Single and multiple property CD control of sheet forming processes via reduced order infinite horizon MPC algorithm

Abstract

In this article, a reduced order infinite horizon model predictive control (MPC) algorithm for sheet forming processes is explained, and its closed loop performance is studied by using a paper production process as a typical sheet forming process. The proposed algorithm has a very light computational burden due to a significant decrease in the number of variables which is achieved by applying Karhunen-Loeve transformation (KLT) to the sheet profile and finding the lower order subspace which extracts the significant features of the disturbance. Then, the optimal control action in the lower order subspace is found by solving the infinite horizon MPC formulation, and the corresponding solution of the optimization problem is projected back to the original space to be implemented on the real plant. Also, a novel approach is introduced for the solution of multiple property control problem in sheet forming processes, where two or more sheet profiles with different process dynamics are to be controlled by using a single set of actuators. It is explained that the dimensional mismatch problem for the reduced order controller can be solved by using an intermediate subspace, and simulations show that the proposed algorithm performs successfully for paper production processes.