Page 7 - IJOCTA-15-3

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.3, pp.379-395 (2025)
https://doi.org/10.36922/ijocta.8407

RESEARCH ARTICLE

Improving the performance of a chaotic nonlinear system of
fractional-order brushless direct current electric motor using
fractional-order sliding mode control

2*
1
Amin Kaveh , Mohammad Vahedi , and Majid Gandomkar 1
1
Department of Electrical Engineering, College of Technical, Islamic Azad University, Saveh, Iran
2
Department of Mechanical Engineering, College of Technical, Islamic Azad University, Saveh, Iran
Amin.kaveh@iau.ac.ir, Mo.Vahedi@iau.ac.ir, majid.gandomkar@iau.ac.ir
ARTICLE INFO ABSTRACT

Article History:
Brushless direct current (BLDC) motors are widely used in industrial appli-
Received: January 14, 2025
cations due to their high efficiency and reliability. However, these motors
Revised: March 7, 2025
exhibit inherent nonlinear and chaotic behavior, which can degrade perfor-
Accepted: March 24, 2025
Published Online: April 22, 2025 mance and cause instability under certain operating conditions. This paper
proposes a fractional-order sliding mode controller (FO-SMC) for robust chaos
Keywords: suppression and improved stability in BLDC motor systems to address this
Brushless direct current motor issue. The proposed controller leverages fractional-order calculus to enhance
Fractional-order sliding mode robustness, mitigate chattering, and provide better disturbance rejection than
control Chaos conventional control approaches. A comprehensive Lyapunov-based stability
Lyapunov stability analysis is conducted to ensure finite-time convergence and system stability un-
Robust control der parameter uncertainties and external disturbances. The effectiveness of the
AMS Classification 2010: proposed FO-SMC is evaluated through extensive numerical simulations, com-
34A08, 26A33, 34H10, 93C10 paring its performance against the integer-order sliding mode control method.
The results demonstrate that FOS-MC significantly outperforms traditional
controllers regarding settling time, overshoot reduction, and robustness to ex-
ternal perturbations. Additionally, the study explores the practical feasibility
of implementing the proposed control strategy in real-time applications us-
ing Grunwald–Letnikov fractional derivatives, which enable efficient numerical
approximation and digital implementation in field-programmable gate array-
based and microcontroller-driven control systems. The findings confirm that
FOS-MC provides a highly adaptive and resilient solution for stabilizing BLDC
motors, making it a strong candidate for advanced industrial automation and
high-performance motor control applications.

1. Introduction decreases linearly with increasing speed. How-
ever, due to the square wave shape of the cur-
Nowadays, vehicles are increasingly being rent and the commutation action between the
equipped with permanent magnet synchronous phases, they exhibit torque ripple, which can
motors. One of the most widely used motors impact their performance. Various techniques
in industrial applications is the brushless direct have been developed to minimize torque ripple in
current (BLDC) motor, which is particularly fa- BLDC motors. 1–4
vored in the automotive industry due to its sen-
sorless operation. These motors provide max- By examining the performance of different
imum torque at a standstill, and their torque electric motors, it is evident that conventional DC
*Corresponding Author
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