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Optimal Tuning of Digital PID Controllers for Commercial BLDC Motors Using the Nelder–Mead Method

Son T. Nguyen

Son T. Nguyen

School of Electrical and Electronic Engineering, Hanoi University of Science and TechnologyHanoi, Vietnam
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Nguyen, Son T.
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Tu M. Pham

Tu M. Pham

School of Electrical and Electronic Engineering, Hanoi University of Science and TechnologyHanoi, Vietnam
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Pham, Tu M.
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Anh Hoang

Anh Hoang

School of Electrical and Electronic Engineering, Hanoi University of Science and TechnologyHanoi, Vietnam
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Hoang, Anh
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Trung T. Cao

Trung T. Cao

School of Electrical and Electronic Engineering, Hanoi University of Science and TechnologyHanoi, Vietnam
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Cao, Trung T.
  
29 lug 2025
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Categoria dell'articolo: Research Paper
Pubblicato online: 29 lug 2025
Pagine: 210 - 226
Ricevuto: 15 apr 2025
Accettato: 27 giu 2025
DOI: https://doi.org/10.2478/pead-2025-0015
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© 2025 Son T. Nguyen et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Block diagram of a BLDC motor drive. BLDC, brushless DC.
Block diagram of a BLDC motor drive. BLDC, brushless DC.

Figure 2.

Simulink diagram of the trapezoidal control of BLDC motors. BLDC, brushless DC; EMF, electromotive force; PWM, pulse-width modulation.
Simulink diagram of the trapezoidal control of BLDC motors. BLDC, brushless DC; EMF, electromotive force; PWM, pulse-width modulation.

Figure 3.

Motor speed and stator current of the BLDC motor with the trapezoidal control method. BLDC, Brushless DC.
Motor speed and stator current of the BLDC motor with the trapezoidal control method. BLDC, Brushless DC.

Figure 4.

Simulink diagram of the FOC method of BLDC motors. BLDC, Brushless DC; FOC, field-oriented control; SVPWM, space vector PWM.
Simulink diagram of the FOC method of BLDC motors. BLDC, Brushless DC; FOC, field-oriented control; SVPWM, space vector PWM.

Figure 5.

Motor speed and stator current of the BLDC motor with the FOC method. BLDC, brushless DC; FOC, field-oriented control.
Motor speed and stator current of the BLDC motor with the FOC method. BLDC, brushless DC; FOC, field-oriented control.

Figure 6.

The hardware. BLDC, brushless DC.
The hardware. BLDC, brushless DC.

Figure 7.

Response of the real motor speed to a step voltage of 5 V.
Response of the real motor speed to a step voltage of 5 V.

Figure 8.

Motor speed responses for reference speeds of 500 rpm (a), 700 rpm (b) and 900 rpm (c).
Motor speed responses for reference speeds of 500 rpm (a), 700 rpm (b) and 900 rpm (c).

Performance comparison between the initial and optimised PID controllers at a speed of 900 rpm_

Controller Rise time (s) Settling time (s) Overshoot (%)
Initial PID controller 3.5867 6.3841 0.1332
Optimised PID controller 1.3312 2.4900 0.2745

Performance comparison between the initial and optimised PID controllers at a speed of 500 rpm_

Controller Rise time (s) Settling time (s) Overshoot (%)
Initial PID controller 3.5867 6.8628 0.0899
Optimised PID controller 1.6477 2.8985 0.6736

Performance comparison between the initial and optimised PID controllers at a speed of 700 rpm_

Controller Rise time (s) Settling time (s) Overshoot (%)
Initial PID controller 3.7983 6.5593 0.4619
Optimised PID controller 1.6200 3.8898 0.2130
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