Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Results of a steady-state analysis performed for a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the system with two state variables and two boundary inputs, the analytical expressions for the steady-state distribution of the state variables are derived, both in the exponential and in the hyperbolic form. The influence of the location of the boundary inputs on the steady-state response is demonstrated. The considerations are illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.
Czasopismo
Rocznik
Tom
Strony
295--310
Opis fizyczny
Bibliogr. 35 poz., rys., wzory
Twórcy
autor
- Institute of Control and Computer Engineering, Opole University of Technology, ul. Sosnkowskiego 31, 45-272 Opole, Poland
Bibliografia
- [1] F. Ancona and G. M. Coclite: On the boundary controllability of first-order hyperbolic systems. Nonlinear Analysis: Theory, Methods & Applications, 63(5-7), (2005), e1955-e1966.
- [2] M. A. Arbaoui, L. Vernieres-Hassimi, D. Seguin and M. A. Abdelghani- Idrissi: Counter-current tubular heat exchanger: Modeling and adaptive predictive functional control. Applied Thermal Engineering, 27(13), (2007), 2332-2338
- [3] G. M. Bahaa and M.M. Tharwat: Optimal control problem for infinite variables hyperbolic systems with time lags. Archives of Control Sciences, 21(4), (2010), 373-393.
- [4] K. Bartecki: Comparison of frequency responses of parallel- and counter-flow type of heat exchanger. In Proc. of the 13th IEEE IFAC Int. Conf. on Methods and
- [5] K. Bartecki: Frequency- and time-domain analysis of a simple pipeline system. In Proc. of the 14th IEEE IFAC Int. Conf. on Methods and Models in Automationand Robotics, Miedzyzdroje, Poland, (2009), 366-371.
- [6] K. Bartecki: PCA-based approximation of a class of distributed parameter systems: classical vs. neural network approach. Bulletin of the Polish Academy of Sciences- Technical Sciences, 60(3), (2012). 651-660.
- [7] K. Bartecki: A general transfer function representation for a class of hyperbolic distributed parameter systems. Int. J. of Applied Mathematics and Computer Science, 23(2), (2013), 291-307.
- [8] K. Bartecki and R. Rojek: Instantaneous linearization of neural network model in adaptive control of heat exchange process. In Proc. of the 11th IEEE Int. Conf. onMethods and Models in Automation and Robotics, Miedzyzdroje, Poland, (2005), 967-972.
- [9] H. Bounit: The stability of an irrigation canal system. Int. J. of Applied Mathematicsand Computer Science, 3(4), (2003), 453-468.
- [10] F. M. Callier and J. Winkin: Infinite dimensional system transfer functions. In Analysis and Optimization of Systems: State and Frequency Domain Approachesfor Infinite-Dimensional Systems, ser. Lecture Notes in Control and Information Sciences, C.R.F., A. Bensoussan, and J.L. Lions, Eds. Springer Berlin Heidelberg, 185 (1993), 75-101.
- [11] B. Chentouf and J.M. Wang: Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients. J. ofDifferential Equations, 246(3), (2009), 1119-1138.
- [12] P. D. Christofides and P. Daoutidis: Robust control of hyperbolic PDE systems. Chemical Engineering Science, 53(1), (1998), 85-105.
- [13] R. Curtain and K. Morris: Transfer functions of distributed parameters systems: A tutorial. Automatica, 45(5), (2009), 1101-1116.
- [14] J. Czeczot, M. Metzger And M. N. J. Babary: Monitoring and control of a class of distributed parameter bioreactors with application of the substrate consumption rate. Archives of Control Sciences, 11(1/2), (2001), 5-22.
- [15] C. C. Delnero, D. Dreisigmeyer, D. C. Hittle, P. M. Young, C. W. Anderson and M. L. Anderson: Exact solution to the governing PDE of a hot water-to-air finned tube cross-flow heat exchanger. HVAC&R Research, 10(1), (2004), 21-31.
- [16] A. Diagne, G. Bastin and J.-M. Coron: Lyapunov exponential stability of 1-d linear hyperbolic systems of balance laws. Automatica, 48(1), (2012), 109-114.
- [17] J. C. I. Dooge and J. J. Napiorkowski: The effect of the downstream boundary conditions in the linearized St Venant equations. The Quarterly J. of Mechanicsand Applied Mathematics, 40(2), (1987), 245-256.
- [18] V. Dos Santos, G. Bastin, J.-M. Coron and B. D’Andréa Novel: Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments. Automatica, 44(5), (2008), 1310-1318
- [19] L. C. Evans: Partial Differential Equations. Providence: American Mathematical Society, 1998.
- [20] J.C. Friedly: Dynamic Behaviour of Processes. New York: Prentice Hall, 1972.
- [21] K. Fujarewicz: Identification and suboptimal control of heat exchanger using generalized back propagation through time. Archives of Control Sciences, 10(3/4), (2001), 167-183.
- [22] H. Górecki, S. Fuksa, P. Grabowski and A. Korytowski: Analysis andSynthesis of Time Delay Systems. New York: Wiley, 1989.
- [23] D. D. Gvozdenac: Transient response of the parallel flow heat exchanger with finite wall capacitance. Archive of Applied Mechanics, 60 (1990), 481-490.
- [24] A. Kowalewski: Time-optimal control of infinite order hyperbolic systems with time delays. Int. J. of Applied Mathematics and Computer Science, 19 (2009), 597-608.
- [25] A. Kowalewski and A. Krakowiak: Optimal distributed control problems of retarded parabolic systems. Archives of Control Sciences, 19(3), (2009), 279-294.
- [26] J. Kukal and O. Schmidt: Useful approximation of discrete transcendent transfer function. Archives of Control Sciences, 17(1), (2007), 5-13.
- [27] A. Maidi, M. Diaf and J.-P. Corriou: Boundary control of a parallel-flow heat exchanger by input-output linearization. J. of Process Control, 20(10), (2010), 1161-1174.
- [28] R. M. M. Mattheij, S. W. Rienstra and J. H. M. Ten Thije Boonkkamp: Partial Differential Equations: modeling, analysis, computation. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 2005.
- [29] D. A. Spaulding: Synthesis of rational transfer function approximations using a tapped distributed RC line with feedback. The Bell System Technical J., 47(9), (1968), 2051-2070.
- [30] J. C. Sutherland and C. A. Kennedy: Improved boundary conditions for viscous, reacting, compressible flows. J. of Computational Physics, 191(2), (2003), 502-524.
- [31] P. Tatjewski: Advanced Control of Industrial Processes: Structures and Algorithms, ser. Advances in Industrial Control. Springer, 2007.
- [32] W. Wu and C.-T. Liou: Output regulation of two-time-scale hyperbolic PDE systems. J. of Process Control, 11(6), (2001), 637-647.
- [33] C.-Z. Xu and G. Sallet: Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control, Optimisationand Calculus of Variations, 7 (2002), 421-442.
- [34] A. Zavala-Rio, C.M. Astorga-Zaragoza and O. Hernández-Gonzá-Lez: Bounded positive control for double-pipe heat exchangers. Control EngineeringPractice, 17(1), (2009), 136-145.
- [35] H. Zwart: Transfer functions for infinite-dimensional systems. Systems and ControlLetters, 52(3-4), (2004), 247-255.
Uwagi
EN
Typ dokumentu
Bibliografia
Identyfikator YADDA
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