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Learning and Current Prediction of PMSM Drive via Differential Neural Networks

Wenjie Mei, Xiaorui Wang, Yanrong Lu, Ke Yu, Shihua Li

TL;DR

The paper addresses the challenge of accurately predicting PMSM current trajectories in continuous time despite nonlinear dynamics and disturbances. It proposes differential neural networks (DDNNs) with learning laws that adapt weights in real time, and proves local asymptotic convergence of the current error using Lyapunov analysis, ensuring reliable long- and short-term predictions. Experimental validation on a semi-physical PMSM setup shows that DDNNs outperform CNNs and Transformers in MAE, RMSE, and $R^2$ across no-load and various load disturbances, closely matching the continuous-time nature of the physical system. The work advances safe, accurate current forecasting for PMSMs, with potential implications for robotics, aerospace, and electric drives where real-time, robust predictions are critical.

Abstract

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model nonlinear systems, specifically permanent magnet synchronous motors (PMSMs), and to predict their current trajectories. The efficacy of our approach is validated through experiments conducted under various load disturbances and no-load conditions. The results demonstrate that our method effectively and accurately reconstructs the original systems, showcasing strong short-term and long-term prediction capabilities and robustness. This study provides valuable insights into learning the inherent dynamics of complex dynamical data and holds potential for further applications in fields such as weather forecasting, robotics, and collective behavior analysis.

Learning and Current Prediction of PMSM Drive via Differential Neural Networks

TL;DR

The paper addresses the challenge of accurately predicting PMSM current trajectories in continuous time despite nonlinear dynamics and disturbances. It proposes differential neural networks (DDNNs) with learning laws that adapt weights in real time, and proves local asymptotic convergence of the current error using Lyapunov analysis, ensuring reliable long- and short-term predictions. Experimental validation on a semi-physical PMSM setup shows that DDNNs outperform CNNs and Transformers in MAE, RMSE, and across no-load and various load disturbances, closely matching the continuous-time nature of the physical system. The work advances safe, accurate current forecasting for PMSMs, with potential implications for robotics, aerospace, and electric drives where real-time, robust predictions are critical.

Abstract

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model nonlinear systems, specifically permanent magnet synchronous motors (PMSMs), and to predict their current trajectories. The efficacy of our approach is validated through experiments conducted under various load disturbances and no-load conditions. The results demonstrate that our method effectively and accurately reconstructs the original systems, showcasing strong short-term and long-term prediction capabilities and robustness. This study provides valuable insights into learning the inherent dynamics of complex dynamical data and holds potential for further applications in fields such as weather forecasting, robotics, and collective behavior analysis.

Paper Structure

This paper contains 7 sections, 1 theorem, 17 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Differential neural networks for Learning and Prediction
  4. Experiments
  5. Experimental Setup
  6. Test Results
  7. Conclusion

Key Result

Theorem 1

Suppose that the neural networks eq:DDNN can approximate the dynamics eq:PMSM well and let the DNN identify eq:DDNN with the learning laws where $p, c_i, d_j$ are positive scalars, $e = \hat{x} - x$, $\tilde{s}_i = s_i - s_i^*$, and $\mathcal{D}_{f_i} = \frac{\partial f_i(\cdot)}{\partial (\cdot)}$. If there exists a scalar $C>0$ such that $p>0$ (the same as that in Equation eq:learning_law) is a

Figures (4)

  • Figure 1: The current prediction framework of PMSMs with DNN.
  • Figure 2: Prediction result comparison among (a) Ground Truth. (b) DNN (Ours). (c) CNN. (d) Transformer.
  • Figure 3: Prediction comparison among (a) Ground Truth. (b) DNN (Ours). (c) CNN. (d) Transformer.
  • Figure 4: DNN prediction results under different load disturbances: (a) Step load disturbance. (b) Ramp load disturbance. (c) Sinusoidal load disturbance. (d) Loss/R$^2$ values under the three load disturbances.

Theorems & Definitions (3)

  • Theorem 1
  • Proof 1
  • Remark 1