A constriction-based PSO method with an enhanced cost function for PI optimization in FOC speed controllers

ABSTRACT The performance of Field-Oriented Control (FOC)-based PMSM speed control is greatly influenced by the quality of PI parameter tuning. However, conventional approaches such as Ziegler-Nichols or trial-and-error often result in high overshoot and suboptimal stability. PSO has been widely used for automatic tuning, but its standard version still risks premature convergence and has not effectively suppressed overshoot and transient energy. This study proposes a constriction-based PSO with an enhanced ITAE function incorporating overshoot and energy penalties. Validation results show a significant performance improvement. Conventional FOC produces a speed overshoot of around 0.5 PU with a settling time of approximately 2 seconds and a peak torque transient of 0.08 PU, while standard PSO reduces the classical speed overshoot to 0.02 PU but worsens the initial transient dynamics, introducing severe speed oscillations with peak amplitudes reaching ±3.3 PU and a peak torque transient of ±1.0 PU with steady-state torque ripple of ±0.1–0.2 PU, indicating that the standard ITAE cost function does not sufficiently penalize transient energy and overshoot. The proposed method provides the most significant improvement: the speed overshoot is reduced to 0.01 PU, the settling time reaches 1.5 seconds, and the peak torque transient is maintained at 0.18 PU, with a more stable steady-state torque ripple of ±0.025 PU, making it the most stable among all methods. Additionally, the steady-state error is approximately 0.002 (almost zero), and recovery after a load disturbance occurs more quickly, with a deviation of only about 0.01 PU before returning to stability.