Real-time nonlinear model predictive control of a glass forming process using a finite element model

The control of complex forming processes (e.g., glass forming processes) is a challenging topic due to the mostly strongly nonlinear behavior and the spatially distributed nature of the process. In this paper a new approach for the real-time control of a spatially distributed temperature profile of an industrial glass forming process is presented. As the temperature in the forming zone cannot be measured directly, it is estimated by the numerical solution of the partial differential equation for heat transfer by a finite element scheme. The numerical solution of the optimization problem is performed by the solver HQP (Huge Quadratic Programming). In order to meet real-time requirements, in each sampling interval the full finite element discretization of the temperature profile is reduced considerably by a spline approximation. Results of the NMPC concept are compared with conventional PI control results. It is shown that NMPC stabilizes the temperature of the forming zone much better than PI control. The proposed NMPC scheme is robust against model mismatch of the disturbance model. Furthermore, the allowed parameter settings for a real-time application (i.e., control horizon, sampling period) have been determined. The approach can easily be adapted to other forming processes where the temperature profile shall be controlled.