Metaheuristic-Based PI Controller Tuning Using a Multi-Error ITAE Objective Function for FOC-Controlled PMSM Drives in Electric Vehicle Applications

Permanent Magnet Synchronous Motors (PMSMs) are widely employed in electric vehicle (EV) propulsion systems because of their high efficiency, high power density, and superior dynamic performance. The performance of field-oriented control (FOC)-based PMSM drives strongly depends on accurate tuning of the proportional–integral (PI) controllers governing the speed and current loops. Conventional tuning approaches often optimize a single performance index and therefore fail to simultaneously enhance the dynamic behavior of all control loops. This paper proposes a multi-error Integral of Time-weighted Absolute Error (ITAE)-based optimization framework for simultaneous tuning of the PI controllers by minimizing a composite objective function that incorporates the time-weighted absolute errors of the rotor speed, q-axis current, and d-axis current. To validate the effectiveness and optimizer independence of the proposed framework, five metaheuristic optimization algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), Gazelle Optimization Algorithm (GOA), and White Shark Optimization (WSO)—are evaluated under identical optimization settings. MATLAB/Simulink simulations are performed for reference-speed tracking, load disturbance rejection, and variable-speed operation. The results demonstrate that the proposed optimization framework consistently improves tracking accuracy and dynamic response regardless of the selected optimizer, while WSO provides the best overall performance. In the variable-speed tracking scenario, WSO achieved the lowest RMSE of 0.96 rad/s and the minimum ITAE value of 0.1716, confirming its effectiveness as the most suitable optimizer for the proposed framework in high-performance PMSM drive applications.