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

Brushless direct current (BLDC) motors are widely used in industrial applications due to their high efficiency and reliability. However, these motors exhibit inherent nonlinear and chaotic behavior, which can degrade performance and cause instability under certain operating conditions. This paper proposes a fractional-order sliding mode controller (FO-SMC) for robust chaos suppression and improved stability in BLDC motor systems to address this issue. The proposed controller leverages fractional-order calculus to enhance robustness, mitigate chattering, and provide better disturbance rejection than conventional control approaches. A comprehensive Lyapunov-based stability analysis is conducted to ensure finite-time convergence and system stability under parameter uncertainties and external disturbances. The effectiveness of the proposed FO-SMC is evaluated through extensive numerical simulations, comparing 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 external perturbations. Additionally, the study explores the practical feasibility of implementing the proposed control strategy in real-time applications using 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.