Abstract
This article presents a mathematical model in the form of static equations of dependencies of input and output flows based on the equations of material and heat balance for the purposes of operational planning and control of the complex technological complex of Vanyukov melting (PV). Dynamic characteristics are presented for the purpose of controlling the thermal regime based on the technology of the developed melting process with blowing from below. As a result of the study, the developed mathematical model for controlling the smelting process when calculating the material flows of the charge will allow tracking changes in the thermal state of the smelting (by the copper content in the matte). This model can quite well describe the dynamics of the state of the process, both when establishing the impacts aimed at increasing the heating of the furnace, and at reducing its heating. Based on the equations, a computer model based on the dynamic programming method in the MATLAB software package has been developed. The scientific novelty lies in the fact that for the first time, the structure of a mathematical model has been developed that describes the processes occurring in the over-tuyere zone and the sludge zone of the smelting products.