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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
 und 
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. Juli 2025
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Artikel-Kategorie: Research Paper
Online veröffentlicht: 29. Juli 2025
Seitenbereich: 210 - 226
Eingereicht: 15. Apr. 2025
Akzeptiert: 27. Juni 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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Englisch
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Informatik, Künstliche Intelligenz, Technik, Elektrotechnik, Elektronik
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