Starting from a partial differential equation describing the heat transfer in the continuous casting of steel, the Kirchhoff transformation is used to obtain a more simplified governing heat equation. A boundary state and control transformation is then introduced to obtain a nonlinear heat equation with boundary control. The semi-discrete approximation is applied in the investigation to obtain an ordinary differential equation model. The derived lumped parameter control model can be used to get an approximate solution for the system as well as for finite dimensional system control studies. Finally, local controllability is proved for the system using a linearization technique.
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