Modeling and Optimization of Control Processes for Compressible Liquid Flow in Pipeline Systems

Abstract Modeling and optimization of control processes for compressible fluid flow in pipeline systems are considered. A mathematical model of controlled elements with distributed parameters is proposed to describe the dynamical behavior of a long rigid tube with transported liquid supplied by a control pump. Functions describing effective displacements and linear approximations of fluidic resistances are used to reduce the original initial-boundary value problem to a variational formulation on the basis of the method of integrodifferential relations. Moreover, this approach makes use of a novel finite element technique. Optimal control procedures are derived for changing either the outlet pressure or the mass flow to desired operating points and to damp undesirable elastic oscillations at the end of the control process. A projection approach is implemented on the basis of a modification of the Galerkin method in combination with the semi-discretization of unknown functions over the spatial coordinate. This procedure is applied to reliable numerical modeling of a simple pipeline system and to the design of an efficient control procedure. Numerical results obtained for different system parameters and control objectives are analyzed and discussed.