Customization strategies for the solution of linear programming problems arising from large scale MPC of a paper machine

This paper presents an application of a customized linear programming (LP) based model predictive control strategy to the paper machine cross direction (CD) control problem. The objective of CD control is to maintain flat profiles of variables of interest by minimizing worst case deviations from setpoints (defects). These control problems can have as many as 200 actuators (inputs) and 400 sensor measurements (outputs). This large size coupled with the stringent real-time requirement of computing a control move in a few seconds poses a very challenging control problem. Computational results that demonstrate the effectiveness of this strategy are presented. For typical disturbances this algorithm can compute provably optimal control moves for a 400 input×400 output control problem in approximately 5 seconds versus approximately 90 seconds for a generic LP algorithm on a HP 9000/770 workstation