Pressure Control of Centrifugal Fan Using Softsign-PI Controller Tuned by Hybrid Starfish Optimization Algorithm with Differential Evolution

This study addresses pressure regulation in an induction-motor-driven centrifugal fan and introduces two complementary novelties: a Softsign-PI controller that shapes the tracking error via a Softsign nonlinearity before PI regulation and a hybrid starfish optimization with a differential evolution (hSFOA-DE) scheme for automatically tuning the controller parameters. The approach is evaluated on an experimentally validated nonlinear fan–motor model and benchmarked against modern metaheuristics—starfish optimization algorithm (SFOA), animated oat optimization (AOO), electric eel foraging optimization (EEFO), differential evolution (DE), particle swarm optimization (PSO)—as well as classical tunings—Murrill-based 2-DOF PID, Tyreus–Luyben PID and Ziegler–Nichols PI. Statistical summaries and boxplots indicate superior central tendency with reduced run-to-run variability; fitness–evolution curves show faster convergence; and time-domain performance metrics confirm improved transient and steady-state behaviour. Objective function comparisons further show the lowest values of both the Zwe-Lee Gaing (ZLG) and integral of absolute error (IAE), supporting advantages in robustness and tracking accuracy of the proposed approach. These gains reduce overshoot and cumulative error, which can lessen throttling losses and actuator duty in fan/pump service, suggesting potential energy and maintenance benefits.