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The proportional-integral-differential (PID) law is often used to control the induction heating process. Mathematical modeling of induction heating in a three-dimensional formulation is associated with high costs of machine time to solve the electromagnetic field equations. The need to recalculate the heat dissipation field due to changing the power of the inductors at a small sampling period of PID controller leads to an excessive amount of calculations. Two methods of calculation of temperature fields of inducti...