Optimization-based reduction of contour errors of heavy plates in hot rolling

This paper deals with the reduction of top view contour errors in the hot rolling process. Deviations between the actual plate contour and the desired shape may result from asymmetric rolling conditions caused by, e.g., temperature gradients or non-homogeneous input thickness profiles. Under real rolling conditions these disturbances are hard to predict and hence cannot be compensated in a feedforward approach. Therefore, it seems suitable to apply feedback when contour errors occur. This approach essentially requires a measurement of the plate contour and a mathematical model to predict the plate contour after the roll pass. This model is the basis for an optimization-based approach to determine the necessary adjustment of the rolling mill to reduce contour errors. The optimization problem allows to systematically incorporate constraints on the asymmetry of the output plate thickness. Generally, the compliance of the mill stand is not strictly symmetric and may deteriorate the result of the presented approach. The asymmetric compliance results in an asymmetric deflection of the mill stand which is compensated in an empirical approach utilizing the forces applied during the roll pass. Simulation results and measurements of plates rolled during the normal production demonstrate the effectiveness of the proposed method.