A Novel Gudermannian Function-Driven Controller Architecture Optimized by Starfish Optimizer for Superior Transient Performance of Automatic Voltage Regulation

This paper proposes a Gudermannian function-based proportional-integral-derivative (G-PID) controller to enhance the transient performance of automatic voltage regulator (AVR) systems operating under highly dynamic conditions. By embedding the smooth and bounded nonlinear mapping of the Gudermannian function into the classical PID structure, the proposed controller improves adaptability to large signal variations while effectively suppressing overshoot. The controller parameters are optimally tuned using the starfish optimization algorithm (SFOA), which provides a robust balance between exploration and exploitation in nonlinear search spaces. Simulation results demonstrate that the SFOA-optimized G-PID controller achieves superior transient performance, with a rise time of 0.0551 s, zero overshoot, and a settling time of 0.0830 s. Comparative evaluations confirm that the proposed approach outperforms widely used optimization algorithms (particle swarm optimization, grey wolf optimizer, success history-based adaptive differential evolution with linear population size, and Kirchhoff's law algorithm) and advanced AVR control schemes, including fractional-order and higher-order PID-based designs. These results indicate that the proposed SFOA optimized G-PID controller offers a computationally efficient and structurally simple solution for high-performance voltage regulation in modern power systems.