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| Neural Network-Based Inductance Identification for PMSM with Current Derivative and Geometric Constraints |
| Zhou Yangwei1,2, Nie Ziling2,3, Peng Li1, Zou Xudong1, Li Huayu2,3 |
1. School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China;
2. National Key Laboratory of Science and Technology on Electromagnetic Energy Naval University of Engineering Wuhan 430033 China;
3. East Lake Laboratory Wuhan 430204 China |
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Abstract Traditional online inductance identification methods for permanent magnet synchronous motors (PMSM) often rely on steady-state currents and fundamental voltages in the d-q frame, which limits their applicability to control strategies without voltage modulation, such as finite-set model predictive control (FCS-MPC) or direct torque control (DTC). These methods are also sensitive to rotor position errors and struggle to model non-ideal factors such as sampling noise and system nonlinearities. Therefore, this paper proposes a current derivative and geometric information-driven neural network-based online inductance identification observer (CDGI-NNIO). The method uses geometric coordinates derived from current derivatives as inputs, enabling inductance estimation without requiring fundamental voltages or rotor position.
The CDGI-NNIO method first establishes a geometric relationship between the current derivative and inductance parameters based on the PMSM physical model. This relationship is derived from the motor’s voltage equations at inverter switching, where the current-derivative term retains inductance information. By introducing a virtual voltage vector reference frame, the method decouples the inductance model from rotor position, reducing sensitivity to position errors. The extracted geometric features are then used as constraints during neural network training, enhancing the network’s physical interpretability. To improve generalization, additional training data are generated from geometric shapes. During online inference, geometric constraints ensure that the estimated inductance aligns with the physical model.
The neural network architecture uses a single hidden layer of 60 neurons with ReLU activation functions to balance computational efficiency and performance. The training process uses a custom loss function that combines mean squared error (MSE) with a geometric-constraint loss. The geometric constraint loss is based on a ring-shaped boundary, dynamically adjusted according to the experimental data’s offset range.
Experimental validation was conducted on a PMSM prototype using a dSPACE MicroLabBox controller. The proposed method was compared with offline inductance tests specified in the IEEE 1812 standard. For the q-axis inductance, the root-mean-square error (RMSE) between the online estimation and the offline tests was less than 2%, whereas for the d-axis inductance, the RMSE was approximately 5%. This discrepancy is attributed to the d-axis inductance measurement, which is affected by initial saturation caused by permanent magnets. Additionally, dynamic tests under speed and load variations confirmed the method’s stability and accuracy, with inductance estimates converging rapidly even during current step changes.
In summary, the CDGI-NNIO method provides a robust and accurate solution for online inductance identification in PMSMs, particularly suitable for control strategies that do not use voltage modulation. By leveraging current derivative and geometric information, it overcomes the limitations of traditional methods, offering a new approach for high-performance motor control.
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Received: 17 March 2025
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2026, Vol. 41 
