Comparative numerical statistical analysis.

Shell and tube heat exchangers are pivotal for efficient heat transfer in various industrial processes. Effective control of these structures is essential for optimizing energy usage and ensuring industrial system reliability. In this regard, this study focuses on adopting a fractional-order proportional-integral-derivative (FOPID) controller for efficient control of shell and tube heat exchanger. The novelty of this work lies in the utilization of an enhanced version of cooperation search algorithm (CSA) for FOPID controller tuning, offering a novel approach to optimization. The enhanced optimizer (en-CSA) integrates a control randomization operator, linear transfer function, and adaptive p-best mutation integrated with original CSA. Through rigorous testing on CEC2020 benchmark functions, en-CSA demonstrates robust performance, surpassing other optimization algorithms. Specifically, en-CSA achieves an average convergence rate improvement of 23% and an enhancement in solution accuracy by 17% compared to standard CSAs. Subsequently, en-CSA is applied to optimize the FOPID controller for steam condenser pressure regulation, a crucial aspect of heat exchanger operation. Nonlinear comparative analysis with contemporary optimization algorithms confirms en-CSA’s superiority, achieving up to 11% faster settling time and up to 55% reduced overshooting. Additionally, en-CSA improves the steady-state error by 8% and enhances the overall stability margin by 12%.