Optimal Xenon Control in Heterogeneous Reactors

A two-group diffusion-theory heterogeneous reactor model in two-dimensional plane geometry is developed for optimal control analysis with xenon and samarium feedback. The resulting system equations are linearized around an equilibrium operating point, which is determined with the steady-state form of the original nonlinear system equations. A poisonless criticality analysis is also carried out to determine the optimal spacing between the fuel rods and to see the effect of including the control rods. The problem of optimally controlling xenon-induced spatial flux oscillations is then formulated as a linear-regulator problem of optimal control theory. A numerical example for a graphite-moderated reactor illustrates the theoretical analysis.