The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

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