Optimal Feedback Control of Spatial Xenon Oscillations in a Nuclear Reactor

Citation

Wiberg, Donald Martin (1965) Optimal Feedback Control of Spatial Xenon Oscillations in a Nuclear Reactor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KFA4-3K71. https://resolver.caltech.edu/CaltechETD:etd-01222004-113136

Abstract

A kinetic model of spatial processes in a nuclear power reactor is formulated according to the state space approach. The model is very general, and may include the spatial effects of control rods, temperature, and almost any other deterministic spatial process that can be described by a finite set of partial differential equations. It is noted that any locally unstable process may induce a spatial instability, and that a spatial instability will occur only if a local process is unstable. The concept of a temperature coefficient of reactivity is extended to include spatial variations. A linearization about an operating point is performed, and the resulting linear equations are solved by using a non-interacting modal expansion. Some properties of this type of mode and applications to other physical processes are discussed. It is shown that non-interacting modes exist whenever any other modal expansion exists. An efficient computational procedure for exact numerical solution for the non-interacting modes is given in the case of spatial separability. Simple linear stability estimates for spatial processes are formed by variational techniques which permit evaluation of the effects of spatially varying parameters upon stability. A theorem presents mathematical proof of the linear controllability of any finite number of modes by very few control rods. The circumstances under which an infinite number of modes can be controlled are discussed. Finally, methods of optimal feedback control are used for the analytical design of a spatial control system for minimum integrated quadratic loss, and detailed examples are given.

Thesis Files