Boundary identification and control of distributed parameter systems using singular functions

Chemical Engineering Science

Volumn 54, Issue 9, 1999, Pages 1181-1204

  Chakravarti, Shrikar ^a   Harmon Ray, W ^a  

^a Wisconsin Electric Machines and Power Electronics Consortium   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; IDENTIFICATION (CONTROL SYSTEMS);

PSEUDO-MODAL CONTROL SCHEMES; SINGULAR FUNCTIONS;

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

BOUNDARY CONDITIONS; CHEMICAL ENGINEERING; MATHEMATICAL MODELING;

EID: 0033133651     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0009-2509(98)00500-4     Document Type: Article

References (41)

1. Alvarez, J., Romagnoli, J.A., & Stephanopoulos, (1981). Variable measurement structures for the control of a tubular reactor. Chem. Engng Sci., 36 (10), 1695-1712.
2. Aubry, N., Guyonnet, R., & Lima, R. (1991). Spatiotemporal analysis of complex signals: Theory and applications. J. Stat. Phys. 64, 683.
3. Berkooz, G., Holmes, P. & Lumley, J.L. (1993). The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539-575.
4. Butkovskiy, A.G. (1969). Distributed Control Systems, New York: American Elsevier.
5. Butkovskiy, A.G. (1982). Green's Functions and Transfer Functions HandBook. Chicester: Ellis Horwood.
6. Caracotsios, M., & Stewart, W.E. (1985). Sensitivity analysis of initial value problems with mixed odes and algebraic equations, Comput. Chem. Engng., 9, 359-365.
7. Carey, G.F., & Finlayson, B.A. (1975). Orthogonal collocation on finite elements. Chem. Engng. Sci., 30, 587-596.
8. Chakravarti, S., Marek, M., & Ray, W.H. (1995). Reaction-diffusion system with Brusselator kinetics - control of quasiperiodic routes to chaos, Phys. Rev. E, 52 (3), 2407-2423.
9. Chakravarti, S., & Ray, W.H. (1997). Boundary identification and control of distributed parameter systems using singular functions. In Proceedings of the American Control Conference, Albuquerque, NM (pp. 2223-2227).
10. Chien-Chong Chen, & Hseuh-Chin Chang (1992). Accelerated disturbance damping of an unknown distributed system by nonlinear feedback, A.I.Ch.E. J, 38 (9), 1461-1476.
11. Chien-Chong Chen, Wolf, E.E., & Hseuh-Chia Chang (1993). Low-dimensional spatiotemporal thermal dynamics on nonuniform catalytic surfaces, J. Phy. Chem. 97, 1055-1064.
12. Cochran, J.A. (1972). The Analysis of Linear Integral Equations, New York: Mc-Graw-Hill.
13. Fattorini, H.O. (1968). Boundary control systems, SIAM J. Control 6 (3), 349-385.
14. Fukunaga, K. (1990). Introduction to Statistical Pattern Recognition. Boston: Academic Press.
15. Gay, D.H. (1989). Identification and Control of Distributed Parameter Systems by Means of the Singular Value Decomposition, PhD thesis, University of Wisconsin at Madison.
16. Gay, D.H., & Ray, W.H. (1988). Application of singular value methods for identification and model based control of distributed parameter systems. In McAvoy, J.T. Arkun, Y. & Zzflriou, E. (Eds.), Proceedings of the IFAC Workshop on Model-Based Process Control, Atlanta, GA (pp. 95-102). Oxford: Pergamon Press.
17. Gay, D.H. & Ray, W.H. (1995). Identification and control of distributed parameter systems by means of the singular value decomposition. Chem. Engng Sci. 50 (10), 1519-1539.
18. Golub, G.H., & van Loan, C.F. (1989). Matriz Computations. Baltimore: Johns Hopkins University Press.
19. Graham, M.D., Lane, S.L., & Luss, D. (1993). Proper orthogonal decomposition analysis of spatiotemporal temporal patterns, J. Phys. Chem. 97 (4), 889-894.
20. Hanczyc, E.M., & Palazoglu, A. (1996). Use of symmetry groups in sliding mode control of nonlinear distributed parameter systems, Int. J. Control, 63 (6), 1149-1166.
21. LAPACK Users' Guide (1992).
22. LINPACK Users' Guide (1989).
23. Lorenz, E.N. (1956). Empirical Orthogonal Functions and Statistical Weather Prediction. Technical report, MIT.
24. Lumley, J.L. (1970). Stochastic Tools in Turbulence. New York: Academic Press.
25. Naylor, A.W., & Sell, G.R. (1982). Linear Operator Theory in EngineerIng and Science. New York: Springer.
26. Olivei, A. (1974). Boundary modal control of the temperature of the melt for crystal-growing in crucibles. Int. J. Control, 20 (1), 129-157.
27. Olmstead, W.E. (1980). Boundary controllability of the temperature in a long rod, Int. J. Control, 31 (3), 593-600.
28. Olmstead, W.E., & Schmitendorf, W.E. (1977). Optimal control of the end-temperature in a semi-infinite rod. J. Appl. Math. Phys., 28, 697-706.
29. Park, H.M., & Cho, D.H. (1996). The use of the Karhunen-Loéve decomposition for the modeling of distributed parameter systems, Chem. Engng Sci., 51(1), 81-98.
30. Ramkrishna, D., & Amundson, N.R. (1985). Linear Operator Methods in Chemical Engineering. Englewood Cliffs. NJ: Prentice-Hall.
31. Rigopoulos, A., Arkun, Y., & Kayihan, F. (1997). Identification of full profile disturbance models for sheet forming processes, A.I.Ch.E. J. 43(3), 727-739.
32. Schumaker, L.L. (1981). Spline Functions: Basic Theory. New York: Wiley-Interscience.
33. Sirovich, L. (1987). Turbulence and the dynamics of coherent structures-parts I,II,III, Quart. Appl. Math. XLV (3), 561-590.
34. Smithies, F. (1958). Integral Equations. Cambridge: University Press.
35. Stakgold, I. (1979). Green's Functions and Boundary Value Problems. New York: Wiley.
36. Stewart, G.W. (1993) On the early history of singular value decomposition. SIAM Rev., 35(4), 551-566.
37. Villadsen, J., & Michelsen, M.L. (1978). Solution of Differential Equation Models by Polynomial Approximation. Englewood Cliffs, NJ: Prentice-Hall.
38. Villadsen, J.V., & Stewart, W.E. (1967). Solution of boundary-value problems by orthogonal collocation. Chem. Engng Sci., 22, 1483-1501.
39. Windes, L.C. (1986). Modelling and Control of a Packed Bed Reactor. PhD thesis, University of Wisconsin at Madison.
40. Zhou, X.G., Liu, L.H., Dai, Y.C., Yuan, W.K., & Hudson, J.L. (1996). Modeling of a fixed-bed reactor using the K-L expansion and neural networks. Chem. Engng Sci., 51 (10), 2179-2188.
41. Zolesio, J.P. (Ed.), (1991). Boundary Control and Boundary Variation. New York: Springer.