Optimal control of xenon concentration in a nuclear reactor via observer design

Abstract

The optimal control of xenon concentration in a nuclear reactor is posed as a linear quadratic regulator problem with state feedback control. The reactor kinetics system considered is a one-energy group point reactor model with reactivity feedbacks such as xenon absorption, fuel and coolant temperature effects. Since it is not possible to measure the state variables such as xenon and iodine concentrations directly, implementation of the optimal state feedback control law requires estimation of the unmeasurable state variables. The estimation method used is based on the Luenberger observer. The set of the reactor kinetics equations is a stiff system. This singularly perturbed system arises form the interaction of slow dynamic modes (iodine and xenon concentrations) and fast dynamic modes(neutron flux, fuel and coolant temperatures). The singular pertubation technique is used to overcome this stiffness problem. The singular perturbation method allows mode separation of the original stiff system into the slow reduced subsystem and the fast subsystem in different time scales. The observer-based controller of the original system is effected by separate design of the observer and controller of the reduced subsystem and the fast subsystem. In particular, since in the reactor kinetics control problem analyzed in the study the fast mode dies out quickly (i.e., $A_{22}$ is uniformly asymptotically stable), we need only design the observer for the reduced slow subsystem. The results of the test problems demonstrated that the state feedback control of the xenon oscillation can be accomplished efficiently and without sacrificing accuracy by using the observer combined with the singular perturbation method.