Model-based feedforward and feedback control of the verticalgradient-freeze-crystal growth process using distributed parameter methods

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An important process for the production of mono crystalline materials is the vertical gradient freeze (VGF) process. Here, poly-crystalline material is molten in a crucible. Then crystallization starts from the bottom into upward direction until the complete melt is solidified. For this purpose the temperature field surrounding the crucible is manipulated in such a way that the melting point isotherm travels slowly from the bottom to the top of the crucible. The required controls are realized by resistance heaters placed around the crucible. In order to drive the process in an appropriate manner information about the actual state is required, especially of the crystallization rate. However, this cannot be captured. This is due to high process temperature, the reactivity of the used materials and the requirements with respect to the purity of the product preventing any measurement devices to be placed within the crucible. Only the temperatures at the resistance heaters can be measured. Because of this it is not possible to establish a real closed loop control. It is only feed forward black box controlled. From a control theoretic point of view the VGF process is a typical candidate of a distributed parameter system with free boundaries (the solid-liquid-interface) and lumped control input (the heaters). The objective of the proposed project is to develop theoretical and practical methods for a real feedback control of the process. This also includes methods for the reconstruction of the system state from available or newly introduced measurements. For this purpose it is planned to use distributed parameter methods that have been developed by the Institute of Control Theory (TU Dresden) as one of the leading institutes in this subject for several years now. Up to now the focus was mainly on the feedforward control and the parameter identification of such systems. The work will be accompanied with intensive work on modeling of the VGF process by the Institute of Crystal Growth Berlin (IKZ). These models are required for controller and observer design as well as for the validation of the developed control and reconstruction algorithms so experimental effort can be reduced. Here, the challenge is to find mathematical models of the process which on the one hand side are sufficiently precise for control and on the other hand side are real time capable. Furthermore they must meet the structural requirements given by the selected distributed parameter methods. Although the control methods developed during the project will found a highly sophisticated theoretical framework the practical meaningfulness will be guaranteed by experimental tests at the VGF growth plants.