A Novel Algebraic Saturation-Based PID Controller Optimized by Animated Oat Algorithm for Ultra-Fast Dynamic Response of Automatic Voltage Regulation

This paper presents a novel algebraic saturation-based Proportional-Integral-Derivative (ASB-PID) controller for achieving ultra-fast and well-damped dynamic response in automatic voltage regulator (AVR) systems. The proposed controller incorporates an algebraic saturation-based nonlinear transformation applied to both the error signal and its derivative, enabling adaptive control sensitivity across different operating regions. This formulation preserves high sensitivity near the equilibrium point while effectively limiting excessive control action under large transient deviations, thereby overcoming the inherent trade-off between response speed and overshoot observed in conventional PID-based controllers. To address the highly nonlinear and multimodal tuning problem, the controller parameters are optimally determined using the Animated Oat Optimization Algorithm (AOOA), which provides strong global exploration capability and stable convergence behavior. The effectiveness of AOOA is first validated through comparative analysis with widely used metaheuristic algorithms, including Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Sine Cosine Algorithm (SCA). Furthermore, the proposed controller is benchmarked against recently developed high-performance AVR control strategies, including Gudermannian-PID (G-PID), fractional-order PID (FOPID), and higher-order PID-based controllers. Simulation results demonstrate that the proposed AOOA-optimized ASB-PID controller achieves a rise time of 0.0215 s and a settling time of 0.0383 s with zero overshoot and negligible steady-state error, significantly outperforming both competing optimization algorithms and state-of-the-art control designs. Comprehensive benchmarking further confirms that the proposed method consistently delivers superior performance in terms of speed, stability, and robustness, indicating that it provides an effective, computationally efficient, and scalable solution for high-performance AVR systems and broader nonlinear control applications. Unlike conventional nonlinear PID designs based on hyperbolic or sigmoid mappings, the proposed algebraic formulation provides a more explicit and effective saturation mechanism, enabling a superior balance between transient speed and overshoot suppression without increasing controller complexity.