Optimal Control of Cross-Machine Direction Web Profile with Constraints on the Control Effort

Spatial coupling between the control points in a cross-machine profile of a sheet property is a primary concern in cross-machine control problems. The goal of the cross-machine direction (CD) control is to minimize the deviation from a desired profile with certain constraints on the control action. Two approaches, quadratic programming (QP) and quadratic penalty function (QPF), were evaluated for inclusion in a commercial CD control product. The optimal control is obtained from the QP approach, but the QPF which produces near-optimal control, is more robust and easier to implement in real-time applications. A comparison between QP and QPF results is shown by simulated examples. Field test results of the QPF method are also included. The QPF approach is well suited for practical applications and has been successfully incorporated in over 40 commercial installations.