Optimal control of plate motion and camber in a reversing rolling mill

Abstract

In plate rolling, reversing roughing mills are commonly used as a first processing step after casting. They are typically equipped with edger rolls for width reduction. During a rolling pass, lateral asymmetries like temperature gradients or thickness inhomogeneities can cause two major problems. The plate may rotate in the rolling gap and thus move in lateral direction. Another problem is that the plate may leave the mill stand with a cambered shape. In the worst case, these problems entail collisions with the mill stand or other equipment along the roller table. It is an essential control task to avoid such problems. In general, the exit thickness profile and the motion of the plate are controlled by adjusting the roll gap height. The latter has also an influence on the contour shape but, for active control of the plate width and contour shape, the use of edger rolls is more common. This is especially true if the roll gap adjustment is self-retaining, meaning that it cannot be adjusted during a rolling pass. In this work, such a roughing mill and its edger rolls are considered. A mathematical model for the motion and the camber of the plate is derived. Based on this model, a linear quadratic regulator (LQR) for both the plate motion and the resulting camber is developed. It uses the lateral forces of the edgers as control inputs. In a cascaded control structure, these forces are regulated by a subordinate admittance controller. The developed control system is validated in simulation studies.