Fractional PI-PIμD Controllers with Neural Network Adaptation in Control System of BLDC Motor Electric Drives

This paper investigates, for the first time, the synthesis of a controller that incorporates a fractional-order integral component to achieve a closed-loop astaticism order greater than one. To enhance both static and dynamic accuracy, the controller integrates direct-signal-propagation neural networks within each control channel. The controlled plant is the BLDCM speed loop, which is modeled using a fractional-order differential equation. The study compares the performance of four controller types: a classical PID regulator tuned close to the optimal modulus criterion (IntPID); a fractional PI–PIμD controller (FrPID) that achieves an astaticism order of at least 1.8; and two hybrid neuro-controllers, NN–IntPID and NN–FrPID. While the FrPID controller reduces the root-mean-square error by nearly a factor of five compared with IntPID, the best results are delivered by NN–FrPID. Specifically, it decreases overshoot eight-fold during a reference step (from 2.98% to 0.35%), lowers the root-mean-square error during linear reference tracking by a factor of eleven, and reduces the relative speed error by more than thirty-five times. When combined with a fast learning algorithm executed at each control-cycle iteration, the controller enables the closed loop to adapt not only to variations in gain coefficients, but also to changes in the fractional-aperiodic order of the plant. These results demonstrate that neural fractional-integral controllers offer strong potential for improving accuracy and robustness in BLDC motor drives and are applicable to a wide range of electromechanical systems.