Systematic flow graph analysis and applications



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A generalized technique for the solution of engineering problems which can be represented in the form of flow graphs has been developed. The fundamental algorithm is one whereby the paths and loops in a flow graph can be systematically and selectively enumerated. This algorithm serves as the basis for a procedure whereby Mason's rule can be efficiently applied to generate characteristic equations, system determinants, transfer functions defining input-output relationships, sensitivity functions, and other important network functions related to signal flow graphs. The theory developed provides the basis for a comprehensive computing system which is instrumental in solving many types of flow graph problems. The value of flow graph analysis in engineering science, and the diversified utility of the techniques developed herein are illustrated by six example problems: sensitivity analysis of a heat exchanger network, simulation and analysis of a chemical reactor control system, generation of closed-form expressions describing the steadystate performance of an absorption column, ordering of recycle calculations for a chemical process simulation, computation of eigenvalues, and the solution of a typical transportation problem.