Fractional PI-PIμD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives

Busher, Victor; Kuznetsov, Valeriy; Kovalenko, Viktor; Babyak, Mykola; Druzhinin, Valeriy; Tytiuk, Valerii; Rojek, Artur; Klochko, Kateryna; Gurin, Ievgen; Shramko, Yurii

doi:10.3390/en18236132

This is an early access version, the complete PDF, HTML, and XML versions will be available soon.

Open AccessArticle

Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives

by

Victor Busher

¹

,

Valeriy Kuznetsov

^2,*

,

Viktor Kovalenko

^3,*,

Mykola Babyak

⁴,

Valeriy Druzhinin

^5,*,

Valerii Tytiuk

⁶

,

Artur Rojek

²

,

Kateryna Klochko

⁷,

Ievgen Gurin

³

and

Yurii Shramko

⁸

¹

Department of Electrical Engineering and Electronics, National University “Odessa Maritime Academy”, Didrikhson Str., 8, 65052 Odesa, OR, Ukraine

²

Electric Energy Department, Railway Research Institute, 50 Józefa Chłopickiego Street, 04-275 Warsaw, Poland

³

Department of Electrical Engineering and Cyber-Physical Systems, Y. M. Potebnia Engineering Educational and Scientific Institute, Zaporizhzhia National University, 66 Universytetska Street, 69600 Zaporizhzhia, ZR, Ukraine

⁴

Department of Railway Transport, Lviv Polytechnic National University, 12, Stepan Bandera Str., 79013 Lviv, Ukraine

⁵

Department of Power Engineering, Faculty of Energy, Transport and Management Systems, Non-Profit Joint-Stock Company «Karaganda Industrial University», Republic Avenue, 30, Temirtau 101400, KR, Kazakhstan

⁶

Department of Electromechanics, Electrotechnical Faculty, Kryvyi Rih National University, Vitaly Matusevich, Str., 11, 50027 Kryvyi Rih, DR, Ukraine

⁷

Department of Electronics and Electronic Communications, Faculty of Electronics and Computer Engineering, Dniprovsky State Technical University, Dniprobudivska Street, 2, 51918 Kamianske, DR, Ukraine

⁸

Department of Automation, Electrical and Robotic Systems, Faculty of Production Automation and Digital Technologies, Technical University “Metinvest Polytechnic” LLC, Pivdenne Highway, 80, 69008 Zaporizhzhia, ZR, Ukraine

^*

Authors to whom correspondence should be addressed.

Energies 2025, 18(23), 6132; https://doi.org/10.3390/en18236132 (registering DOI)

Submission received: 31 October 2025 / Revised: 18 November 2025 / Accepted: 20 November 2025 / Published: 23 November 2025

(This article belongs to the Section F3: Power Electronics)

Download Versions Notes

Abstract

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–PI^μD 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.

Keywords: BLDCM; PID regulator; neural network fractional PI^μD regulator

Share and Cite

MDPI and ACS Style

Busher, V.; Kuznetsov, V.; Kovalenko, V.; Babyak, M.; Druzhinin, V.; Tytiuk, V.; Rojek, A.; Klochko, K.; Gurin, I.; Shramko, Y. Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives. Energies 2025, 18, 6132. https://doi.org/10.3390/en18236132

AMA Style

Busher V, Kuznetsov V, Kovalenko V, Babyak M, Druzhinin V, Tytiuk V, Rojek A, Klochko K, Gurin I, Shramko Y. Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives. Energies. 2025; 18(23):6132. https://doi.org/10.3390/en18236132

Chicago/Turabian Style

Busher, Victor, Valeriy Kuznetsov, Viktor Kovalenko, Mykola Babyak, Valeriy Druzhinin, Valerii Tytiuk, Artur Rojek, Kateryna Klochko, Ievgen Gurin, and Yurii Shramko. 2025. "Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives" Energies 18, no. 23: 6132. https://doi.org/10.3390/en18236132

APA Style

Busher, V., Kuznetsov, V., Kovalenko, V., Babyak, M., Druzhinin, V., Tytiuk, V., Rojek, A., Klochko, K., Gurin, I., & Shramko, Y. (2025). Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives. Energies, 18(23), 6132. https://doi.org/10.3390/en18236132

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Article metric data becomes available approximately 24 hours after publication online.

Article Menu

Fractional PI-PI^μD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives

Abstract

Share and Cite

Article Metrics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI