Tuning a Proportional-Integral-Derivative (PID) controller by the HLOA Algorithm for the Sloshing Dynamics Problem

Abstract The motion of liquid in chemical tanks and reactors can cause instability, hinder mixing, reduce heat and mass transfer, and even compromise process safety. This phenomenon, known as the Sloshing Dynamics Problem (SDP), refers to the back-and-forth motion of a liquid surface in partially filled containers. In this work, the Ball-and-Hoop System (BHS) is employed as a physical representation of the SDP, since it consists of a steel ball rolling inside a rotating circular hoop whose oscillatory behavior mimics liquid sloshing. A Proportional-Integral-Derivative (PID) controller was implemented to maintain the ball oscillating within its trajectory, minimizing overshoot and settling time. To optimize the controller, five bio-inspired algorithms were employed: Horned Lizard Optimization Algorithm (HLOA), Coot Optimization (COOT), Chaos Game Optimization (CGO), Golden Eagle Optimizer (GEO), and Mexican Axolotl Optimization (MAO). The comparison shows that the HLOA algorithm provides the best overall control strategy for the sloshing dynamics problem. It delivers a fast response (rise time around 2 s), an extremely short settling time (≈3.3 s), and virtually zero overshoot (3.26E-04%). Future work will involve robust analyses that include closed-loop perturbations of liquid movement in chemical tanks.