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

Abstract

Effectively tuning the parameters of proportional-integral-derivative (PID) controllers has persistently posed a challenge in control engineering. This study proposes enhanced hippopotamus optimization (EHO) to address this challenge. Latin hypercube sampling and adaptive lens reverse learning are used to initialize the population to improve population diversity and enhance global search. Additionally, an adaptive perturbation mechanism is introduced into the position update in the exploration phase. To validate the performance of EHO, it is benchmarked against hippopotamus optimization and four classical or state-of-the-art intelligent algorithms using the CEC2022 test suite. The effectiveness of EHO is further evaluated by applying it in tuning PID controllers for different types of systems. The performance of EHO is compared with five other algorithms and the classical Ziegler-Nichols method. Analysis of convergence curves, step responses, box plots, and radar charts indicates that EHO outperforms the compared methods in accuracy, convergence speed, and stability. Finally, EHO is used to tune the cascade PID controller for trajectory tracking in a quadrotor unmanned aerial vehicle to assess its applicability. The simulation results indicate that the integrals of the time absolute error for the position channels (x, y, z), when the system is optimized using EHO over an 80 s runtime, are 59.979, 22.162, and 0.017, respectively. These values are notably lower than those obtained by the original hippopotamus optimization and manual parameter adjustment.

Keywords

PID controllers / Parameter tuning / Hippopotamus optimization / Latin hypercube sampling / Adaptive lens reverse learning / Adaptive perturbation mechanism

RIGHTS & PERMISSIONS

Zhejiang University Press