PMSM control with inverter nonlinearity compensation based on adaptive super-twisting sliding mode

doi:10.3785/j.issn.1008-973X.2026.05.022

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (5): 1128-1138 DOI: 10.3785/j.issn.1008-973X.2026.05.022

PMSM control with inverter nonlinearity compensation based on adaptive super-twisting sliding mode

Haoran WU(

),Yanming LI*(

),Fujing ZHANG,Fenghe JIANG,Hai LIN

School of Electronics and Control Engineering, Chang’an University, Xi’an 710064, China

Download:

HTML

PDF(2106KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

To solve the inherent chattering problem of the sliding mode observer (SMO) in the sensorless control technology of permanent magnet synchronous motors (PMSM), an improved adaptive super-twisting sliding mode observer (IAST-SMO) was proposed. By introducing a linear term and parameter adaptation into the super-twisting sliding mode structure, the accuracy and control performance of the observer over a wide speed range were significantly improved. Aiming at the problem of decreased observation accuracy caused by the nonlinear effects of voltage source inverters (VSI) in practical engineering, an online VSI compensation strategy was proposed, which improved the performance of the observer under real working conditions by compensating for the distorted voltage. A PMSM experimental platform was built to verify the proposed control strategy. Experimental results show that the proposed control strategy can effectively suppress observation chattering when the PMSM rotor speed is 50?1500 r/min; compared with the traditional super-twisting sliding mode observer, the position estimation error is reduced by 50%, and the total harmonic distortion (THD) of the current does not exceed 2%.

Key words： permanent magnet synchronous motor(PMSM) sliding mode observer super-twisting algorithm nonlinear compensation sensorless control

Received: 16 June 2025 Published: 06 May 2026

CLC:

TM 301

Fund: 陕西省重点研发计划项目（2025ZG-JBGS-010）.

Corresponding Authors: Yanming LI E-mail: 2022232023@chd.edu.cn;ymli@chd.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Haoran WU
	Yanming LI
	Fujing ZHANG
	Fenghe JIANG
	Hai LIN

Cite this article:

Haoran WU,Yanming LI,Fujing ZHANG,Fenghe JIANG,Hai LIN. PMSM control with inverter nonlinearity compensation based on adaptive super-twisting sliding mode. Journal of ZheJiang University (Engineering Science), 2026, 60(5): 1128-1138.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.05.022 OR https://www.zjujournals.com/eng/Y2026/V60/I5/1128

基于自适应超扭曲滑模观测与逆变器非线性补偿的PMSM控制

为了解决永磁同步电机（PMSM）无传感器控制技术中滑模观测器（SMO）的固有抖振问题，提出改进自适应超扭曲滑模观测器（IAST-SMO）. 通过在超扭曲滑模结构中引入线性项和参数自适应，显著提升观测器在宽速度范围内的精度与控制性能. 针对实际工程中电压源逆变器（VSI）的非线性效应导致的观测精度下降问题，提出在线VSI补偿策略，通过补偿失真电压改善观测器在真实工况下的性能. 搭建PMSM实验平台，对所提控制策略进行验证. 实验结果表明，所提控制策略在PMSM转速为50~1500 r/mim时能够有效抑制观测抖振；与传统超扭曲滑模观测器相比，位置估计误差降低了50%，电流总谐波畸变（THD）不超过2%.

关键词： 永磁同步电机, 滑模观测器, 超扭曲算法, 非线性补偿, 无传感器控制

Tab.1 PMSM parameters for experimental setup

Fig.1 Principle block diagram of improved adaptive super-twisting sliding mode observer

Tab.2 Key parameter settings for comparative experiments of super-twisting sliding mode observer

Fig.2 Comparison of observation results for different observers at various motor speeds

Tab.3 Comparison of observation performance parameters for different observers at various motor speeds

Fig.3 Experimental results of improved adaptive super-twisting sliding mode observer under acceleration and deceleration conditions

Fig.4 Experimental results of improved adaptive super-twisting sliding mode observer under load disturbance conditions

Fig.5 Output voltage affected by nonlinear effects of voltage source inverters

Fig.6 Simulation waveforms of current characteristic functions

Fig.7 Schematic diagram of distorted voltage calculation

Fig.8 Minimization flowchart of compensated distorted voltage

Fig.9 Comparison of main current indexes before and after compensation strategy implementation (n=1000 r/min)

Fig.10 PMSM control based on improved adaptive super-twisting sliding mode observer and inverter nonlinearity compensation

Fig.11 PMSM experimental platform

Fig.12 Experimental results of improved adaptive super-twisting sliding mode observer before and after compensation strategy implementation


[1]	MEESALA R E K, UDUMULA R R, NIZAMI T K, et al Development of enhanced direct torque control for surface-mounted permanent magnet synchronous motor drive operation[J]. IET Power Electronics, 2023, 16 (11): 1814- 1827 doi: 10.1049/pel2.12504

[2]	PETKAR S G, THIPPIRIPATI V K A novel duty-controlled DTC of a surface PMSM drive with reduced torque and flux ripples[J]. IEEE Transactions on Industrial Electronics, 2023, 70 (4): 3373- 3383 doi: 10.1109/TIE.2022.3181405

[3]	TANG X, ZHANG Z, LIU X, et al A novel field-oriented control algorithm for permanent magnet synchronous motors in 60° coordinate systems[J]. Actuators, 2023, 12 (2): 92 doi: 10.3390/act12020092

[4]	SONG W, LI J, MA C, et al A simple tuning method of PI regulators in FOC for PMSM drives based on deadbeat predictive conception[J]. IEEE Transactions on Transportation Electrification, 2024, 10 (4): 9852- 9863 doi: 10.1109/TTE.2024.3385114

[5]	YAN H, WANG W, XU Y, et al Position sensorless control for PMSM drives with single current sensor[J]. IEEE Transactions on Industrial Electronics, 2023, 70 (1): 178- 188 doi: 10.1109/TIE.2022.3148748

[6]	YU K, WANG Z An online compensation method of VSI nonlinearity for dual three-phase PMSM drives using current injection[J]. IEEE Transactions on Power Electronics, 2022, 37 (4): 3769- 3774 doi: 10.1109/TPEL.2021.3127990

[7]	LIAN C, XIAO F, LIU J, et al Parameter and VSI nonlinearity hybrid estimation for PMSM drives based on recursive least square[J]. IEEE Transactions on Transportation Electrification, 2023, 9 (2): 2195- 2206 doi: 10.1109/TTE.2022.3206606

[8]	WANG G, VALLA M, SOLSONA J Position sensorless permanent magnet synchronous machine drives: a review[J]. IEEE Transactions on Industrial Electronics, 2020, 67 (7): 5830- 5842 doi: 10.1109/TIE.2019.2955409

[9]	BI G, ZHANG G, WANG Q, et al High-frequency injection angle self-adjustment based online position error suppression method for sensorless PMSM drives[J]. IEEE Transactions on Power Electronics, 2023, 38 (2): 1412- 1417 doi: 10.1109/TPEL.2022.3210105

[10]	WANG C, GOU L, DONG S, et al Sensorless control of IPMSM based on super-twisting sliding mode observer with CVGI considering flying start[J]. IEEE Transactions on Transportation Electrification, 2022, 8 (2): 2106- 2117 doi: 10.1109/TTE.2021.3131860

[11]	SU R, WANG Y, DENG H, et al A power-RPM reduced-order model and power control strategy of the dual three-phase permanent magnet synchronous motor in a V/f framework for oscillation suppression[J]. Energies, 2024, 17 (18): 4563 doi: 10.3390/en17184563

[12]	DATTA S, CHANDRA A, CHOWDHURI S High performance sensor-less V/f control of surface PMSM in voltage vector plane with ZVV injection and SMO-based position estimation method[J]. Electrical Engineering, 2022, 104 (2): 657- 666 doi: 10.1007/s00202-021-01325-2

[13]	SONG Z, YAO W, LEE K, et al An efficient and robust I-f control of sensorless IPMSM with large startup torque based on current vector angle controller[J]. IEEE Transactions on Power Electronics, 2022, 37 (12): 15308- 15321 doi: 10.1109/TPEL.2022.3193565

[14]	NING B, ZHAO Y, CHENG S An improved sensorless hybrid control method of permanent magnet synchronous motor based on I/F startup[J]. Sensors, 2023, 23 (2): 635 doi: 10.3390/s23020635

[15]	JANSEN P L, LORENZ R D Transducerless position and velocity estimation in induction and salient AC machines[J]. IEEE Transactions on Industry Applications, 1995, 31 (2): 240- 247 doi: 10.1109/28.370269

[16]	WU T, LUO D, WU X, et al Square-wave voltage injection based PMSM sensorless control considering time delay at low switching frequency[J]. IEEE Transactions on Industrial Electronics, 2022, 69 (6): 5525- 5535 doi: 10.1109/TIE.2021.3094444

[17]	LIU L, JIN D, SI J, et al A novel nonsingular fast terminal sliding mode observer combining I-F method for wide-speed sensorless control of PMSM drives[J]. IET Power Electronics, 2023, 16 (5): 843- 855 doi: 10.1049/pel2.12427

[18]	KASHIF M, SINGH B Modified active-power MRAS based adaptive control with reduced sensors for PMSM operated solar water pump[J]. IEEE Transactions on Energy Conversion, 2023, 38 (1): 38- 52 doi: 10.1109/TEC.2022.3197564

[19]	SUN X, ZHANG Y, TIAN X, et al Speed sensorless control for IPMSMs using a modified MRAS with gray wolf optimization algorithm[J]. IEEE Transactions on Transportation Electrification, 2022, 8 (1): 1326- 1337 doi: 10.1109/TTE.2021.3093580

[20]	ZWERGER T, MERCORELLI P Using a bivariate polynomial in an EKF for state and inductance estimations in the presence of saturation effects to adaptively control a PMSM[J]. IEEE Access, 2022, 10: 111545- 111553 doi: 10.1109/ACCESS.2022.3215511

[21]	DAN L EKF-based fault detection and isolation for PMSM inverter[J]. Sustainable Energy Technologies and Assessments, 2022, 52: 101846 doi: 10.1016/j.seta.2021.101846

[22]	DING H, QIN X, WEI L Sensorless control of surface-mounted permanent magnet synchronous motor using adaptive robust UKF[J]. Journal of Electrical Engineering and Technology, 2022, 17 (5): 2995- 3013 doi: 10.1007/s42835-022-01061-y

[23]	WANG S, DING D, ZHANG G, et al Flux observer based on enhanced second-order generalized integrator with limit cycle oscillator for sensorless PMSM drives[J]. IEEE Transactions on Power Electronics, 2023, 38 (12): 15982- 15995 doi: 10.1109/TPEL.2023.3314009

[1]	Yueming LIU,Jinfeng HUANG,Zhenyang HU,Ruize XUE,Xing LI. Improved sliding mode active disturbance rejection control for grid-forming photovoltaic hybrid power conversion system[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(1): 158-168.

[2]	Xin LI,Xiaoning LUO. Sensorless control based on a three-parameter notch filter for pulsating high-frequency voltage injection[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(12): 2655-2666.

[3]	Wanshun ZANG,Gang SHEN,Jun ZHAO,Kejiang ZANG. Extended sliding mode observer-based robust tracking control scheme for electro-hydraulic servo systems[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 611-621.

[4]	Zheng-yin YANG,Jian HU,Jian-yong YAO,Ying-zhe SHA,Qiu-yu SONG. Fault-tolerant control based on adaptive neural network sliding mode observer[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1656-1665.

[5]	Qi-jin ZHAO,Zi-li LIAO,Cheng-lin MIAO,Chun-guang LIU,Jian-yi XIE,Li-chun CAI. Constant torque flux-weakening control strategy of hub motor for electric drive vehicle[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 195-202.

[6]	WANG Ting, CHEN Bin, YAO Wen-xi, LV Zheng-yu. Pefrormance analysis of holtz flux observer in speed-sensorless induction motor drive[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(9): 1690-1695.

[7]	GAI Jiang-tao, HUANG Qing, HUANG Shou-dao, LIU Wang,ZHOU Tao-tao, PAN Xia. Active-disturbance rejection controller for permanent magnet synchronous motor based on model compensation[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(4): 581-588.

[8]	WANG Meng, YANG Jia-qiang, ZHU Chang-sheng. Sensorless control of permanent magnet synchronous machines in polar coordinates [J]. Journal of ZheJiang University (Engineering Science), 2014, 48(10): 1893-1900.

Viewed

Full text

Abstract

Cited

Shared

Discussed