Fractional PI-PIμD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives
Busher V. Kuznetsov V. Kovalenko V. Babyak M. Druzhinin V. Tytiuk V. Rojek A. Klochko K. Gurin I. Shramko Y.
December 2025Multidisciplinary Digital Publishing Institute (MDPI)
Energies
2025#18Issue 23
This paper investigates, for the first time, the synthesis of a controller that incorporates a fractional-order integral component to achieve a closed-loop astaticism order greater than one. To enhance both static and dynamic accuracy, the controller integrates direct-signal-propagation neural networks within each control channel. The controlled plant is the BLDCM speed loop, which is modeled using a fractional-order differential equation. The study compares the performance of four controller types: a classical PID regulator tuned close to the optimal modulus criterion (IntPID); a fractional PI–PIμD controller (FrPID) that achieves an astaticism order of at least 1.8; and two hybrid neuro-controllers, NN–IntPID and NN–FrPID. While the FrPID controller reduces the root-mean-square error by nearly a factor of five compared with IntPID, the best results are delivered by NN–FrPID. Specifically, it decreases overshoot eight-fold during a reference step (from 2.98% to 0.35%), lowers the root-mean-square error during linear reference tracking by a factor of eleven, and reduces the relative speed error by more than thirty-five times. When combined with a fast learning algorithm executed at each control-cycle iteration, the controller enables the closed loop to adapt not only to variations in gain coefficients, but also to changes in the fractional-aperiodic order of the plant. These results demonstrate that neural fractional-integral controllers offer strong potential for improving accuracy and robustness in BLDC motor drives and are applicable to a wide range of electromechanical systems.
BLDCM , neural network fractional PIμD regulator , PID regulator
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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 Electrical Engineering and Cyber-Physical Systems, Y. M. Potebnia Engineering Educational and Scientific Institute, Zaporizhzhia National University, 66 Universytetska Street, ZR, Zaporizhzhia, 69600, Ukraine
Department of Railway Transport, Lviv Polytechnic National University, 12, Stepan Bandera Str., Lviv, 79013, Ukraine
Department of Power Engineering, Faculty of Energy, Transport and Management Systems, Non-Profit Joint-Stock Company «Karaganda Industrial University», Republic Avenue, 30, KR, Temirtau, 101400, Kazakhstan
Department of Electromechanics, Electrotechnical Faculty, Kryvyi Rih National University, Vitaly Matusevich, Str., 11, DR, Kryvyi Rih, 50027, Ukraine
Department of Electronics and Electronic Communications, Faculty of Electronics and Computer Engineering, Dniprovsky State Technical University, Dniprobudivska Street, 2, DR, Kamianske, 51918, Ukraine
Department of Automation, Electrical and Robotic Systems, Faculty of Production Automation and Digital Technologies, Technical University “Metinvest Polytechnic” LLC, Pivdenne Highway, 80, ZR, Zaporizhzhia, 69008, Ukraine
Department of Electrical Engineering and Electronics
Electric Energy Department
Department of Electrical Engineering and Cyber-Physical Systems
Department of Railway Transport
Department of Power Engineering
Department of Electromechanics
Department of Electronics and Electronic Communications
Department of Automation
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