Optimal Active Deflection Compensation of a Hot Leveler

A validated, mathematical deflection model of the work rolls and the machine frame of a hot leveler is presented. The model calculates the roll gap along both planar directions of the plate. The work rolls are loaded by distributed leveling forces, which are calculated based on the local roll gap and the material properties of the leveled plate. Furthermore, the rolls are supported by machine frames, which may be modeled by linear force-deflection relations. The model is well suited for analyzing the influence of the various adjustment and control inputs on the roll gap, which is important for the leveling result. Moreover, control laws providing active symmetric deflection compensation are developed. By minimizing a cost function that depends, inter alia, on the curvature of the plate, optimal reference values for the adjustment cylinders and the bending mechanism are generated. Force constraints are integrated into the optimization problem so that overloading of the leveler is systematically avoided. Numerical results demonstrate the feasibility of the proposed approach.