-486.
Wei Yao, Fu Junrong, Wang Gaolin, Wang Fengxiang. Notch Anti-Stagnation Based Model-Free Predictive Current Sliding Mode Control of Permanent Magnet Synchronous Motor Drives. Transactions of China Electrotechnical Society, 2026, 41(2): 475-486.
[1] 甘醇, 曲荣海, 石昊晨, 等. 宽调速永磁同步电机全域高效运行控制策略综述[J]. 中国电机工程学报, 2023, 43(7): 2496-2512. Gan Chun, Qu Ronghai, Shi Haochen, et al.Review of high-efficiency control strategy for permanent magnet synchronous motors under wide speed range[J]. Proceedings of the CSEE, 2023, 43(7): 2496-2512. [2] 肖虎, 吴公平, 龙卓, 等. 参数失配下永磁同步电机无模型定子磁链滑模控制[J]. 电工技术学报, 2025, 40(12): 3883-3894. Xiao Hu, Wu Gongping, Long Zhuo, et al.Model-free stator flux sliding mode control for permanent magnet synchronous motors considering parameter mis- match[J]. Transactions of China Electrotechnical Society, 2025, 40(12): 3883-3894. [3] 梅三冠, 卢闻州, 樊启高, 等. 基于滑模观测器误差补偿的永磁同步电机无位置传感器控制策略[J]. 电工技术学报, 2023, 38(2): 398-408. Mei Sanguan, Lu Wenzhou, Fan Qigao, et al.Sensor- less control strategy of permanent magnet syn- chronous motor based on error compensation esti- mated by sliding mode observer[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 398-408. [4] 曹亚丽, 曹竣奥, 宋昕, 等. 一种改进滑模观测器的PMSM矢量控制研究[J]. 电力系统保护与控制, 2021, 49(16): 104-111. Cao Yali, Cao Jun’ao, Song Xin, et al.Research on vector control of PMSM based on an improved sliding mode observer[J]. Power System Protection and Control, 2021, 49(16): 104-111. [5] 石欣然, 刘景林, 肖明朗, 等. 基于可变边界层的PMSM滑模观测器无位置传感器控制系统设计[J]. 中国电机工程学报, 2025, 45(14): 5657-5669. Shi Xinran, Liu Jinglin, Xiao Minglang, et al.Position sensorless control system design based on sliding mode observer using variable boundary layer for PMSM[J]. Proceedings of the CSEE, 2025, 45(14): 5657-5669. [6] 李扬, 杨芳艳, 李清都, 等. 永磁同步电机全局积分终端滑模矢量控制[J]. 电力系统及其自动化学报, 2025, 37(4): 21-29. Li Yang, Yang Fangyan, Li Qingdu, et al.Global integral terminal sliding mode vector control of permanent magnet synchronous motor[J]. Proceedings of the CSU-EPSA, 2025, 37(4): 21-29. [7] 廖凯举, 徐伟, 葛健, 等. 基于积分滑模观测器的直线振荡电机谐振频率跟踪控制[J]. 电工技术学报, 2024, 39(14): 4366-4376. Liao Kaiju, Xu Wei, Ge Jian, et al.Resonant frequency tracking control of linear oscillatory machine based on integral sliding mode observer[J]. Transactions of China Electrotechnical Society, 2024, 39(14): 4366-4376. [8] 史婷娜, 赵梦圆, 夏长亮. 基于数据驱动观测器的永磁同步电机显式模型预测直接速度控制[J]. 中国电机工程学报, 2025, 45(4): 1248-1260. Shi Tingna, Zhao Mengyuan, Xia Changliang.Explicit model predictive direct speed control strategy for permanent magnet synchronous motors based on data driven observer[J]. Proceedings of the CSEE, 2025, 45(4): 1248-1260. [9] 赵凯辉, 殷童欢, 张昌凡, 等. 永磁同步电机无模型滑模控制方法研究[J]. 电子测量与仪器学报, 2018, 32(4): 172-180. Zhao Kaihui, Yin Tonghuan, Zhang Changfan, et al.Research on model-free sliding mode control of permanent magnet synchronous motor[J]. Journal of Electronic Measurement and Instrumentation, 2018, 32(4): 172-180. [10] 杨公德, 杨雲静, 林明耀. 基于超螺旋积分滑模观测器的永磁同步电机三矢量无模型预测电流控制[J]. 中国电机工程学报, 2025, 45(16): 6505-6517. Yang Gongde, Yang Yunjing, Lin Mingyao.Three vector model-free predictive current control of permanent magnet synchronous motor based on super- twisting integral sliding mode observer[J]. Proceedings of the CSEE, 2025, 45(16): 6505-6517. [11] 魏尧, 汪凤翔. 基于仿射超局部的交流电机无模型预测控制策略[J]. 东北电力大学学报, 2024, 44(3): 47-54, 130. Wei Yao, Wang Fengxiang.Affine ultra-local-based model-free predictive control strategy on AC motor drives[J]. Journal of Northeast Electric Power University, 2024, 44(3): 47-54, 130. [12] 尹政, 邓富金, 王青松, 等. 双有源桥变换器移动离散控制集无模型预测电压控制策略[J]. 电工技术学报, 2025, 40(6): 1853-1863. Yin Zheng, Deng Fujin, Wang Qingsong, et al.Model-free predictive voltage control with moving- discrete-control-set for dual active bridge con- verters[J]. Transactions of China Electrotechnical Society, 2025, 40(6): 1853-1863. [13] 魏尧, 柯栋梁, 黄东晓, 等. 基于超局部化时间序列的永磁同步电机无模型预测电流滑模控制策略[J]. 电工技术学报, 2024, 39(4): 1022-1032. Wei Yao, Ke Dongliang, Huang Dongxiao, et al.Model-free predictive sliding mode control using ultra-localized time-series for permanent magnet synchronous motor drives[J]. Transactions of China Electrotechnical Society, 2024, 39(4): 1022-1032. [14] 芮涛, 徐婉伦, 胡存刚, 等. 改进的三相并网逆变器双矢量无模型预测控制策略[J]. 电工技术学报, 2025, 40(18): 6029-6039. Rui Tao, Xu Wanlun, Hu Cungang, et al.Improved model-free predictive control strategy for three-phase grid-connected inverter with double-vector[J]. Transa- ctions of China Electrotechnical Society, 2025, 40(18): 6029-6039. [15] Wu Wenjie, Qiu Lin, Liu Xing, et al.Dynamic- linearization-based predictive control of a voltage- source inverter[J]. IEEE Transactions on Industrial Electronics, 2024, 71(4): 3275-3284. [16] Manzoor W A, Rawashdeh S, Mohammadi A.Vehicular applications of koopman operator theory: a survey[J]. IEEE Access, 2023, 11: 25917-25931. [17] Rui Tao, Yin Zheng, Hu Cungang, et al.Modulated model-free predictive current control for voltage source inverters with stagnation elimination and sampling disturbance suppression[J]. IEEE Transa- ctions on Power Electronics, 2023, 38(6): 6996-7008. [18] Rui Tao, Feng Zhuangzhuang, Hu Cungang, et al.Double-vector model-free predictive current control method for voltage source inverters with sampling noise suppression[J]. IEEE Transactions on Industrial Electronics, 2024, 71(6): 5797-5806. [19] Hu Cungang, Xu Wanlun, Yin Zheng, et al.A novel modulated model-free predictive control for LC- filtered grid-forming inverters with double-difference updating[J]. IEEE Transactions on Industrial Elec- tronics, 2024, 71(9): 10806-10817. [20] Carlet P G, Tinazzi F, Bolognani S, et al.An effective model-free predictive current control for synchronous reluctance motor drives[J]. IEEE Transactions on Industry Applications, 2019, 55(4): 3781-3790. [21] Wang Fengxiang, Wei Yao, Rodriguez J, et al.State- of-art, development, and challenges of model-free predictive control on motor drives[J]. IEEE Transa- ctions on Power Electronics, 2025, 40(8): 10846-10864. [22] 冯壮壮, 曹文平, 芮涛, 等. 基于LUT全更新的无模型预测电流控制方法[J]. 电力电子技术, 2022, 56(3): 76-80. Feng Zhuangzhuang, Cao Wenping, Rui Tao, et al.A model-free predictive current control method based on LUT full update[J]. Power Electronics, 2022, 56(3): 76-80. [23] Yu Feng, Zhou Chenhui, Liu Xing, et al.Model-free predictive current control for three-level inverter-fed IPMSM with an improved current difference updating technique[J]. IEEE Transactions on Energy Con- version, 2021, 36(4): 3334-3343. [24] Ma Chenwei, Li Huayu, Yao Xuliang, et al.An improved model-free predictive current control with advanced current gradient updating mechanism[J]. IEEE Transactions on Industrial Electronics, 2021, 68(12): 11968-11979. [25] Wang Fengxiang, Wei Yao, Young H, et al.Continuous-control-set model-free predictive funda- mental current control for PMSM system[J]. IEEE Transactions on Power Electronics, 2023, 38(5): 5928-5938. [26] 方崇智, 萧德云. 过程辨识[M]. 北京: 清华大学出版社, 1988. [27] Li Wanrong, Yuan Huawei, Li Sinan, et al.A revisit to model-free control[J]. IEEE Transactions on Power Electronics, 2022, 37(12): 14408-14421.
2026, Vol. 41 
