Development of a Digital Twin of a DC Motor Using NARX Artificial Neural Networks
Busher V. Kuznetsov V. Ciekanowski Z. Rojek A. Grudniewski T. Druzhinina N. Kuznetsov V. Tryputen M. Hubskyi P. Batyrbek A.
December 2025Multidisciplinary Digital Publishing Institute (MDPI)
Energies
2025#18Issue 24
This study presents the development process of a digital twin for a complex dynamic object using Artificial Neural Networks. A separately excited DC motor is considered as an example, which, despite its well-known electromechanical properties, remains a non-trivial object for neural network modeling. It is shown that describing the motor using a generalized neural network with various configurations does not yield satisfactory results. The optimal solution was based on a separation into two distinct nonlinear autoregressive with exogenous inputs (NARX) artificial neural networks with cross-connections for the two main machine variables: one for modeling the armature current with exogenous inputs of voltage and armature speed, and another for modeling the angular speed with inputs of voltage and armature current. Both neural networks are characterized by a relatively small number of neurons in the hidden layer and a time delay of no more than 3 time steps. This solution, consistent with the physical understanding of the motor as an object where electromagnetic energy is converted into thermal and mechanical energy (and vice versa), allows the model to be calibrated for the ideal no-load mode and subsequently account for the influence of torque loads of various natures and changes in the control object parameters over a wide range. The study demonstrates that even for modeling an object such as a DC electric drive with cascaded control, reducing errors at the boundaries of the known operating range requires generating test signals covering approximately 120% of the nominal speed range and 250–400% of the nominal current. Analysis of various test signals revealed that training with a sequence of step changes and linear variations across the entire operating range of armature current and speed provides higher accuracy compared to training with random or uniform signals. Furthermore, to ensure the neural network model’s functionality under varying load torque, a mechanical load observer was developed, and a model architecture incorporating an additional input for disturbance was proposed. The SEDCM_NARX_LOAD neural network model demonstrates a theoretically justified response to load application, although dynamic and static errors arise. In the experiment, the current error was 7.4%, and the speed error was 0.5%. The practical significance of the research lies in the potential use of the proposed model for simulating dynamic and static operational modes of electromechanical systems, tuning controllers, and testing control strategies without employing a physical motor.
digital twin , load torque observer , NARX neural network , separately excited DC motor
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Department of Electrical Engineering and Electronics, National University “Odessa Maritime Academy”, Didrikhson Str., 8, OR, Odesa, 65052, Ukraine
Electric Energy Department, Railway Research Institute, 50 Józefa Chłopickiego Street, Warsaw, 04-275, Poland
Department of Security Education, War Studies University, av. Chruściela 103, Warsaw, 00-910, Poland
John Paul II Academy in Biała Podlaska, Rector’s Office, Sidorska Str. 95/97, Biała Podlaska, 21-500, Poland
Department of History of Kazakhstan and General Educational Disciplines, Faculty of Economics and Construction, Non-Profit Joint-Stock Company “Karaganda Industrial University”, Republic Avenue, 30, KR, Temirtau, 101400, Kazakhstan
Department of Electrical Engineering, Faculty of Electomechanic and Electrometallurgy, Dnipro Metallurgical Institute, Ukrainian State University of Science and Technologies, 2 Lazaryana Street, DR, Dnipro, 49000, Ukraine
Department of Cyberphysical and Information-Measuring Systems, Faculty of Electrical Engineering, Institute of Power Engineering, Dnipro University of Technology, 19 Dmytro Yavornytskyi Avenue, DR, Dnipro, 49005, Ukraine
Department of Artificial Intelligence Technologies, Faculty of Energy, Transport and Management Systems, Non-Profit Joint-Stock Company “Karaganda Industrial University”, Republic Avenue, 30, KR, Temirtau, 101400, Kazakhstan
Department of Electrical Engineering and Electronics
Electric Energy Department
Department of Security Education
John Paul II Academy in Biała Podlaska
Department of History of Kazakhstan and General Educational Disciplines
Department of Electrical Engineering
Department of Cyberphysical and Information-Measuring Systems
Department of Artificial Intelligence Technologies
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