Input Design Minimizing the ~-gap in Cross-Directional Models of Paper Machines

Modeling uncertainties resulting from input-output identification are inevitable. In this paper, input design minimizing the uncertainties in the static spatial model of paper machines is presented. A technique that was developed for temporal transfer functions was adapted to the spatial domain. The spatial response is modeled by a non-causal transfer function as it propagates in both the forward and backward directions of space. As the robustness of the closed loop is a crucial issue, the uncertainties are quantified using the nu-gap metric and the worst case nu-gap resulting from a prediction error experiment over all plants in the uncertainty region is minimized. The nu-gap stability criterion is extended to accommodate the non-causal system. Simulation results illustrate the advantage of using the designed input and the significance of the spatial nu-gap