Reduced order cross-directional controller design for sheet forming processes

This paper presents a novel control strategy that efficiently addresses the issue of the large number of cross machine direction actuators with which sheet-forming processes are equipped. The approach relies on using the Karhunen-Loeve expansion (KLE) to model the disturbances affecting the properties of interest together with vector autoregressive processes to design a low-order representation of the disturbances. Subsequently, the control space is also reduced by appropriate transformations that rely on the use of KLE. Model predictive control is then implemented on the reduced order model and an optimal solution is obtained in that space, satisfying various types of actuator constraints defined on the full-order system and minimizing the cross-directional variability. The solution from the reduced order model is then projected back to the original space for implementation on the real plant. Simulation examples are included to illustrate the method.