Two-Dimensional Frequency Analysis of Structured Uncertainty for Multiple Array Paper Machine Cross-Directional Processes

Abstract

This paper provides a two-dimensional frequency analysis technique for robust controllers of large-scale multiple array paper machine cross-directional (CD) processes with structured model uncertainty. For such spatially-distributed dynamical systems, the process model and its realistic structured uncertainty are assumed to be linear, spatially-invariant, and time-invariant. These large-scale MIMO systems are rectangular circulant matrix blocks that can be conveniently transformed into a family of small dimension transfer functions in the two-dimensional frequency domain. This significantly simplifies the controller design and gives a better physical insight about the realistic structured uncertainty problem. Given a linear feedback controller, we can easily derive the robust stability condition for the closed-loop CD system in the two-dimensional frequency domain.