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

This paper presents an automated tuning method of a large-scale multivariable model predictive controller for multiple array paper machine cross-directional (CD) processes. 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 real industrial multiple array CD process is used for illustrating the effectiveness of this method