  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.
