Parametric identification and induction heating process optimal control

In the paper the experimental induction heating installation for through heating of steel cylindrical workpieces is considered. It is well known that the use of an industrial heating system presupposes incomplete information about its main characteristics due to the complex nature of changes in some parameters both from the ambient temperature and from the temperature of the heated part. These parameters primarily include the coefficients of convective and emissive heat transfer from the surface of the workpiece. At the first step, it is necessary to obtain the values of unknown parameters, which also include the voltage of the power source, and then solve the optimal control problem. The problem of identifying these parameters is solved using the alternance method of parametric optimization of systems with distributed parameters, using experimental data from thermocouples. The obtained values of unknown parameters are then used in a numerical finite-element FLUX model of the considered process. Based on the developed model, the problem of time-optimal control with an additional phase restriction on the maximum temperature is formulated. This problem is solved using the alternance method. The solution of the problem made it possible to obtain a emperature field with a maximum deviation of $32 ^{\circ}$C from the required temperature $T^* = 1 200 ^{\circ}$C. This value is less than $3\%$ of the desired temperature value and fully meets the technological requirements for induction through heating processes prior subsequent plastic deformation. The maximum temperature in this case does not exceed the maximum permissible value of $1 300 ^{\circ}$C during the entire heating process.