Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Results of the impulse response analysis for a class of dynamical systems, described by two weakly coupled linear partial differential equations of hyperbolic type, defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs of the Dirichlet type, the analytical expressions for the impulse response functions are derived based on the inverse Laplace trans form of the 2×2 transfer function matrix of the system. The influence of the boundary inputs configuration on the impulse response functions is demonstrated. The considerations are illustrated with a practical example of a thin-walled double-pipe heat exchanger operating in parallel- and countercurrent-flow modes, which correspond to the analyzed boundary conditions.
Czasopismo
Rocznik
Tom
Strony
327--355
Opis fizyczny
Bibliogr. 42 poz., rys.
Twórcy
autor
- Institute of Control and Computer Engineering Opole University of Technology ul. Sosnkowskiego 31, 45-272 Opole, Poland
Bibliografia
- [1] Ancona, F. and Coclite, G. M. (2005) On the boundary controllability of first-order hyperbolic systems. Nonlinear Analysis: Theory, Methods & Applications, 63(5-7), e1955–e1966.
- [2] Bagui, F., Abdelghani-Idrissi, M.A. and Chafouk, H. (2004) Heat exchanger Kalman filtering with process dynamic acknowledgement. Computers & Chemical Engineering, 28(8), 1465–1473.
- [3] Baranowski, J. and Mitkowski, W. (2012) Stabilisation of LC ladder network with the help of delayed output feedback. Control and Cybernetics, 41(1), 13–34.
- [4] Bartecki, K. (2009) Frequency- and time-domain analysis of a simple pipeline system. In: Proceedings of the 14th IEEE IFAC International Conference on Methods and Models in Automation and Robotics. IFAC, www.ifacpapersonline.net/Detailed/41106.html, 366–371.
- [5] Bartecki, K. (2013a) Computation of transfer function matrices for 2×2 strongly coupled hyperbolic systems of balance laws. In: Proceedings of the 2nd Conference on Control and Fault-Tolerant Systems. IEEE, http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6693813,578– 583.
- [6] Bartecki, K. (2013b) A general transfer function representation for a class of hyperbolic distributed parameter systems. International Journal of Applied Mathematics and Computer Science, 23(2), 291–307.
- [7] Bartecki, K. (2013c) Steady-state analysis for a class of hyperbolic systems with boundary inputs. Archives of Control Sciences, 23(3), 295–310.
- [8] Bartecki, K. (2015) Transfer function–based analysis of the frequency-domain properties of a double pipe heat exchanger. Heat and Mass Transfer, 51(2), 277–287.
- [9] Bonelli, S. and Radzicki, K. (2008) Impulse response function analysis of pore pressures in earthdams. European Journal of Environmental and Civil Engineering, 12(3), 243–262.
- [10] Bounit, H. (2003) The stability of an irrigation canal system. International Journal of Applied Mathematics and Computer Science, 13(4), 453–468.
- [11] Bressan, A. (1999) Hyperbolic systems of conservation laws. Revista Matemática Complutense, 12(1), 135–200.
- [12] Callier, F. M. and Winkin, J. (1993) Infinite dimensional system transfer functions. In: Curtain, Bensoussan, Lions, (eds), Analysis and Optimization of Systems: State and Frequency Domain Approaches for InfiniteDimensional Systems. Lecture Notes in Control and Information Sciences, 185. Springer, Berlin – Heidelberg.
- [13] Chentouf, B. and Wang, J. M. (2009) Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients. Journal of Differential Equations, 246(3), 1119–1138.
- [14] Curtain, R. and Morris, K. (2009) Transfer functions of distributed parameters systems: A tutorial. Automatica, 45(5), 1101–1116.
- [15] Dafermos, C. M. (2010) Hyperbolic Conservation Laws in Continuum Physics. Comprehensive Studies in Mathematics. Springer, Berlin – Heidelberg.
- [16] Diagne, A., Bastin, G. and Coron, J.-M. (2012) Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws. Automatica, 48(1), 109–114.
- [17] Dooge, J. C. I. and Napiorkowski, J. J. (1987) The Effect of the Downstream Boundary Conditions in the Linearized St Venant Equations. The Quarterly Journal of Mechanics and Applied Mathematics, 40(2), 245–256.
- [18] Evans, L. C. (1998) Partial Differential Equations. American Mathematical Society, Providence, USA.
- [19] Friedly, J. C. (1975) Dynamic Behaviour of Processes (Polish edition). Wydawnictwa Naukowo-Techniczne, Warszawa.
- [20] Grabowski, P. (2007) Stability of a heat exchanger feedback control system using the circle criterion. International Journal of Control, 80(9), 1388–1403.
- [21] Guo, L.Z., Billings, S. A. and Coca, D. (2010) Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems. International Journal of Control, 83(1), 40–48.
- [22] Gvozdenac, D. D. (1990) Transient response of the parallel flow heat exchanger with finite wall capacitance. Archive of Applied Mechanics, 60(7), 481–490.
- [23] Jacob, B. and Zwart, H. J. (2012) Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces. Operator Theory: Advances and Applications, 223. Springer, Basel.
- [24] Jaswon, M.A. (1954) Countercurrent transfer processes in the non-steady state. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 225(1161), 226–244.
- [25] Kociecki, A. (2010) A Prior for Impulse Responses in Bayesian Structural VAR Models. Journal of Business & Economic Statistics, 28(1), 115–127.
- [26] Lasiecka, I. and Triggiani, R. (2008) Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation. Control and Cybernetics, 37(4), 935–969.
- [27] Lax, P. and Wendroff, B. (1960) Systems of Conservation Laws. Communications on Pure and Applied Mathematics, 13(2), 217–237.
- [28] Lee, P. J., Vítkovský, J. P., Lambert, M. F., Simpson, A. R. and Liggett, J. (2007) Leak location in pipelines using the impulse response function. Journal of Hydraulic Research, 45(5), 643–652.
- [29] LeFloch, P. G. (2002) Hyperbolic Systems of Conservation Laws. Birkhäuser, Basel.
- [30] Li, H.-X. and Qi, C. (2010) Modeling of distributed parameter systems for applications – A synthesized review from time-space separation. Journal of Process Control, 20(8), 891–901.
- [31] Litrico, X. and Fromion, V. (2009) Modeling and Control of Hydrosystems. Springer, London. Maidi, A., Diaf, M. and Corriou, J.-P. (2010) Boundary control of a parallel-flow heat exchanger by input–output linearization. Journal of Process Control, 20(10), 1161–1174.
- [32] Mattheij, R. M. M., Rienstra, S. W. and ten Thije Boonkkamp, J. H. M. (2005) Partial Differential Equations: modeling, analysis, computation. Society for Industrial and Applied Mathematics, (SIAM), Philadelphia.
- [33] Mitkowski, W. (2014) Finite-dimensional approximations of distributed RC networks. Bulletin of the Polish Academy of Sciences: Technical Sciences, 62(2), 263–269.
- [34] Murawski, K. and Lee, D. (2012) Godunov-type algorithms for numerical modeling of solar plasma. Control and Cybernetics, 41(1), 35–56.
- [35] Polyanin, A. D. and Manzhirov, A. V. (1998) Handbook of Integral Equations. CRC Press, Boca Raton. Rabenstein, R. (1999) Transfer function models for multidimensional systems with bounded spatial domains. Mathematical and Computer Modelling of Dynamical Systems, 5(3), 259–278.
- [36] Strupczewski, W. and Kundzewicz, Z. (1979) On a method of determination of parameters of conceptual models of open channel flow. Control and Cybernetics, 8(4), 281–295.
- [37] Uciński, D. (2012) Sensor network scheduling for identification of spatially distributed processes. International Journal of Applied Mathematics and Computer Science, 22, 25–40.
- [38] Wang, B.-Z., Wang, X.-H. and Hong, J.-S. (2005) On the Generalized Transmission-Line Theory. Journal of Electromagnetic Waves and Applications, 19(3), 413–425.
- [39] Wu, Ch., Yang, F., Zhou, J. and Ouyang, H. (2012) An Improved QuasiAnalytic Method for Direct Impulse Response Analysis of an Offset Reflector. Electromagnetics, 32(7), 375–388.
- [40] Xu, C.-Z. and Sallet, G. (2002) Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems. ESAIM: Control, Optimisation and Calculus of Variations, 7, 421–442.
- [41] Ziółko, M. (2000) Modeling of wave phenomena (in Polish). Poland: AGH University of Science and Technology Press, Kraków.
- [42] Zwart, H. (2004) Transfer functions for infinite-dimensional systems. Systems and Control Letters, 52(3-4), 247–255.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d5f69e1c-2ceb-4bbb-a463-ad23e92ae56a