Starfish Optimization Algorithm-Tuned PID Controller for Automatic Voltage Regulation: A Multi-Criteria Time- and Frequency-Domain Study

Reliable terminal-voltage regulation is essential for preserving power quality and the secure operation of synchronous generators, yet the dynamic performance of an automatic voltage regulator (AVR) depends strongly on the tuning of its controller parameters. This study proposes a starfish optimization algorithm (SFOA)-tuned proportional-integral-derivative (PID) controller for the standard linearized AVR benchmark. The proportional, integral and derivative gains are optimized simultaneously by minimizing a composite objective function that accounts for overshoot, steady-state error, rise time and settling time. Performance is benchmarked against PID controllers tuned by the reptile search algorithm (RSA), genetic algorithm (GA), and symbiotic organisms search (SOS) under identical plant and operating conditions. SFOA determines the gain set K_P = 0.6329, K_I=0.5165, and K_D=0.2275. The resulting controller achieves a rise time of 0.2900 s, a settling time of 0.4405 s, an overshoot of 1.1624%, a steady-state error of 4.7740×〖10〗^(-13)%, and the lowest objective-function value of 0.0627 among the compared methods. Frequency-domain analysis further shows that the phase margin increases from 16.1028 degrees to 68.3451 degrees, the gain margin from 4.6176 dB to 26.4043 dB, and the bandwidth from 6.9454 rad/s to 7.7374 rad/s. The controller also follows a multi-level time-varying voltage command without persistent offset or growing oscillations. These results indicate that SFOA provides an effective multi-criteria PID-tuning framework that improves transient response, relative stability, and reference-tracking performance for the investigated AVR system.