State Space Analysis using Incidence-matrix-based Rigid Water Column Model of Analyzing Slow Transients in Pipelines

Abstract

The incidence-matrix-based rigid water column model dealing with slow transients in pipelines is a lumped model described by ordinary differential equations of the first order (ODE). Therefore, the model has great possibility in analyzing hydraulic pipeline systems through application of the control theory in state space. Since the variables employed in the ODE are not the state variables (the minimum ones), it is impossible to carry out state-space analysis. This paper presents a theory for deriving the state variables and state equations in the incidence-matrix-based model. The state variables and state equations can be automatically determined with a computer for not only arborescence pipeline systems but network ones as well.