Multinode Reactor Stability and Optimal Estimates of Domains of Attraction

A multinode treatment of the problem of nonlinear reactor stability is given. The nodal kinetics equations account for nodal powers, precursor concentrations, and temperatures. Nonlinear power-plus-temperature feedbacks are admitted in each node. Quadratic and logarithmic Lyapunov functions are considered. By formulating and solving a suitable nonlinear programming problem, the optimal estimate of the domain of attraction of the reactor-operating equilibrium state that can be afforded by the aforesaid V functions is explicitly constructed. An example of a reactor with two nodal power feedbacks (one destabilizing) and two destabilizing nodal temperature feedbacks is given. These feedbacks are seen to give rise to an unstable equilibrium reactor state, in the region of all-positive perturbations, which is extremely well approached by the boundary of the estimate of the domain of attraction.