Estimation and control of space - dependent reactor cores via observer - based control theory

Abstract

In this thesis modern control theory is applied to control of a nuclear reactor described as a distributed-parameter system: It concerns mainly with the infinite-dimensional observer theory and the finite-dimensional compensator theory. The first half of the thesis describes a dynamic estimation method for reconstructing the measurable and unmeasurable state variables in a nuclear reactor from output measurement data, which can be used to generate input of a feedback control system and can be also served as a core estimator of a reactor in transient. The method is based on the Luenberger-type observer theory that is extended to infinite-dimensional systems (distributed-parameter systems). The infinite-dimensional observer theory is described from a theoretical point of view. The concept of strategic sensors is introduced and a theorem that provides a relationship between the construction of an observer and the structure of sensors is given. If the properties of the eigenvalues and eignenfunctions of the spatial operator are known, the modal decomposition of the state spaces enables us to use the pole assignment algorithms developed in finite-dimensional systems to obtain the stabilizing observer gain. This allows us to estimate or reconstruct the states of a transient reactor using only a few output measurement data and arbitrary initial conditions. The dynamic estimation method is applied to several reactor model problems: estimation of flux with and without precursor or xenon-iodine distributions using flux measurement by a finite number of sensors. Three reactor models considered are: i) a time-dependent one-group neutron diffusion equation with and ii) without precursor dynamics, and iii) with xenon dynamics in their linearized forms which exhibited spatial power oscillations. The observer designed is tested by using the model-based data through numerical simulations. The results show that the spatial distributions of the state variables, i.e., neutron flux...