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    Enhanced automatic voltage regulation using an extended PIDA controller optimised by the snake algorithm
    (Elsevier, 2025) Chetty, Nelson Dhanpal; Gandhi, Ravi; Sharma, Gulshan; Celik, Emre; Kumar, Rajesh
    Maintaining voltage stability within acceptable limits is crucial in power systems, with Automatic Voltage Regulation (AVR) ensuring consistent performance. Traditionally, PID controllers have been widely used; however, they struggle in complex, nonlinear environments with fluctuating conditions and disturbances. This study proposes an Extended PID-Acceleration (ePIDA) controller incorporating a novel state observer-based Disturbance Observer (DOB) for enhanced voltage regulation. The Snake Optimiser (SO) is introduced for the first time in AVR tuning, leveraging its dynamic leader-follower mechanism to achieve faster convergence and optimal controller gains. The SO-ePIDA framework extends the traditional PIDA structure with a three-degree-offreedom (3DOF) approach, enhancing setpoint tracking and disturbance rejection. The proposed approach is evaluated against six widely used optimisation strategies through comparative statistical and graphical analyses, considering step-load variations and system parameter settings. Results demonstrate that the SO-ePIDA controller achieves a rise time of 0.1679 s, a settling time of 0.3123 s, and the lowest ISTAE value of 0.0046, ensuring superior transient response and steady-state accuracy. Furthermore, under a 30 % step-load disturbance, the proposed controller exhibits the fastest recovery time of 0.1065 s, significantly outperforming other methods. The AVR system was tested with +25 % and +50 % variations in system parameters to assess robustness under parametric uncertainty. The results confirm that the SO-ePIDA controller maintains stability, with rise time deviations limited to 0.1577 and 0.2004 s and ISTAE variations between 0.0116 and 0.1891, demonstrating strong adaptability under extreme operating conditions. These findings establish the SO-ePIDA framework as a robust, high-performance solution for real-world AVR applications.