A novel hyperbolic tangent-based PID controller tuned by the artificial lemming algorithm for nonlinear steam...

Precise pressure regulation in nonlinear shell-and-tube steam condensers is essential for maintaining thermal efficiency and operational safety in power generation plants; however, conventional proportional-integral (PI) and proportional-integral-derivative (PID) controllers struggle with nonlinear dynamics, leading to overshoot, slower settling, and reduced robustness. In this regard, a novel hyperbolic tangent-based PID (tanh-PID) controller is developed in this study to introduce smooth nonlinear gain modulation, enabling enhanced damping behavior and improved transient shaping. The recently introduced artificial lemming algorithm (ALA) is employed to optimally tune the proposed controller for integral of time-weighted absolute error minimization. Extensive simulation studies are performed using a comprehensive nonlinear condenser model incorporating steam-air interactions and hot-well dynamics. The proposed strategy is benchmarked against four competitive optimization algorithms (coati optimization algorithm, dandelion optimizer, success-history based adaptive differential evolution with linear population size reduction, and adaptive artificial electric field algorithm) and compared with state-of-the-art PI and fractional-order PID (FOPID) controllers reported in the literature. The ALA-tuned tanh-PID achieves the lowest integral of time-weighted absolute error (2.1189), fastest rise time (0.5960 s), minimal settling time (12.4799 s) and overshoot (5.8056%), along with near-zero steady-state error (4.0776 × 10⁻⁴%), outperforming all compared methods in both transient response and steady-state accuracy. Robustness analyses further confirm superior disturbance rejection and reliable reference tracking under dynamic uncertainties. These results demonstrate that the proposed methodology offers an efficient, low-complexity, and high-performance control solution suitable for real-time deployment in industrial steam condenser systems.