Mathematical modeling, estimation, and control of the contour evolution in heavy-plate rolling

This work deals with the mathematical modeling, the estimation, and the control of the contour evolution in heavy-plate rolling. Reversing mill stands are used to reduce the thickness of heavy plates in consecutive rolling passes. During the rolling process, asymmetric rolling conditions in the lateral direction may lead to a deviation between the actual and the desired plate contour. This may cause a reduced product quality, product rejects, and in the worst case even damaged plant components around the rolling mill. Asymmetric rolling conditions are generally unknown and cannot be compensated in advance to prevent the plate from cambering. Therefore, a useful approach is to apply feedback if a shape defect occurs. Clearly, this requires a measurement of the contour of the plate. Precise measurements of the contour (longitudinal boundaries and shape of the head and tail end) can be used to optimize the adjustment of the mill stand to reduce the camber. First, the estimation of the plate contour is discussed. Infrared cameras mounted at the ceiling of the rolling mill are used to capture images of the plate during the rolling passes. A validation by means of a downstream contour measurement device shows a high accuracy of the proposed contour estimation method. Second, a static model of the contour evolution is derived. The continuum-mechanics-based model predicts the contour of the plate after the rolling pass based on the contour before the rolling pass and the input and output thickness profiles. The mathematical model is used in different control approaches for the reduction of contour errors. Measurements from the considered industrial rolling mill show that the proposed measures can significantly improve the contour of the rolled plates.