Analysis of the Constraint Characteristics of a Sheet Forming Control Problem Using Interval Operability Concepts

An Interval Operability-based approach [1, 2] is applied to calculate operable output constraints for the Sheet Forming Control Problem (SFCP) from DuPont. The SFCP attempts to control the sheet thickness at 15 different points, which represent 15 output variables, using 9 manipulated variables in the presence of 3 disturbances. Thus, this problem represents a computationally complex, high-dimensional non-square system with more outputs than inputs. The SFCP is addressed here under two study cases: 1) a non-square, where all the 15 outputs are controlled independently of each other; 2) a square, where 6 outputs are combined in pairs, or zone variables, and controlled within their corresponding zone. Results show that significant reduction of the constrained region of process operation can be achieved for different output targets specified. Specifically, the hyper-volume ratio of the initial to the designed constrained regions range between 10 – 10. The calculated constraints are validated by running DMCplus (AspenTech) simulations for the extreme values of the disturbances. These constraints are intended for use online in model-based controllers (e.g., Model Predictive Control) to calculate the tightness with which each of the outputs can be controlled.