State‐Space Analysis and Control of Slow Transients in Pipes

Abstract

The incidence method, graph‐theoretically formulated using incidence matrices, is useful as a rigid water‐column model for analyzing slow transients in complex pipeline systems. This incidence method is enhanced by state‐space notation and combined with the control theory. It leads to a more comprehensive analysis of transients than do numerical computations of initial‐ and boundary‐value problems. The number of variables required in the incidence method is reduced to a minimum, i.e., state variables for describing behavior of the system. To constitute state variables, linearly dependent discharges of pipes are explicitly expressed by linearly independent ones, using one of the incidence submatrices. To determine usefulness of the state‐space method, adequate valve operations for smoothly controlled transients are predicted by associating the theory of discrete optimal regulator with the actual valve characteristics, such as the speed of valves and the adequate range of valve opening.