Enhanced hippopotamus optimization algorithm for tuning proportional–integral–derivative controllers

• Enhanced Hippopotamus Optimization (EHO) integrates Latin hypercube sampling, adaptive lens reverse learning, and an adaptive perturbation mechanism to improve population diversity and global search for PID parameter tuning. • EHO demonstrates superior accuracy, convergence speed, and stability compared to five other algorithms and the classical Ziegler–Nichols method across diverse system types. • In CEC2022 benchmark tests, EHO outperforms the original hippopotamus optimization and multiple classical/state-of-the-art intelligent algorithms. • For quadrotor UAV cascade PID trajectory tracking, EHO achieves significantly lower integral time absolute error (ITAE) values—59.979, 22.162, and 0.017 for x, y, z channels—than baseline methods.