Method of designing model predictive control for cross directional flat sheet manufacturing processes to guarantee spatial robustness and to prevent actuator picketing

Abstract

Automated parameter tuning techniques for cross-directional model predictive control for paper-making under user-specified parametric uncertainties to reduce variability of the actuator and measurement profiles in the spatial domain is proposed. Decoupling properties of the spatial and temporal frequency components permit separate controller design and parameter tuning. CD-MPC design that explicitly accounts for parametric model uncertainty while finding MPC cost function weighing matrices that prevent actuator picketing and guarantee robust stability of the spatial CD profile. Picketing refers to periodic variation patterns in the actuator array. The inventive technique includes: (i) determining the worst case cutoff frequency of all process models, given parametric uncertainty, (ii) designing a weighing matrix to penalize high frequency actuator variability based on the process model and worst case cutoff frequency, and (iii) finding a multiplier for the spatial frequency weighted actuator variability term in the MPC cost function that assures robust spatial stability.