<![CDATA[Water level control is a critical problem in various industrial processes, such as water treatment, power generation, chemical industry, and irrigation. Although proportional–integral–derivative (PID) controllers are widely used due to their simple structure and ease of implementation, determining the parameters Kp, Ki, and Kd remains challenging for systems with nonlinear dynamics and actuator limitations. This study presents a comparative evaluation of five population-based metaheuristic algorithms—Firefly Algorithm (FA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Orca Predation Algorithm (OPA)—for automatic tuning of PID parameters in a second-order water tank model with actuator saturation of ±5 pu. The objective function employed is the Integral of Time-multiplied Absolute Error (ITAE) with an overshoot penalty. The comparison was conducted under identical conditions, including population size, number of iterations, parameter search ranges, initial conditions, and objective function. Simulation results demonstrate that ACO-PID achieves the lowest ITAE value of 0.2352 and the fastest settling time of 1.32 s. FA-PID, GWO-PID, and OPA-PID yield closely comparable performance, whereas PSO-PID produces zero overshoot at the expense of the highest ITAE value of 0.2668 and the longest settling time of 1.66 s. The execution times of all five algorithms are relatively similar, ranging from 4.84 to 5.16 s. These findings indicate that ACO is the most suitable method for the plant configuration and objective function examined in this study; however, the performance differences among ACO, FA, GWO, and OPA are relatively small and cannot be considered statistically significant without multi-run testing and statistical analysis.]]>
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