Improving the Performance of the Chaotic Nonlinear System of the Fractional-Order Brushless Direct Current Electric Motor by Using Fractional-Order Sliding Mode Control

Abstract

Chaos is a dynamic phenomenon that occurs over time in discrete and continuous nonlinear systems for some parameters, and chaotic systems are very sensitive to initial conditions. Controlling a chaotic system means eliminating its chaotic behavior and bringing the system to its origin equilibrium point or another desirable point. Moreover, as most natural systems have fractional dynamics, there is a clear need to study fractional systems. Nowadays, Brushless Direct Current (BLDC) electric motors are widely used as actuator components in many industries. Controlling these nonlinear and multivariable systems is of great importance. Additionally, these systems are often accompanied by parameter uncertainties and external disturbances, which may lead to undesirable and even unstable system behavior. In this research, a three-state-variable chaotic model is presented, and with the help of fractional-order sliding mode control strategy, the performance of the system is improved and controlled compared to conventional sliding mode control. It can be seen that the resistance of the fractional-order BLDC system with fractional-order sliding mode control is significantly higher than that of the conventional BLDC system with conventional sliding mode control against parameter uncertainties and external disturbances. Finally, the controller's performance is evaluated using MATLAB software.