The Controllability of the Point Reactor Neutron Kinetics Equations

In this paper, the conditions to ensure the controllability of the point reactor neutron kinetics equations are studied. In a nuclear reactor, due to the delayed neutron precursor concentration and the internal reactivity, the kinetics equations of the nuclear reactor are nonlinear. To solve the problem of the pole placement, the controllability of the point kinetics equations must be guaranteed. Then, a new method to analysis of the controllability conditions of the point kinetics equations of a reactor is carried out here. The method is based on the controllability matrix directly denoted by relevant symbols, and a formula used for controllability analysis is showed with symbols by calculating the determinant of the matrix. First, with using the linearization technique, the equations are linearized with respect to any possible equilibrium point. Subsequently, an analysis of the controllability of the general linear model that includes only one group delayed neutron precursor is performed, obtaining the interesting result that the controllability of the equations are controllable except when the effective precursor radioactive decay constant and the reciprocal of the fuel-to-coolant heat transfer mean time have the same value, which does not occur in practice. Thus, with the same method, the other analysis obtained the conditions to guarantee the controllability of the point kinetics equations with different groups delayed neutron precursor, which includes two-group, three-group and six-group models. Then, the results are compared with that of the numerical controllability matrix, obtaining the final conclusion that the results of the new analysis method give the closer results to the actual situation and list the restrictions that guarantee the controllability of the point reactor neutron kinetics equations.