Multidimensional Effects in Optimal Control Calculations for Time-Dependent Nuclear Systems
Physically realistic step function control rod models are shown to be unsolvable under traditional formulations of distributed parameter optimal control theory. Extensions to the theory are proposed, and the method of reduced dimensional control is derived to allow systems of this type to be analyzed using generalized optimality conditions. Distributed parameter optimal control is shown to be a special case of this theory. Reduced dimensional control is shown to be adequate for the analysis of most optimality problems where there are differences in the number of dimensions on which the state variables are defined. The method is then applied to a xenon-iodine oscillation problem in two dimensions. A step function control rod model is examined and compared with an axially homogeneous model. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The optimality and normalization conditions are solved numerically for a severe xenon transient. Differences are noted between the cases which can be directly attributed to the proper axial modeling of the control rod.
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations
University of Illinois at Urbana-Champaign