This section proposes the optimal f

This section proposes the optimal flatness feedback con-trol method using the model described by (2). As a problem of the conventional method, since the target elongation rate is fixed, the rolling force required to achieve the target value affects work roll deflection, possibly affecting flat-ness controllability. In the proposed method, the quadratic programming problem is solved at each time step to obtain the optimal manipulated variables which minimize the objective function composed of the sum of squares of deviations between the flatness after one control period and the target value under constraints described by linear inequalities such as the con-trol range of elongation and thickness. Flatness prediction is executed based on the model shown as (2), and the obtained manipulated variables are applied to the system. The rolling force manipulation is calculated under the constraint of the control rangeof the elongation rate to optimize flatness in the objective function. Physically, this is equivalent to setting the rolling force in consideration of the effect of work roll deflection on flatness and the elongation rate control range.