Abstract
This article reports on feedback control algorithms for thermal systems modeled via the network approach. These networks belong to the class of descriptor systems. They are subject to nondecaying disturbances and, therefore, integral action is required for zero offset. The article includes the derivation of optimal integral controllers for general linear descriptor systems and a detailed study on decentralized control for thermal networks. Feasibility of decentralized control is established via two theorems regarding stability and decentralized integral controllability of thermal networks. Additionally, a particular strategy for the synthesis of decentralized controllers is proposed. This article concludes with a sample of the numerical tests that we performed to demonstrate the efficiency of the proposed algorithms.
Issue Section:
Technical Papers
Keywords:
feedback,
optimal control,
linear systems,
decentralised control,
stability,
controllability,
control system synthesis,
thermal stability,
heat systems,
temperature control,
Thermal Networks,
Descriptor Systems,
Differential-Algebraic Equations,
Integral Control,
Decentralized Control,
Decentralized Integral Controllability
1.
Welty, J. R., 1974, Engineering Heat Transfer, John Wiley, New York.
2.
Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1996, Numerical Solution of Initial-Value Problems in Differential Algebraic Equations, SIAM, Philadelphia PA.
3.
Campbell, S. L., 1980, Singular Systems of Differential Equations, Research Notes in Mathematics, Vol. 40, Pitman, San Francisco, CA.
4.
Campbell, S. L., 1982, Singular Systems of Differential Equations, II, Research Notes in Mathematics, Vol. 60, Pitman, San Francisco, CA.
5.
Dai, L., 1989, Singular Control Systems, Springer, Berlin.
6.
Lewis
, F. L.
, 1986
, “A Survey of Linear Singular Systems
,” Circuits Syst. Signal Process.
, 5
, pp. 3
–36
.7.
Verghese
, G. C.
, Levy
, B. C.
, and Kailath
, T.
, 1981
, “A Generalized State-Space for Singular Systems
,” IEEE Trans. Autom. Control
, AC-26, pp.
811
–831
.8.
Papalexandris
, M. V.
, and Milman
, M. H.
, 2001
, “Active Control and Parameter Updating Techniques for Nonlinear Thermal Network Models
,” Comput. Mech.
, 27
, pp. 11
–22
.9.
Papalexandris
, M. V.
, Milman
, M. H.
, and Levine
, M.
, 2002
, “Nodal Temperature Estimation Algorithms for Nonlinear Thermal Network Models
,” AIAA J.
, 40
, pp. 1451
–1461
.10.
Bender
, D. L.
, and Laub
, A. J.
, 1987
, “The Linear-Quadratic Optimal Regulator for Descriptor Systems
,” IEEE Trans. Autom. Control
, AC-32
, pp. 672
–688
.11.
Varga, R. S., 1961, Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, NJ.
12.
Milman
, M. H.
, and Petrick
, W.
, 2002
, “A Note on the Solution to a Common Thermal Network Problem Encountered in Heat Transfer Analysis of Spacecraft
,” Appl. Math. Modeling
, 24
, pp. 861
–879
.13.
Cobb
, D. J.
, 1984
, “Controllability, Observability, and Duality in Singular Systems
,” IEEE Trans. Autom. Control
, AC-29
, pp. 1076
–1082
.14.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley Interscience, New York.
15.
Anderson, B. D. O., and Moore, J. B., 1971, Linear Optimal Control, Prentice-Hall, Englewood Cliffs, NJ.
16.
Jonckheere
, E. A.
, 1988
, “Variational Calculus for Descriptor Problems
,” IEEE Trans. Autom. Control
, AC-33
, pp. 491
–495
.17.
Morari, M., and Zafiriou, E., 1989, Robust Process Control Systems, Prentice-Hall, Englewood Cliffs, NJ.
18.
Bryant, G. F., and Yeung, L., 1996, Multivariable Control System Design Techniques: Dominance and Direct Methods, John Wiley, England.
19.
Skogestad
, S.
, and Morari
, M.
, 1992
, “Variable Selection for Decentralized Control
,” Modeling, Identification Control
, 13
, pp. 113
–125
.20.
Campo
, P. G.
, and Morari
, M.
, 1994
, “Achievable closed-loop properties of systems under decentralized control: conditions involving the steady-state gain
,” IEEE Trans. Autom. Control
, AC-39
, pp. 932
–943
.21.
Bao
, J.
, McLellan
, B. J.
, and Fraser Forbes
, J.
, 2002
, “A Passivity-Based Analysis for Decentralized Integral Controllability
,” Automatica
, 38
, pp. 243
–247
.22.
Lee
, J.
, and Edgar
, T. F.
, 2002
, “Conditions for Decentralized Integral Controllability
,” J. Process Control
, 12
, pp. 797
–805
.23.
Samyudia
, Y.
, Lee
, P. L.
, and Cameron
, I. T.
, 1995
, “A New Approach to Decentralized Control Design
,” Chem. Eng. Sci.
, 50
, pp. 1695
–1706
.24.
Petzold, L. R., 1983, “A Description of DASSL: A Differential/Algebraic System Solver,” Scientific Computing (Stepleman, R. S., et al., ed.), North-Holland, Amsterdam, pp. 65–68.
25.
Berman, A., and Plemmons, R. J., 1977, Non-Negative Matrices in the Mathematical Sciences, Academic, San Diego, CA.
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