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

Open access


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.

[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.

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 95 95 13
PDF Downloads 16 16 4