Optimal FOPID Controller Design for an AVR SystemUsing a Chaotic-Enhanced Phototropism GrowthAlgorithm (C-PGA)

To address the high-dimensional, non-convex optimization challenge of tuning fractional-order PID (FOPID) controllers for Automatic Voltage Regulator (AVR) systems, we propose a Chaotic-Enhanced Phototropic Growth Algorithm (C-PGA). The standard Phototropic Growth Algorithm (PGA) suffers from premature convergence due to insufficient population diversity; thus, we integrate a Logistic chaotic map for optimized population initialization and dynamic perturbations during stagnation, enhancing global exploration and local exploitation. A weighted multi-objective function incorporating integral time absolute error (ITAE), overshoot, and steady-state error guides the optimization process. MATLAB/Simulink simulations demonstrate that the C-PGA-tuned FOPID controller achieves near-zero overshoot, improved transient responses, satisfactory stability under ±50\% parameter perturbations, and effective disturbance rejection. Wilcoxon rank-sum tests confirm its competitive performance compared to classical (PSO, GA) and modern (RIME, DBO) algorithms, indicating its potential as an effective solution for AVR voltage regulation.