Automatic tuning of paper machines cross-direction controllers via linear matrix inequalities

The paper machine cross-direction (CD) process is a large-scale spatially distributed system. It is known to be severely ill-conditioned as the gain rolls down to zero for some of the process directions. This article presents an automatic tuning technique for loop-shaping low order spatially localized CD controllers. Following closed-loop identification of the process model, the CD controller is synthesized through a Linear Matrix Inequalities (LMI) feasibility problem to guarantee nominal stability, performance and robustness to model uncertainties. Robust stability and performance of the controller in the presence of parametric uncertainties are investigated through the ν-gap metric. The performance of the LMI loop-shaped controller is illustrated through comparing it to an industrial CD controller that has been implemented in paper mills.