Automated tuning of large-scale multivariable model predictive controllers for spatially-distributed processes

Abstract

An automated tuning method of a large-scale multivariable model predictive controller for multiple array papermaking machine cross-directional (CD) processes can significantly improve the performance of the controller over traditional controllers. Paper machine CD processes are large-scale spatially-distributed dynamical systems. Due to these systems' (almost) spatially invariant nature, the closed-loop transfer functions are approximated by transfer matrices with rectangular circulant matrix blocks, whose input and output singular vectors are the Fourier components of dimension equivalent to either number of actuators or number of measurements. This approximation enables the model predictive controller for these systems to be tuned by a numerical search over optimization weights in order to shape the closed-loop transfer functions in the two-dimensional frequency domain for performance and robustness. A novel scaling method is used for scaling the inputs and outputs of the multivariable system in the spatial frequency domain.