Optimal control of a heat flow system via novel enhanced quadratic interpolation optimization tuned 2DOF-PID...

This study addresses the optimal temperature regulation problem of a laboratory-scale heat flow system using a two-degree-of-freedom proportional-integral-derivative (2DOF-PID) controller tuned by a newly developed enhanced quadratic interpolation optimization (eQIO) algorithm. The main contribution lies in improving the original quadratic interpolation optimization (QIO) framework by integrating two lightweight enhancement mechanisms: a periodic parabolic local search to strengthen local exploitation and a stagnation-aware diversity recovery strategy to prevent premature convergence. The enhanced formulation preserves the deterministic interpolation-based structure of QIO while increasing convergence reliability and robustness without introducing additional algorithmic complexity. The effectiveness of eQIO is first evaluated on ten benchmark functions from the CEC-2019 test suite and compared with QIO, mountain gazelle optimization, tuned moss growth optimization, whale optimization algorithm, and superb fairy-wren optimization algorithm. Statistical results obtained from 500 independent runs indicate that eQIO consistently improves average solution quality and reduces standard deviation relative to QIO, while achieving competitive performance against population-based metaheuristic algorithms. Subsequently, eQIO is employed to tune the parameters of the 2DOF-PID controller for real-time temperature regulation experiments under step, square, and sinusoidal reference signals. The experimental results demonstrate reduced overshoot, lower steady-state error, improved tracking accuracy, and smoother control effort compared with alternative optimizer-based tuning approaches. Quantitatively, the proposed eQIO-based 2DOF-PID controller reduces the total mean absolute error (MAE) by 14.8% under step-square reference signals and by 45.8% under step-sinusoidal reference signals compared with the original QIO-based controller, while also providing smoother control action and improved tracking robustness. Overall, the proposed eQIO-driven 2DOF-PID framework establishes a computationally efficient and experimentally validated methodology for reliable thermal system control.