Optimal control of induction heating of steel workpieces with respect to minimal scale formation criteria

Efficiency of heat treatment production processes of metals is measured by different characteristics, including productivity, energy consumption and quality of end product. Increasing each of them is possible through optimization with respect to corresponding integral criteria. The quality of end product, which is made of high iron alloys, after heat treatment operations depends on metal loss to scale, that is inevitably formed during high-intensity heating in induction installation. Thus, to reduce the amount of defective details it is necessary to obtain the optimal operating mode of inductor, which will minimize the mentioned losses. The paper is devoted to optimization of static induction heating of steel cylindrical billets before the subsequent plastic deformation operations. The 2D numerical mathematical model of induction heating process, developed in Altair FLUX, is considered as a control object with distributed parameters. The optimal control problems with respect to time-optimal, minimal energy consumption and minimal scale formation criteria are formulated. The solution of formulated problems after their parametrization and reduction to semi-infinite optimization problems can be carried out using alternance method of parametric optimization of objects with distributed parameters. As an example for minimal scale formation problem, the system of transcendental equations closed with respect to all unknowns of the heating process is written based on alternance method. Solving of the system is provided by automatized procedure, which is developed in program package MATLAB. The analysis of numerical results shows that solving this one-criteria optimal control problem allows to reduce the amount of scale with significant increasing of heating time in comparison with time-optimal and minimal energy consumption problems. That is why on the next stages of the investigation it is planned to solve a multi-criteria optimization problem in order to take onto account several typical goal functions simultaneously.