Nonlinear model predictive control of a glass forming process based on a Finite Element Model

A complex glass forming process as an example of a complex, nonlinear distributed parameter system is investigated. The system is modeled by four coupled and strongly nonlinear partial differential equations (Trouton model) which are numerically solved by Finite Element method (FEM). As large steps in the setpoint can hardly be controlled with linear controllers and the controlled variables can only be measured with dead time we investigate nonlinear model predictive control (NMPC) as control methodology for the forming process. The use of FEM models in NMPC has not attracted much attention so far although it has a huge potential for process optimization. One reason for the absence of FEM models in control engineering is that the calculation of FEM models in many cases are very time consuming. Hence the NMPC scheme is designed in a way that a trade-off between computational effort and control performance is met. A large step in the setpoint of the two controlled variables (diameter and cross section area of the tube) is investigated as a realistic scenario. The impact of important design parameters of the NMPC is worked out. The good performance of the control and its potential for industrial application is shown.