A Robust Speed Controller Design for PMSM Using $\text{PI}^\lambda \mathrm{D}^{\mu}$ Controllers

This study proposes the design of Fractional-Order Proportional-Integral-Derivative
$\text{PI}^\lambda \mathrm{D}^{\mu}$
controllers for Permanent Magnet Synchronous Motors (PMSMs). PMSMs are essential in high-precision industrial applications due to their high efficiency and outstanding speed regulation.
$\text{PI}^\lambda \mathrm{D}^{\mu}$
controllers, unlike conventional PID controllers, use fractional calculus to provide an extra degree of flexibility, allowing the system to change and diversify over a wide range of operating states. By performing a series of simulations, we analyze the performance metrics of controllers and compare it with integer-order PID controllers. Our main focus is on the evaluation of speed control response time, overshoot, and steady state error. The results show that the
$\text{PI}^\lambda \mathrm{D}^{\mu}$
controller effectively improves the dynamic and static performance of PMSM without loss of stability. As a result, the design methodology from simulations and comparative statistics confirm that
$\text{PI}^\lambda \mathrm{D}^{\mu}$
controllers have the potential to be superior in maintaining precise control over integer-order PIDs in complex electromechanical systems.