Signal-Flow Graphs and Stability Analysis of Nuclear Reactors

Signal-flow graphs have long been exploited in feedback-control analysis, and can greatly aid in kinetic studies of nuclear reactors and nuclear reactor systems. The signal-flow graph is a means for conveniently and compactly displaying a set of linear differential equations. Such a flow graph can be easily and quickly formulated from a set of equations, or, with experience, directly by inspection from the physical system. A powerful method developed by S. J. Mason permits rapid determination of the transfer function between any two points in the system. The above techniques are illustrated for an elementary nuclear reactor. The usual transfer function is quickly obtained, as is also the transfer function for a reactor operating in a sub-or supercritical condition. Other methods of reactor control suggested by the analysis are discussed.