On the optimal cooling control for continuous casting problem

In this paper we present a solution of the optimal control problem connected with water cooling in the continuous casting process. We use, as a simulation model, the diffusion-convection equation with phase transition. The heat transfer coefficients in the boundary condition are the control variables. Several constraints are imposed to the temperature field inside cast and on surface. In the formulated optimal control problem some of these constraints are included in the cost function as a penalty terms and others are to be satisfied exactly. Finite element approximation of this problem is constructed and gradient information is derived. Nonlinear programming methods are used for solving this finite dimensional optimal control problem. Numerical results are presented.