Flatness based approach to a heat conduction problem in a crystal growth process

Lecture Notes in Control and Information Sciences

Volumn 322, Issue , 2005, Pages 387-401

  Rudolph, Joachim ^a   Winkler, Jan ^a,b   Woittennek, Frank ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b Institut für Kristallüchtung Berlin   (Germany)

Author keywords

Boundary control; Crystal growth; Distributed parameter systems; Flatness; Free boundary; Heat equation; Trajectory planning

Indexed keywords

CRYSTAL GROWTH; DISTRIBUTED PARAMETER CONTROL SYSTEMS; PHASE INTERFACES;

BOUNDARY CONTROLS; DISTRIBUTED PARAMETER SYSTEMS; FLATNESS; FREE BOUNDARY; HEAT EQUATION; TRAJECTORY PLANNING;

HEAT CONDUCTION;

EID: 33748762803     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/11529798_24     Document Type: Conference Paper

References (37)

1. Y. Aoustin, M. Fliess, H. Mounier, P. Bouchon, and J. Rudolph. Theory and practice in the motion planning and control of a flexible robot arm using Mikusiński operators. In Proc. 5th Symposium on Robot Control, pages 287-293, Nantes, France, 1997.
2. S. Boschert, K.G. Siebert, E. Bänsch, K.W. Benz, G. Dziuk, and T. Keiser. Simulation of industrial crystal growth by the vertical Bridgman method. In W. Jäger and H.-J. Krebs, editors, Mathematics - Key Technology for the Future, pages 315-342. Springer, 2003.
3. S. Brandon and J. J. Derby. Heat transfer in vertical Bridgman growth of oxides: effects of conduction, convection, and internal radiation. J. of Crystal Growth, 121:473-494, 1992.
4. H. Chen and L. Rodino. General theory of pde and Gevrey classes. In Qi Minyou and L. Rodino, editors, General Theory of Partial Differential Equations and Microlocal Analysis, pages 6-81. Addison Wesley Longman, Harlow, Essex, 1996.
5. W. B. Dunbar, N. Petit, P. Ronchon, and P. Martin. Motion planning for a nonlinear Stefan problem. ESAIM: COCV (Control, Optimisation and Calculus of Variations), 9:275-296, 2003.
6. M. Fliess, J. Lévine, P. Martin, and P. Rouchon. A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Control, AC-44:922-937, 1999.
7. M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon. Flatness and defect of non-linear systems: introductory theory and examples. Internat. J. Control, 61:1327-1361, 1995.
8. M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph. Systèmes linéaires sur les opérateurs de Mikusiński et commande d'une poutre flexible. In ESAIM Proc., volume 2, pages 183-193, 1997. (http://www.emath.fr/proc).
9. M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph. Controlling the transient of a chemical reactor: a distributed parameter approach. In Proc. Computational Engineering in Systems Application IMACS Multiconference, (CESA'98), Hammamet, Tunisia, 1998.
10. M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph. A distributed parameter approach to the control of a tubular reactor: a multi-variable case. In Proc. 37th IEEE Conference on Decision and Control, pages 439-442, Tampa, FL, 1998.
11. M. Gevrey. La nature analytique des solutions des équations aux dérivées partielles. Ann. Sci. Ecole Norm. Sup., 25:129-190, 1918.
12. W. Haas and J. Rudolph. Steering the deflection of a piezoelectric bender. In Proc. 5th European Control Conference, Karlsruhe, Germany, 1999.
13. G. D. Hill. Parabolic equations in one space variable and the non-characteristic Cauchy problem. Communications on Pure and Applied Mathematics, XX:619-633, 1967.
14. A.S. Jordan. Some thermal and mechanical properties of InP essential to crystal growth modelling. J. of Crystal Growth, 71:559-565, 1985.
15. A. Kugi. Infinite-dimensional control of piezoelectric structures. In Proc. 3rd European Conference on Structural Control (3ECSC), 12-15 July 2004, volume 2, Vienna, Austria.
16. B. Laroche. Extension de la notion de platitude à des systèmes décrits par des équations aux dérivé es partielles linéaires. Thèse de Doctorat, École Nationale Supérieure des Mines de Paris, 2000.
17. B. Laroche, Ph. Martin, and P. Rouchon. Motion planning for the heat equation. Int. J. Robust and Nonlinear Control, 10:629-643, 2000.
18. A. F. Lynch and J. Rudolph. Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems. Internat. J. Control, 2002.
19. Ph. Martin, R. M. Murray, and P. Rouchon. Flat systems, equivalence and feedback. In A. Baños, F. Lamnabhi-Lagarrigue, and F. J. Montoya, editors, Advances in the Control of Nonlinear Systems, volume 264 of Lecture Notes in Control and Inform. Sci., pages 3-32. Springer-Verlag, 2001.
20. Ph. Martin, R. M. Murray, and P. Rouchon. Flat systems: open problems, infinite dimensional extension, symmetries and catalog. In A. Baños, F. Lamnabhi-Lagarrigue, and F. J. Montoya, editors, Advances in the Control of Nonlinear Systems, volume 264 of Lecture Notes in Control and Inform. Sci., pages 33-57. Springer-Verlag, 2001.
21. T. Meurer, J. Becker, and M. Zeitz. Flatness based feedback tracking control of a distributed parameter tubular reactor model. In Proc. European Control Conference (ECC), Cambridge, 2003.
22. T. Meurer and M. Zeitz. A novel design approach to flatness-based feedback boundary control for nonlinear reaction-diffusion systems with distributed parameters. In W. Kang, C. Borges, and M. Xiao, editors, New Trends in Nonlinear Dynamics and Control, Lecture Notes in Control and Information Sciences, pages 221-236. Springer-Verlag, New-York, 2003.
23. T. Meurer and M. Zeitz. Feedforward and feedback tracking control of nonlinear diffusion-convection-reaction systems using summability methods. Industrial & Engineering Chemistry Research, 44:2532-2548, 2004.
24. T. Meurer and M. Zeitz. Flatness-based feedback control of diffusion-convection-reaction systems via k-summable power series. In F. Allgöwer, editor, Preprints 6th IFAC-Symposium on Nonlinear Control Systems (NOLCOS 2004), volume 1, pages 191-196, Stuttgart, 2004.
25. R. Rothfuß, U. Becker, and J. Rudolph. Controlling a solenoid valve - a distributed parameter approach. In Proc. 14th Int. Symp. Mathematical Theory of Networks and Systems - mtns 2000, Perpignan, France, 2000.
26. P. Rouchon. Motion planning, equivalence, infinite dimensional systems. Int. J. Appl. Math. Comput. Sci., 11:165-188, 2001.
27. P. Rouchon and J. Rudolph. Réacteurs chimiques différentiellement plats : planification et suivi de trajectoires. In J. P. Corriou, editor, Automatique et procédés chimiques -Réacteurs et colonnes de distillation, chapter 5, pages 163-200. Hermès Science Publications, 2001.
28. J. Rudolph. Flatness based control of distributed parameter systems. Berichte aus der Steuerungs- und Regelungstechnik. Shaker Verlag, Aachen, 2003.
29. J. Rudolph, J. Winkler, and F. Woittennek. Flatness based control of distributed parameter systems: Examples and computer exercises from various technological domains. Berichte aus der Steuerungs- und Regelungstechnik. Shaker Verlag, Aachen, 2003.
30. J. Rudolph, J. Winkler, and F. Woittennek. Flatness based trajectory planning for two heat conduction problems in crystal growth technology. e-STA (Sciences et Technologies de l'Automatique), 1(2), 2004.
31. J. Rudolph and F. Woittennek. Motion planning for simple elastic structures. In Proc. 3rd European Conference on Structural Control (3ECSC), 12-15 July 2004, volume 1, Vienna, Austria.
32. J. Rudolph and F. Woittennek. Flachheitsbasierte Randsteuerung von elastischen Balken mit Piezoaktuatoren. at - Automatisierungstechnik, 50:412-421, 2002.
33. R. Sheinman, S. Brandon, and D.R. Lewin. Optimal control of vertical Bridgman crystal growth. Thessaloniki, 2003. EMCC-3.
34. C. Stelian, T. Duffar, J.-L. Santailler, and I. Nicoara. Influence of temperature oscillations on the interface velocity during Bridgman crystal growth. J. of Crystal Growth, 237:1701-1706, 2002.
35. D. Vizman, I. Nicoara, and G. Müller. Effects of temperature asymmetry and tilting in the vertical Bridgeman growth of semi-transparent crystals. J. of Crystal. Growth, 212:334-339, 2000.
36. M. O. Wagner, T. Meurer, and M. Zeitz. Feedforward control of nonlinear diffusion-convection-reaction systems using k-summable power series. In F. Allgöwer, editor, Preprints 6th IFAC-Symposium on Nonlinear Control Systems (NOLCOS 2004), volume 1, pages 149-154, Stuttgart, 2004.
37. H. Weimann, J. Amon, Th. Jung, and G. Müller. Numerical simulation of the growth of 2" diameter GaAs crystals by the vertical gradient freeze technique. J. of Crystal Growth, 180:560-565, 1997.