DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

STABILITY OF SOME MODELS OF CIRCULATING FUEL
NUCLEAR REACTORS—A LYAPUNOV APPROACH
SILVIU-IULIAN NICULESCU AND VLADIMIR RĂSVAN
The basic models in circulating fuel nuclear reactors are described by partial differential
equations (PDE): the transients define mixed initial boundary value problems for these
equations. According to a classical technique there are associated to such models some
functional differential equations (FDE) which, generally speaking, are of neutral type.
The paper considers these equations from the point of view of the stability of equilibria
which is studied via a suitably chosen Lyapunov functional, the stability conditions being
expressed through a frequency domain inequality.
Copyright © 2006 S.-I. Niculescu and V. Răsvan. This is an open access article distributed
under the Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
1. Introduction (state of the art)
Dynamics and stability for nuclear reactors have a relatively short history—about 50
years. Various models were considered and analyzed in hundreds of papers and dozens of
books. We cite here just one, the book of Goriačenko et al. [4] which is in fact the third
stage in an evolution marked by two other books of Goriačenko [2, 3], because of the
broad variety of models and long list of references going back to the very beginning of the
problem.
The circulating fuel reactor is somehow different than the other models since the neutron
kinetics is described by PDE hence the overall model displays distributed parameters
regardless the structure of the external feedback block. Only a rough simplification
replaces the PDE by FDE of delayed type [2, 3]. The case of this simplified model being
already considered [2] andsomeerrorscorrected[11], we will consider here the model
with distributed parameters. The paper is therefore organized as follows: starting from
the basic model described by PDE, it is presented its analysis and transformation in order
to obtain the stability analysis model. For this model, a Lyapunov-Krasovskii functional
is proposed and some stability inequalities are described. Finally, a comparison is
performed with other models and some open problems pointing to future research are
discussed.
Hindawi Publishing Corporation
Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 861–870