Optimization-based estimator for the contour and movement of heavy plates in hot rolling

This paper deals with the estimation of the contour of heavy plates during the hot rolling process. Asymmetric rolling conditions lead to a non-rectangular contour. The reasons for this effect, e.g., temperature gradients or nonhomogeneous input thickness profiles, are hard to predict in a real rolling mill. Hence, feedforward compensation of these disturbances is difficult, whereas feedback control could be a suitable means for improving the plate contour. Feedback control essentially requires the actual contour of the plate, which has to be measured or estimated in real-time. The method presented in this paper suggests to capture an image sequence of the plate by means of a thermographic measurement device. In the considered application, an image sequence is required because the whole plate contour cannot be captured by a single image. An optimization-based algorithm takes into account the image data and the restrictions of the plate movement in the rolling gap and uses this information to estimate the actual plate contour. In addition, the algorithm estimates the angular velocity and the speed of the plate. Measurement data from a heavy plate mill is used to validate the effectiveness of the proposed method.