Expansion methods for finding nonlinear stability domains of nuclear reactor models

Abstract

Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are described in this paper: Method A based on expansion of a Lyapunov function and Method B based on expansion of any positive definite function. The methods are established on the stability definitions of Lyapunov itself. Method A provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most reactor systems are stiff. Method B requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for reactor systems that are stiff. These methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared.