Abstract
The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.
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