Mathematical model of brusherless dc motor based on the voltage equation of a three-phase winding

A mathematical model was developed, during which the voltage equations of the three-phase winding of a brushless DC motor with permanent magnets, the electromagnetic torque of a brushless DC motor, electromagnetic power, the induced emf of each winding, and the differential torque equation of the servo system were obtained. Based on the constructed mathematical model of the BLDC for a specific motor with given parameters, simulation modeling was carried out and the dependences of electromechanical quantities were obtained: angular velocity of the rotor, electromagnetic torque, stator phase current and rotor rotation angle on time. The simulation results confirmed the theoretical justification of the mathematical model. The resulting mathematical description of the BLDC can be used to build the architecture of a control unit based on a neural network controller.

1. Mouliswararao, R. Mathematical modeling of brushless DC motor and its speed control using PI controller / R. Mouliswararao, K. Bhaskararao, Ch. Prasad // International journal of engineering research and technology (IJERT). Vol. 08, Issue 05 (May 2019). – 2019. – Pp. 880-883. DOI: 10.17577/IJERTV8IS05044

2. Schagin, A.V. Development of speed control system for BLDC motor with power factor correction. / A.V. Schagin, D.T. Nguyen // 2020 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), St. Petersburg and Moscow, Russia. – 2020. – Pp. 2411-2414. DOI: 10.1109/EIConRus49466.2020.9038981

3. Purnalal, M. Development of mathematical model and speed control of BLDC motor / M. Purnalal, T.K. Sunil kumar. // International Journal of Electrical and Electronics Engineers IJEEE, Vol. 07, Iss. 01, JanJune 2015. – 2015. – Pp. 271-280.

4. Obulesh, Y. Mathematical modeling of BLDC motor with closed loop speed control using PID controller under various loading conditions / Obulesh, Y., Ch, Sai Babu, A., Purna Chandra Rao // ARPN Journal of Engineering and Applied Sciences. Vol. 7 (10). October, 2012. – 2012. – Pp. 1321-1328.

5. Proshutinsky D.A. Development of a mathematical model of a drive based on a low-speed brushless electric motor. Polytechnic youth magazine. – 2020, No. 05(46). DOI: 10.18698/2541-8009-2020-05-60

6. Al Mahturi, F.Sh. Verification of the mathematical model of a contactless DC motor in Simulink using passport and experimental data / F.Sh. Al Makhturi, D.V. Samokhvalov // International conference on soft computing and measurements: St. Petersburg State Electrotechnical University LETI. – 2019. – Vol. 1. – Pp. 304-306.

7. Gavrilov S.V. Control of an electric drive based on a brushless motor with permanent magnets / S.V. Gavrilov, D.T. Zang, N.D. Than // Proceedings of St. Petersburg State Electrotechnical University LETI. – 2016. – No. 8. – Pp. 53-62.

8. Abuzyarov T.Kh. [et al.] Development of a model of high-quality brushless DC electric drive systems // Bulletin of the Ivanovo State Energy University. – 2020. – No. 1. – Pp. 31-45.

9. Radimov I.N. [et al.] Research of a switched-type motor with internal permanent magnets using two methods of connecting the phases of the stator winding // Electrical engineering and electromechanics. – 2010. – No. 6. – Рp. 35-38.

10. Firago B.I. Implementation of a contactless DC motor with ferrite magnets based on the design of an induction motor. / B.I. Firago, A.G. Gulkov, L. Pavlyachik // Energy. News of higher educational institutions and energy associations of the CIS. 2001; (1). – 2001. – Pp. 39-51. DOI: 10.21122/1029-7448-2001-0-1-39-51

11. Firago B.I. On the issue of vector control of asynchronous motors / B.I. Firago, D.S. Vasiliev // Energy. News of higher educational institutions and energy associations of the CIS. – 2015. – No. 5. – Pp. 5-16.