Reduced order distributed boundary control of thermal transients in microsystems

IEEE Transactions on Control Systems Technology

Volumn 13, Issue 6, 2005, Pages 853-867

  Bleris, Leonidas G ^a   Kothare, Mayuresh V ^a  

^a Lehigh University   (United States)

Author keywords

Boundary reduced order control; Empirical eigenfunctions; Microsystems; Receding horizon control (RHC)

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; OPTIMIZATION; ORDINARY DIFFERENTIAL EQUATIONS;

BOUNDARY REDUCED ORDER CONTROL; EMPIRICAL EIGENFUNCTIONS; MICROSYSTEMS; PROPER ORTHOGONAL DECOMPOSITION (POD); RECEDING HORIZON CONTROL (RHC);

MICROELECTROMECHANICAL DEVICES;

EID: 27844531183     PISSN: 10636536     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCST.2005.854332     Document Type: Article

References (54)

1. S. E. Lyshevski, MEMS and NEMS. Boca Raton, FL: CRC, 2002.
2. N. Maluf, An Introduction to Microelectromechanical Systems Engineering. Norwood, MA: Artech House MEMS Library, 2000.
3. L. G. Bleris and M. V. Kothare, "Finite element method simulations of microchannels for control and reduced order modeling applications," in Proc. 1st Int. Conf. Mathematics and Informatics for Industry, Thessaloniki, Greece, Apr. 2003, pp. 162-169.
4. L. G. Bleris and M. V. Kothare, "Model based control of temperature distribution in integrated microchemical systems," in Proc. Amer. Control Conf., Denver, CO, Jun. 2003, pp. 1308-1313.
5. A. S. Pattekar and M. V. Kothare, "A microreactor for hydrogen production in micro-fuel cell applications," J. Microelectromech. Syst., vol. 13, no. 1, pp. 7-18, Feb. 2004.
6. K. F. Jensen, "Microchemical systems: status, challenges and opportunities," AIChE J., vol. 45, no. 10, pp. 2051-2054, Oct. 1999.
7. K. F. Jensen, I.-M. Hsing, R. Srinivasan, M. A. Schmidt, M. P. Harold, I. J. Lerou, and J. F. Ryley, "Reaction engineering for microreactor systems," in Proc. 1st Int. Conf. Microreaction Technology, 1998, pp. 2-9.
8. D. L. Brenchley and R. S. Wegeng, "Status of microchemical systems development in the United States of America," in Proc. 2nd Int. Conf. Microreaction Technology, 1998, pp. 18-23.
9. H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices: microfluidics toward a lab-on-a-chip," Annu. Rev. Fluid Mech., vol. 36, pp. 381-411, 2004.
10. J. M. Ottino, "Mixing chaotic advection and turbulence," Annu. Rev. Fluid Mech., vol. 22, pp. 207-253, 1990.
11. M. W. Losey, R. J. Jackman, S. L. Firebaugh, M. A. Schmidt, and K. F. Jensen, "Design and fabrication of microfluidic devices for multiphase mixing and reaction," J. Microelectromech. Syst., vol. 11, no. 6, pp. 709-717, Dec. 2002.
12. A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone, and G. M. Whitesides, "Chaotic mixer for microchannels," Science, vol. 295, pp. 647-650, Jan. 2002.
13. M. H. Oddy, J. G. Santiago, and J. C. Mikkelson, "Electrokinetic instability micromixing," Anal. Chem., vol. 73, pp. 5822-5832, 2001.
14. C. M. Ho and Y. C. Tai, "Micro-Electro-Mechanical-Systems (MEMS) and fluid flows," Annu. Rev. Fluid Mech., vol. 30, pp. 579-612, 1998.
15. M. M. Athavale, Z. L. Chen, M. Furmanczyk, and A. J. Przekwas, "Coupled multiphysics and chemistry simulations of per microreactors with active control," in Proc. Int. Conf. Modeling and Simulation of Microsystems, 2001, pp. 574-577.
16. W. E. TeGrotenhuis, D. L. King, and K. P. Brooks, "Optimizing microchannel reactors by trading-off equilibrium and reaction kinetics through temperature management," in Proc. 6th Int. Conf. Microreaction Technology, 2002.
17. L. G. Bleris, M. V. Kothare, J. G. Garcia, and M. G. Arnold, "Embedded model predictive control for system-on-a-chip applications," in Proc. 7th IFAC Symp. Dynamics and Control of Process Systems (DYCOPS-7), Boston, MA, Jul. 2004, Paper no. 128.
18. P. D. Christofides, "Control of nonlinear distributed process systems: recent developments and challenges," AIChE J., vol. 47, no. 3, pp. 514-518, Mar. 2001.
19. S. N. Singh, P. Chandler, C. Schumacher, S. Banda, and M. Pachter, "Nonlinear adaptive close formation control of unmanned aerial vehicles," Dynam. Control. vol. 10, no. 2, pp. 179-194, Apr. 2000.
20. P. D. Christofides and P. Daoutidis, "Robust control of hyperbolic PDE systems," Chem. Eng. Sci., vol. 53, no. 1, pp. 85-105, 1998.
21. W. H. Ray, "Some recent applications of distributed parameter systems theory - a survey," Automatica, vol. 14, no. 3, pp. 281-287, May 1978.
22. P. D. Christofides, Nonlinear and Robust Control of PDE Systems. Boston, MA: Birkhäuser, 2001.
23. O. M. Aamo, M. Krstic, and T. R. Bewley, "Fluid mixing by feedback in Poiseuille flow," in Proc. Amer. Control Conf., Arlington, VA, Jun. 2001, pp. 1930-1935.
24. N. Raskin and Y. Halevi, "Control of flexible structures governed by the wave equation," in Proc. Amer. Control Conf., Arlington, VA, Jun. 2001, pp. 2486-2491.
25. J. E. Lagnese, "Recent progress in exact boundary controllability and uniform stabilizability of thin beams and plates," in Distributed Parameter Control Systems: New Trends and Applications, G. Chen, E. B. Lee, W. Littman, and L. Markus, Eds. New York: Marcel Dekker, 1991, vol. 128, Lecture notes in pure and applied mathematics, pp. 61-111.
26. H. C. Khatri and R. E. Goodson, "Optimal control of systems with distributed parameters," ASME Trans. J. Bas. Eng., vol. 88, pp. 337-342, 1966.
27. J. H. Seinfeld, "Optimal control of distributed parameter systems," Ph.D. dissertation, Chem. Eng. Dept., Princeton Univ., Princeton, NJ, 1967.
28. A. C. Robinson, "A survey of optimal control of distributed parameter systems (survey paper)," Automatica, vol. 7, no. 3, pp. 371-388, May 1971.
29. Y. C. Liang, "Proper orthogonal decomposition and its applications," J. Sound Vib., vol. 252, pp. 527-544, 2002.
30. M. Loéve, Probability Theory. New York: Van Nostrand, 1955.
31. J. L. Lumley, Stochastic Tools in Turbulence. New York: Academic, 1970.
32. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, With Application in Fluid Mechanics, Heat and Mass Transfer, R. Bellman, Ed. New York: Academic, 1972, vol. 87, Mathematics in Science and Engineering.
33. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics. Cambridge, U.K.: Cambridge Univ. Press, 1996.
34. H. Hotelling, "Analysis of a complex of statistical variables into principle components," J. Educat. Psychol., vol. 24, pp. 417-441, 1933.
35. S. S. Ravindran, "Proper Orthogonal Decomposition in Optimal Control of Fluids,", NASA/TM-1999-209113, 1999.
36. J. Baker and P. D. Christofides, "Finite-dimensional approximation and control of nonlinear parabolic PDE systems," Int. J. Control, vol. 73, pp. 439-456, 2000.
37. P. D. Christofides and P. Daoutidis, "Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds," J. Math. Anal. Appl., vol. 216, pp. 398-420, 1997.
38. I. Baker, A. Armaou, and P. D. Christofides, "Nonlinear control of incompressible fluid flow: application to burgers equation and 2-D channel flow," J. Math. Anal. Appl., vol. 252, pp. 230-255, 2000.
39. A. Armaou and P. D. Christofides, "Dynamic optimization of dissipative PDE systems using nonlinear order reduction," Chem. Eng. Sci., vol. 57, pp. 5083-5114, 2002.
40. E. Bendersky and P. D. Christofides, "Optimization of transport-reaction processes using nonlinear model reduction," Chem. Eng. Sci., vol. 55, pp. 4349-4366, 2000.
41. C. W. Rowley, T. Colonius, and R. M. Murray, "Model reduction for compressible flows using POD and Galerkin projection," Physica D: Nonlinear Phenomena, vol. 189, pp. 115-129, 2003.
42. H. M. Park and D. H. Cho, "The use of the Karhunen-Loéve decomposition for the modeling of distributed parameter systems," Chem. Eng. Sci., vol. 98, pp. 81-98, 1996.
43. H. V. Ly and H. T. Tran, "Modeling and control of physical processes using proper orthogonal decomposition," Math. Comput. Modeling, vol. 33, pp. 223-236, 2001.
44. M. D. Graham and I. G. Kevrekidis, "Alternative approaches to the Karhunen-Loéve decomposition for model reduction and data analysis," Comput. Chem. Eng., vol. 20, pp. 495-506, 1996.
45. R. Padhi and S. N. Balakrishnan, "Proper orthogonal decomposition based optimal control design of heat equation with discrete actuators using neural networks," in Proc. 15th Triennial World Congr., Barcelona, Spain, 2002.
46. J. A. Atwell and B. B. King, "Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations," Math. Comput. Modeling, vol. 33, pp. 1-19, 2001.
47. L. G. Bleris and M. V. Kothare, "Low-order empirical modeling of distributed parameter systems using temporal and spatial eigenfunctions," Comput. Chem. Eng., vol. 29, p. 817-827, Feb. 2005.
48. L. G. Bleris and M. V. Kothare, "Entropy of spatiotemporal data as a dynamic truncation indicator for model reduction applications," in Proc. Amer. Control Conf., Portland, OR, Jul. 2005, pp. 3145-3150.
49. L. Sirovich, "Turbulence and the dynamics of coherent structures," Quart. Appl. Math., vol. XLV, pp. 561-571, 1987.
50. FEMLAB Reference Manual, Natick, MA, 2001.
51. T. T. Hsu, MEMS and Microsystems - Design and Manufacture. New York: McGraw-Hill, 2002.
52. G. W. Stewart, Matrix Perturbation Theory. New York: Academic, 1990.
53. C. Davis and W. M. Kahan, "The rotation of eigenvectors by a perturbation III," SIAM J. Numer. Anal., vol. 7, no. 1, pp. 1-46, 1970.
54. E. F. Camacho and C. Bordons, Model Predictive Control. New York: Springer-Verlag, 1999.