BLDC motor’s speed and torque modelling through hybrid machine learning based approach of nonlinear autoregressive neural network with exogenous inputs (NARX-NN) - Muhammad Aseer Khan; Husan Ali; Dur-e-Zehra Baig; Fahad R. Albogamy (PLoS ONE, 2025)
Modeling the complex nonlinear dynamics of Brushless DC motors has been a prominent research focus over the past two decades, driven by their superior advantages and widespread industrial applications. Despite extensive efforts, achieving high-efficiency prediction of speed and torque responses remains a challenge. This study proposes a hybrid machine learning-based approach using the Nonlinear Autoregressive Neural Network with Exogenous Inputs. The method combines artificial neural networks and system identification techniques to enhance predictive accuracy in nonlinear dynamic systems. For both speed and torque modeling, optimal time delays and neural network layer sizes are selected to accurately capture the ripple effects under a multi-step input signal applied to a three-phase inverter. The proposed models yield Mean Square Error values as low as 1 0 − 4 for speed and 1 0 − 3 for torque. Regression coefficients of 1.000 for speed and 0.998 for torque are achieved consistently across training, validation, testing, and additional testing phases, following a data split of 70% for training and 15% each for validation and testing. To further evaluate generalization, the approach is tested using a distinct multi-step input voltage signal, with the results confirming the robustness and superiority of the proposed method in both speed and torque prediction. Comparative analysis with existing literature demonstrates the dominance of the proposed models. These high-fidelity models can serve as a foundation for designing advanced controllers aimed at efficient speed regulation and torque ripple mitigation in Brushless DC motors.