On-line control of solid–liquid interface by state feedback

Abstract This paper deals with the problem of controlling the solid–liquid interface shape during directional solidification of a molten material inside a Bridgman–Stockbarger furnace. The necessary convective boundary conditions that would achieve the desired interface shape are found using feedback controls. A state-space model of the solidification process is determined by employing a modified finite-element technique to the governing conduction equation developed using the apparent heat capacity (AHC) formulation. This model is used to design a dynamic controller that would set up a desired interface shape at the desired location and translate it at the desired velocity. The proposed controller is implemented on a multizone transparent Bridgman crystal growth furnace.

[1]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[2]  J. Crank.  Free and moving boundary problems , 1984 .

[3]  Celal Batur,et al.  Application of stereo imaging for recognition of crystal surface shapes , 1994 .

[4]  Spyros G. Tzafestas,et al.  Recent advances in the study of distributed parameter systems , 1983 .

[5]  Brian G. Thomas,et al.  Fixed grid techniques for phase change problems: A review , 1990 .

[6]  Daniel A. Tortorelli,et al.  Optimal design of nonlinear parabolic systems. Part I: Fixed spatial domain with applications to process optimization , 1994 .

[7]  C. J. Chang,et al.  Radial segregation induced by natural convection and melt/solid interface shape in vertical bridgman growth , 1983 .

[8]  Michael P. Polis,et al.  Parameter identification in distributed systems: A synthesising overview , 1974 .

[9]  Harvey Thomas Banks,et al.  Control and Estimation in Distributed Parameter Systems , 1992 .

[10]  J. Z. Zhu,et al.  The finite element method , 1977 .

[11]  Ephraim M Sparrow,et al.  ANALYSIS OF MULTIDIMENSIONAL CONDUCTION PHASE CHANGE VIA THE ENTHALPY MODEL. , 1975 .

[12]  T. Kailath,et al.  A generalized state-space for singular systems , 1981 .

[13]  Leonard Meirovitch,et al.  Parameter identification in distributed systems , 1985 .

[14]  Control of thermal system through finite element based state-space model , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[15]  C. Batur,et al.  The Design of a Transparent Vertical Multizone Furnace: Application to Thermal Field Tuning and Crystal Growth , 1998 .

[16]  W. Duval,et al.  Inverse heat transfer analysis of Bridgman crystal growth , 1989 .

[17]  T. Rajalakshmi,et al.  Double-diffusive convection during growth of lead bromide crystals , 1997, Optics & Photonics.

[18]  R.E. Goodson,et al.  Parameter identification in distributed systems: A synthesizing overview , 1976, Proceedings of the IEEE.

[19]  A. Chait,et al.  APPLICATION OF THE HOMOGRAPHIC APPROXIMATION IN THE ENTHALPY METHOD FOR PHASE CHANGE PROBLEMS , 1993 .

[20]  Antonio Fasano,et al.  Numerical solution of phase-change problems , 1973 .

[21]  Arvind Srinivasan,et al.  Projective Control Design for Multi-Zone Crystal Growth Furnace , 1993, 1993 American Control Conference.

[22]  Robert A. Brown,et al.  Convection and segregation in directional solidification of dilute and non-dilute binary alloys: Effects of ampoule and furnace design , 1987 .