We present a linear-quadratic regulator (LQR) design for a heat transfer model describing the cooling process of steel profiles in a rolling mill. Primarily we consider a feedback control approach for a linearization of the nonlinear model given there, but we will also present first ideas how to use local (in time) linearizations to treat the nonlinear equation with a regulator approach. Numerical results based on a spatial finite element discretization and a numerical algorithm for solving large-scale algebraic Riccati equations are presented both for the linear and nonlinear models.

We present a linear-quadratic regulator (LQR) design for a heat transfer model describing the cooling process of steel profiles in a rolling mill. Primarily we consider a feedback control approach for a linearization of the nonlinear model given there, but we will also present first ideas how to use local (in time) linearizations to treat the nonlinear equation with a regulator approach. Numerical results based on a spatial finite element discretization and a numerical algorithm for solving large-scale algebraic Riccati equations are presented both for the linear and nonlinear models.