OPTIMAL CONTROL OF THE INDUCTION HEATING PROCESS OF STEEL IN TERMS OF SPEED AND ENERGY CONSUMPTION

The article describes the process of induction heating of a cylindrical steel billet before the pressing operation, which is used in industry in the manufacture of hollow and solid products of complex profile, which cannot be obtained using other types of metal processing. Due to the spatial extent of the temperature field of the workpiece, the induction heating process should be considered as an object with distributed parameters. The problem of optimal control is formulated according to the criterion of minimum time and the criterion of minimum energy spent. The solution of the tasks is performed using an alternance method based on the special properties of the temperature distribution at the end of the optimal heating process. The alternance method allows to reduce the solution of the optimal problem according to the appropriate optimality criterion to the solution of a system of transcendental equations, which is closed with respect to all unknown parameters of the induction heating process. The solution of the system of equations is performed using a numerical model developed in the Altair FLUX software, which allows modeling low-frequency electromagnetic and thermal processes. The specificity of the solved problem consists in the fact that the resulting control, which are optimal in the class of two-interval controls, allows heating of a steel cylindrical billet in the shortest possible time with minimal energy consumption.