Nonlinear model predictive temperature control of a cooling process for steel strips undergoing phase transformations

The cooling of hot steel causes phase transformations that are directly influencing the material properties. Precise temperature control is therefore essential for producing high-quality steel products. The paper proposes a nonlinear model predictive controller for accurate tracking control of the strip temperature in a cooling section of a continuous steel strip processing line of voestalpine Stahl GmbH. The controller is based on a dynamic model of the local temperature and phases of the strip material. The controller computes optimal trajectories of the system inputs so that the strip reaches a strip-specific target temperature. A tailored constrained nonlinear dynamic optimization problem is numerically solved in the control algorithm using the Levenberg–Marquardt method. The gradient and the approximate Hessian of the objective function are analytically computed using an adjoint-based approach. Measurements at the real processing line demonstrate the excellent control performance. Long-term analysis shows that the model predictive controller improves both the accuracy and the homogeneity of the strip temperature compared to the previously used PI-control scheme. On average, the reduction of the mean temperature error is 51%, and the improvement of the temperature homogeneity is 25%.