IVANOVA Anna Institute of Applied Mathematics and Mechanics of NASU

The automatic control system of the continuous casting should help to more accurately maintain the prescribed temperature regime and thus produce a higher-quality of continuous-cast semifinished product. The paper is devoted to problems of development of the model predictive control (MPC) algorithms of the secondary cooling modes. Since the thermal physical parameters depend on the temperature of the cast metal and the copper material of the mold walls, the mathematical model of processes of the heat transfer is based on the nonlinear partial differential equations. The position of the boundary between liquid and solid phases is given by the conditions of temperatures equality and the Stefan conditions for the two-dimensional case. The boundary conditions for the wide faces of the ingot in the secondary cooling zone take into account the convective and radiative heat exchange components, as well as the ambient temperature dependence and the heat-transfer coefficients on the locations of the nozzles and water discharge in them. The model is adaptive since it takes into account data coming from the measuring devices and uses the information about the surface temperature of the ingot at the outlet of the secondary cooling zone to adapt to the realities of the process. At each step of the receipt of new measurements, the model calculates the value of control inputs (water rate), which provide the required temperature in the future. The calculated values of water discharge enter to cooling water flow regulators.