Two-dimensional frequency response analysis and insights for weight selection in cross-directional model predictive control

This paper describes the application of a technique for the two-dimensional frequency domain analysis of the closed-loop performance of a cross-directional papermaking process under industrial model predictive control (MPC). For such spatially-distributed systems, the process model and the linear portion of the controller are approximated as linear, spatially-invariant, and time-invariant. The closed-loop performance of these systems can then be analyzed in terms of a family of SISO systems by diagonalizing the large-scale transfer matrices across spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain.