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IMA Journal of Mathematical Control and Information Advance Access originally published online on June 28, 2006
IMA Journal of Mathematical Control and Information 2007 24(1):137-147; doi:10.1093/imamci/dnl016
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Observability and reachability for parallel-flow heat exchanger equations

Hideki Sano**

Computing and Communications Center, Kagoshima University, 1-21-35 Korimoto, Kagoshima 890-0065, Japan

** Email: sano{at}cc.kagoshima-u.ac.jp


  Abstract

This paper is concerned with the dynamical analysis of parallel-flow heat exchanger equations with observation at the outlet of tube/control at the inlet of tube. The parallel-flow heat exchanger equation is super-stable under zero boundary condition. The system can be described by an unbounded operator of lower triangular form through a variable transformation. By calculating a C0-semigroup generated by the operator, it is shown that the system is observable if both fluid temperatures are measured at the outlet, and that the system is observable with respect to the non-negative cone of the state space if either of them is measured at the outlet. Moreover, it is shown that the system is reachable if both fluid temperatures are controlled at the inlet, and that the system is reachable with respect to the non-negative cone of the state space if either of them is controlled at the inlet.

Keywords: parallel-flow heat exchanger equation; C0-semigroup; observability; reachability.

Received on 4 October 2005. Accepted on 25 April 2006.


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