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Finite-dimensional H∞ control of a parallel-flow heat exchange process

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Języki publikacji
EN
Abstrakty
EN
This paper is concerned with the H∞ control problem of a coupled transport-diffusion system with Neumann boundary condition, related to parallel-flow heat exchange process. It is shown that, by using the previous approach for a single diffusion system, the H∞ control problem can be solved by constructing a residual mode filter (RMF)-based controller which is of finite-dimension. A numerical simulation result is given to demonstrate the validity of the proposed method.
Rocznik
Strony
11--19
Opis fizyczny
Bibliogr. 27 poz., rys., wykr.
Twórcy
autor
  • Department of Applied Mathematics, Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-850, Japan
Bibliografia
  • [1] M.J. Balas, “Finite-dimensional controllers for linear distributed parameter systems: exponential stability using residual mode filters”, J. Math. Anal. Appl. 133, 283-296 (1988).
  • [2] P.D. Christofides and P. Daoutidis, “Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds”, J. Math. Anal. Appl. 216, 398-420 (1997).
  • [3] R.F. Curtain, “Finite dimensional compensators for parabolic distributed systems with unbounded control and observation”, SIAM J. Control Optim. 22, 255-276 (1984).
  • [4] R.F. Curtain and H.J. Zwart, An Introduction to InfiniteDimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, Springer-Verlag, New York, 1995.
  • [5] J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis, “State-space solutions to standard H2 and H∞ control problems”, IEEE Trans. Automat. Control AC-34, 831-847 (1989).
  • [6] S. Gümüşsoy and H. Özbay, “On the mixed sensitivity minimization for systems with infinitely many unstable modes”, Systems Control Lett. 53, 211‒216 (2004).
  • [7] G. Hagen and I. Mezić, “Spillover stabilization in finitedimensional control and observer design for dissipative evolution equations”, SIAM J. Control Optim. 42, 746-768 (2003).
  • [8] K. Ito, “Finite-dimensional compensators for infinitedimensional systems via Galerkin approximation”, SIAM J. Control Optim. 28, 1251-1269 (1990).
  • [9] K. Ito and K.A. Morris, “An approximation theory of solutions to operator Riccati equations for H∞ control”, Proc. the 33rd Conference on Decision and Control 3961-3966 (1994).
  • [10] B. van Keulen, H∞-Control for Distributed Parameter Systems: A State-Space Approach, Birkhaüser, Boston, 1993.
  • [11] M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs, SIAM, Philadelphia, 2008.
  • [12] C.H. Li, “Exact transient solutions of parallel-current transfer processes”, ASME J. Heat Transfer 108, 365-369 (1986).
  • [13] W.-Y. Lu and J.-H. Chen, “Observability of the two-stream parallel- flow heat exchanger equation”, IMA J. Math. Control Inf. 27, 91-102 (2010).
  • [14] A. Maidi, M. Diaf, and J.-P. Corriou, “Boundary control of a parallel-flow heat exchanger by input-output linearization”, J. Process Control 20, 1161-1174 (2010).
  • [15] L. Malinowski and J.-H. Chen, “Analytical solutions of the equations for the transient temperature field in the three-fluid parallel- channel heat exchanger with three thermal communications”, Int. J. Heat Mass Transfer 96, 164-170 (2016).
  • [16] K.A. Morris, “H∞-output feedback of infinite-dimensional systems via approximation”, Systems Control Lett. 44, 211‒217 (2001).
  • [17] T. Nambu, “On stabilization of partial differential equations of parabolic type: boundary observation and feedback”, Funkcialaj Ekvacioj, Serio Internacia 28, 267-298 (1985).
  • [18] Y.V. Orlov and L.T. Aguilar, Advanced H∞ Control: Towards Nonsmooth Theory and Applications, Birkhäuser, New York, 2014.
  • [19] S. Pohjolainen and I. Lätti, “Robust controllers for boundary control systems”, Int. J. Control 38, 1189-1197 (1983).
  • [20] Y. Sakawa, “Feedback stabilization of linear diffusion systems”, SIAM J. Control Optim. 21, 667-676 (1983).
  • [21] H. Sano and N. Kunimatsu, “An application of inertial manifold theory to boundary stabilization of semilinear diffusion systems”, J. Math. Anal. Appl. 196, 18-42 (1995).
  • [22] H. Sano and Y. Sakawa, “H∞ control of diffusion systems by using a finite-dimensional controller”, SIAM J. Control Optim. 37, 409-428 (1999).
  • [23] H. Sano, “On reachability of parallel-flow heat exchanger equations with boundary inputs”, Proc. Japan Acad. 83, Ser. A, No. 1, 1-4 (2007).
  • [24] H. Sano and S. Nakagiri, “Stabilization of a coupled transportdiffusion system with boundary input”, J. Math. Anal. Appl. 363, 57-72 (2010).
  • [25] H. Sano, “H∞ control of a parallel-flow heat exchange process”, Proc. CAO’2015 the 16th IFAC Workshop on Control Applications of Optimization 50-55 (2015).
  • [26] J.M. Schumacher, “A direct approach to compensator design for distributed parameter systems”, SIAM J. Control Optim. 21, 823-836 (1983).
  • [27] Hemisphere Handbook of Heat Exchanger Design, ed. by G.F. Hewitt, Hemisphere Pub. Corp., New York, 1990.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c09532fa-4bc0-4258-a34b-0c3cc0243c99
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