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10 January 2026

Research on Torque Estimation Methods for Permanent Magnet Synchronous Motors Considering Dynamic Inductance Variations

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1
School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430070, China
2
Hezhi Digital Energy Technology Co., Ltd., Wuhan 430070, China
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Author to whom correspondence should be addressed.
Energies2026, 19(2), 346;https://doi.org/10.3390/en19020346 
(registering DOI)
This article belongs to the Special Issue Advances in Control Strategies of Permanent Magnet Motor Drive

Abstract

Precise electromagnetic torque estimation for permanent magnet synchronous motors (PMSMs) is crucial for enhancing the dynamic performance and energy efficiency of electric vehicles. To address the dynamic variations in dq-axis inductance caused by magnetic cross-coupling and saturation effects during motor operation—which lead to significant torque estimation errors in traditional fixed-parameter models under variable torque and speed conditions—this paper proposes a dynamic torque estimation method that integrates online dq-axis inductance identification based on a variable-step adaptive linear neural network (ADALINE) with an extended flux observer. The online identified inductance values are embedded into the extended flux observer in real time, forming a closed-loop torque estimation system with adaptive parameter updating. Experimental results demonstrate that, under complex operating conditions with varying torque and speed, the proposed method maintains electromagnetic torque estimation errors within ±3%, with a convergence time of less than 20 ms, while achieving inductance identification accuracy also within ±3%. These results significantly outperform conventional methods that do not incorporate inductance identification. This study provides a highly adaptive and engineering-practical solution for high-precision torque control of interior permanent magnet synchronous motors (IPMSMs) in automotive applications.

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