Reheating time optimization for metal products in batch-type furnaces

A novel approach for the real-time optimization of reheating times of metal products in a batch-type furnace is presented. The considered furnace operates at a constant setpoint temperature and the product temperature asymptotically reaches its final value. The sensitivity of the reheating time with respect to the system parameters increases towards the end of the reheating process. A simple first-principles mathematical model of the furnace is developed as a basis for the parameter estimation and optimization. Unknown parameters of the model are estimated and repeatedly updated based on measurements of the mean product temperature before and after the reheating process. The estimation results are grouped in classes of similar products. Based on the estimated parameters of a product class, the optimal reheating time for a product to reach a desired temperature is calculated. The developed method is tested on a finite-element model of the furnace with perturbed parameters to analyze the efficiency, accuracy and robustness of the proposed approach. The numerical results show that highly accurate results can be achieved at very low computational costs.