Novel consistent approach in controllability evaluations of point reactor kinetics models
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© 2019 Elsevier Ltd The controllability of linearized equations of the equivalent normalized version of the reactor point kinetics equations with six delayed neutron groups and without neutron source at an equilibrium power is analyzed. There exists inconsistency between the results from two kinds of approaches. The equations analyzed are controllable according to the controllability evaluation by analytical derivation while they are uncontrollable by numerical calculation. The reason of this inconsistency is that the large difference between the time effect of prompt neutrons and that of delayed neutrons in reactors reduces the controllability matrix to become a rank-deficient matrix under the conditions of using finite-precision arithmetic. In order to improve the analysis approach and address the divergence in outcomes, a novel definition of degree of controllability is proposed by means of applying matrix norm and singular value decomposition (SVD). This definition resolves the inconsistent conclusions, i.e., the equations analyzed are controllable but their degree of controllability is very low. The calculation of the degree of controllability shows that in the multiple representations of point reactor kinetics, the representations of few-group models are more propitious to analyze and design the control system of nuclear reactor than the representation of six-group model.
author list (cited authors)
Luan, X., & Tsvetkov, P. V.