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This paper presents a complete modeling of two types of multi-phase induction heating systems and the application of resonant control to achieve a perfect current reference tracking. It proposes a global solution including electrical and thermal modeling of the whole system in PSim software, with a reduced simulation time. The paper presents simplified equivalent model based on data extracted from finite element software, for the modeling of energy transfer between the coil currents and the piece to be heated. The required current density distributions are extracted from the finite element software Flux2D® and the impedance matrix that describes the electrical behavior of the coils supplied by the inverters from Inca3D®. A specific optimization procedure leads to the optimal reference inverter currents in order to obtain a uniform heating of the work piece. In that case, the coupling terms between the phases are not negligible and the sampling frequency/switching frequency ration of the resonant inverter is very low. Then, some specific stability zones are defined for the tuning gains of the resonant controllers. [ABSTRACT FROM PUBLISHER]