volume | PIER Journals

Abstract

This paper proposes a model-free direct speed control (MFDC) method based on a second-order ultra-local model to address the speed loop bandwidth issue and difficulty of further improving the dynamic response performance in the speed control of a traditional cascaded permanent magnet synchronous motor drive system. The speed control method based on an accurate mathematical model has poor robustness to unknown disturbances, such as parameter uncertainty and inverter nonlinearity. This method eliminates the double closed-loop cascade structure of the traditional speed outer loop and q-axis current inner loop. By establishing a second-order ultra-local model of the surface-mounted permanent magnet synchronous motor ( SMPMSM ) drive system considering parameter uncertainty and inverter nonlinearity, the mechanical speed of the motor was directly related to the inverter's output voltage, and a model-free direct speed controller integrating speed control and torque current control functions was designed. Simultaneously, a model-free current controller based on the first-order current ultra-local model is used to realize the independent adjustment of the d-axis stator current. In addition, a virtual q-axis current ultra-local model torque limitation method for direct speed control is proposed to realize an effective constraint of electromagnetic torque without a cascade structure. Experimental results demonstrate that the proposed method provides enhanced load-disturbance rejection, particularly under medium- and high-speed conditions. At 500 r/min, load-step speed fluctuation is reduced from 3.6152% to 2.0638%, and recovery time is shortened from 0.0288 s to 0.0080 s. Under the rated-speed step condition, the speed overshoot is reduced from 2.8028% to 2.2136%.

1. Mao, H. S., "Review on the development status and sales forecasting methods of new energy vehicles," China Economic & Trade Herald, No. 4, 88-90, 2025.
doi:10.3969/j.issn.1007-9777.2025.04.028 Google Scholar

2. Cai, Shun, James L. Kirtley, and Christopher H. T. Lee, "Critical review of direct-drive electrical machine systems for electric and hybrid electric vehicles," IEEE Transactions on Energy Conversion, Vol. 37, No. 4, 2657-2668, Dec. 2022.
doi:10.1109/tec.2022.3197351 Google Scholar

3. Li, Teng, Xiaodong Sun, Gang Lei, Youguang Guo, Zebin Yang, and Jianguo Zhu, "Finite-control-set model predictive control of permanent magnet synchronous motor drive systems --- An overview," IEEE/CAA Journal of Automatica Sinica, Vol. 9, No. 12, 2087-2105, Dec. 2022.
doi:10.1109/jas.2022.105851 Google Scholar

4. Kong, Delin, Haiwei Cai, and Wenkai Zeng, "A predefined time fast terminal sliding mode predictive speed control for PMSM drives," IEEE Transactions on Power Electronics, Vol. 40, No. 7, 9068-9079, Jul. 2025.
doi:10.1109/tpel.2025.3544281 Google Scholar

5. Wang, L., H. Zhu, and Z. Yang, "Tuning method for PI controllers of PMSM driving system," Transactions of China Electrotechnical Society, Vol. 29, No. 5, 104-117, 2014.
doi:10.3969/j.issn.1000-6753.2014.05.014 Google Scholar

6. Zhao, Mengyuan, Yanfei Cao, Chen Li, Zhiqiang Wang, Tingna Shi, and Changliang Xia, "Expanded limit boundary explicit model predictive direct speed control for PMSMs," IEEE Transactions on Power Electronics, Vol. 39, No. 5, 6089-6101, May 2024.
doi:10.1109/tpel.2024.3359283 Google Scholar

7. Song, Wensheng, Jiayao Li, Chenwei Ma, Yanbing Xia, and Bin Yu, "A simple tuning method of PI regulators in FOC for PMSM drives based on deadbeat predictive conception," IEEE Transactions on Transportation Electrification, Vol. 10, No. 4, 9852-9863, Dec. 2024.
doi:10.1109/tte.2024.3385114 Google Scholar

8. Tian, Minghe, Tianqing Wang, Yong Yu, Qinghua Dong, Bo Wang, and Dianguo Xu, "Integrated observer-based terminal sliding-mode speed controller for PMSM drives considering multisource disturbances," IEEE Transactions on Power Electronics, Vol. 39, No. 7, 7968-7979, Jul. 2024.
doi:10.1109/tpel.2024.3384991 Google Scholar

9. Liu, Zixuan, Xiaoyan Huang, Qichao Hu, Geng Yang, Yunchong Wang, and Jianxin Shen, "Model-free predictive current control of PMSM using modified extended state observer," IEEE Transactions on Power Electronics, Vol. 40, No. 1, 679-690, Jan. 2025.
doi:10.1109/tpel.2024.3476318 Google Scholar

10. Shi, Tingna, Shiyu Lin, Yanfei Cao, and Yan Yan, "A two-degree-of-freedom explicit model predictive noncascaded direct speed control for SPMSM drives," IEEE Transactions on Transportation Electrification, Vol. 11, No. 1, 510-520, Feb. 2025.
doi:10.1109/tte.2024.3392731 Google Scholar

11. Sun, Xiaodong, Teng Li, Ming Yao, Gang Lei, Youguang Guo, and Jianguo Zhu, "Improved finite-control-set model predictive control with virtual vectors for PMSHM drives," IEEE Transactions on Energy Conversion, Vol. 37, No. 3, 1885-1894, Sep. 2022.
doi:10.1109/tec.2021.3138905 Google Scholar

12. Zhou, Yanan, Hongmei Li, Rundong Liu, and Jingkui Mao, "Continuous voltage vector model-free predictive current control of surface mounted permanent magnet synchronous motor," IEEE Transactions on Energy Conversion, Vol. 34, No. 2, 899-908, Jun. 2019.
doi:10.1109/tec.2018.2867218 Google Scholar

13. Gao, Xiaonan, Mohamed Abdelrahem, Christoph M. Hackl, Zhenbin Zhang, and Ralph Kennel, "Direct predictive speed control with a sliding manifold term for PMSM drives," IEEE Journal of Emerging and Selected Topics in Power Electronics, Vol. 8, No. 2, 1258-1267, Jun. 2020.
doi:10.1109/jestpe.2019.2923285 Google Scholar

14. Liu, Ming, Jiefeng Hu, Ka Wing Chan, Siu Wing Or, Siu Lau Ho, Wenzheng Xu, and Xian Zhang, "Dual cost function model predictive direct speed control with duty ratio optimization for PMSM drives," IEEE Access, Vol. 8, 126637-126647, 2020.
doi:10.1109/access.2020.3007627 Google Scholar

15. Kawai, Hiroaki, Zhenbin Zhang, Ralph Kennel, and Shinji Doki, "Direct speed control based on finite control set model predictive control with voltage smoother," IEEE Transactions on Industrial Electronics, Vol. 70, No. 3, 2363-2372, Mar. 2023.
doi:10.1109/tie.2022.3174298 Google Scholar

16. Zhang, Yang, Chenhui Liu, Sicheng Li, Kun Cao, Yiping Yang, and Zhun Cheng, "No weighting factor pmsm model predictive torque control based on composite sliding mode disturbance observer.," Progress In Electromagnetics Research B, Vol. 113, 63-76, 2025.
doi:10.2528/PIERB25052302 Google Scholar

17. Gong, Zhenjie, Chengning Zhang, Xin Ba, and Youguang Guo, "Improved deadbeat predictive current control of permanent magnet synchronous motor using a novel stator current and disturbance observer," IEEE Access, Vol. 9, 142815-142826, 2021.
doi:10.1109/access.2021.3119614 Google Scholar

18. Liu, Jianxing, Sergio Vazquez, Ligang Wu, Abraham Marquez, Huijun Gao, and Leopoldo G. Franquelo, "Extended state observer-based sliding-mode control for three-phase power converters," IEEE Transactions on Industrial Electronics, Vol. 64, No. 1, 22-31, Jan. 2017.
doi:10.1109/tie.2016.2610400 Google Scholar

19. Fliess, Michel and Cédric Join, "Model-free control," International Journal of Control, Vol. 86, No. 12, 2228-2252, 2013.
doi:10.1080/00207179.2013.810345 Google Scholar

20. Yang, Liguo, Hongmei Li, Jiandong Huang, Zheng Zhang, and Haonan Zhao, "Model predictive direct speed control with novel cost function for SMPMSM drives," IEEE Transactions on Power Electronics, Vol. 37, No. 8, 9586-9595, Aug. 2022.
doi:10.1109/tpel.2022.3155465 Google Scholar

21. Mao, Jingkui, Hongmei Li, Liguo Yang, Xianling Wang, and Rundong Liu, "Adaptive integral-type direct speed control of SMPMSM drive system based on ultra-local model," IEEJ Transactions on Electrical and Electronic Engineering, Vol. 17, No. 4, 592-600, 2022.
doi:10.1002/tee.23546 Google Scholar

22. Han, Jingqing, "From PID to active disturbance rejection control," IEEE Transactions on Industrial Electronics, Vol. 56, No. 3, 900-906, Mar. 2009.
doi:10.1109/tie.2008.2011621 Google Scholar

23. Ma, Yuxiang and Yunhua Li, "Active disturbance compensation based robust control for speed regulation system of permanent magnet synchronous motor," Applied Sciences, Vol. 10, No. 2, 709, 2020.
doi:10.3390/app10020709 Google Scholar

24. Wu, Hui, Chun Gan, Hongzhe Wang, Shuanghong Wang, Ronghai Qu, and Xingzhong Liu, "Active disturbance rejection speed control with double-stage-ESO considering aperiodic and periodic disturbances for PMSM drives," IEEE Transactions on Industrial Electronics, 2025.
doi:10.1109/tie.2024.3519622 Google Scholar

25. Wen, Dingdou, Wenting Zhang, Zhongjian Tang, Xu Zhang, and Zhun Cheng, "Model predictive control with ESO and an improved speed loop for PMSM," Progress In Electromagnetics Research C, Vol. 142, 107-117, 2024.
doi:10.2528/pierc23122906 Google Scholar

26. Huang, Yanguo, Yingmin Xie, Weilong Han, and Liang Ling, "Parameter-adaptive composite active disturbance rejection control for permanent magnet synchronous motor drives," Progress In Electromagnetics Research B, Vol. 114, 13-25, 2025.
doi:10.2528/PIERB25051503 Google Scholar

27. Fliess, Michel and Cédric Join, "An alternative to proportional-integral and proportional-integral-derivative regulators: Intelligent proportional-derivative regulators," International Journal of Robust and Nonlinear Control, Vol. 32, No. 18, 9512-9524, 2022.
doi:10.1002/rnc.5657 Google Scholar

Dr. Yanan Zhou

Dr. Lin Li

Dr. Xinxin Zheng

Dr. Tong Liu

Dr. Yao He