Toward Model-Based Control of the Vertical Gradient Freeze Crystal Growth Process

In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated as well as flatness-based state feedback designs are carried out. To render the setup complete, an observer design is performed, using a flatness-based approximation of the original distributed parameter system. The quality of the provided approximations as well as the performance of the open and closed loop control setups is analysed in several simulations.