Improved beluga whale optimization-based variable universe fuzzy controller for brushless direct current motors of electric tractors

Brushless direct current (BLDC) motors are widely used in electric tractor powertrains, but torque ripple remains a challenge. Proportional Integral Derivative (PID) controllers are effective in steady-state regulation but struggle with load-induced uncertainties. A new method for tuning sensorless BLDC motors by integrating improved Beluga Whale Optimization (IBWO) with an optimal variable universe fuzzy (VUF) controller is proposed. The enhanced IBWO addresses limitations in solving nonlinear systems, optimizing the VUF controller for precise torque control. A fast non-singular terminal sliding mode observer is also introduced for accurate state estimation. The IBWO adjusts the VUF controller parameters in real time, enabling adaptive torque and speed regulation, thereby reducing overshoot and torque ripple. To validate the proposed approach, a dual closed-loop control model is designed to simulate motor behavior under no load, variable load, and variable speed conditions during plowing operations. The results show that the proposed controller reduces torque ripple by at least 75 % and 60 % compared to PID and fuzzy controllers, respectively, and improves speed regulation time by over 26 %, with steady-state errors of 0.6, 0.7, and 0.12 rpm (rpm) under different conditions.