Comparative Analysis of Objective Functions in PSO-PID Control for BLDC Motor Speed Regulation

Abstract

Brushless DC (BLDC) motors are fundamental in applications such as electric vehicles and robotics, where precise speed regulation is crucial. This study presents a BLDC motor speed control system based on a PID controller optimized using Particle Swarm Optimization (PSO). The system was simulated in MATLAB/Simulink under three speed levels (low, medium, high) and three load conditions (no load, half load, full load), with a comparative evaluation of four objective functions: Integral of Time Absolute Error (ITAE), Integral of Time Squared Error (ITSE), Root Mean Squared Error (RMSE), and a hybrid ITAE+ITSE. A total of 720 experiments were conducted and assessed using five performance metrics: rise time (Tr), settling time (Ts), maximum overshoot (Mp), steady-state error (Ess), and mean value of speed after settling time. Results demonstrated that ITAE outperformed the other objective functions in minimizing rise time, settling time, and steady-state error, achieving a rise time of 0.00087 s at high speed, a settling time of 1.6992 s at medium speed, and a steady-state error of 0.6178% at medium speed. However, other objective functions showed superiority in certain cases for specific performance indices. Overall, RMSE exhibited weaker performance, particularly in settling time and steady-state error. These findings highlight the significance of selecting an appropriate objective function and its impact on the quality of BLDC motor speed control, providing valuable insights for designing efficient PSO-PID controllers for practical applications.