Feedback controller design for a spatially distributed system: the paper machine problem

— This article reports on the development and implementation of an algorithm for the design of spatially-distributed feedback controllers for the wide variety of physical processes that are included in cross-directional control of industrial paper machines. The spatial and temporal structure of this class of process models is exploited in the use of the two-dimensional frequency domain for analysis and two-dimensional loop shaping design of feedback controllers. This algorithm forms the basis of a software tool that has recently been implemented in a commercial product and its use is illustrated for tuning CD controllers on two different industrial paper machines. The first example describes the use of the tool in stabilizing an unstable closed-loop system by retuning the distributed controller. The second paper machine example exposes an underperforming controller. Subsequent retuning of the controller resulted in a dramatic performance improvement.