Control-Oriented Modeling of Fluid Networks: A Time-Delay Approach

Abstract

Fluid networks are characterized by complex interconnected flows, involving high order nonlinear dynamics and transport phenomena. Classical lumped models typically capture the interconnections and nonlinear effects but ignore the transport phenomena, which may strongly affect the transient response. To control such flows with regulators of reduced complexity, we improve a classical lumped model (obtained by combining Kirchhoff's laws and graph theory) by introducing the effect of advection as a time delay. The model is based on the isothermal Euler equations to describe the dynamics of the fluid through the pipe. The resulting hyperbolic system of partial differential equations (PDEs) is diagonalized using Riemann invariants to find a solution in terms of delayed equations, obtained analytically using the method of the characteristics. Conservation principles are applied at the nodes of the network to describe the dynamics as a set of (possibly non linear) delay differential equations. Both linearized and nonlinear Euler equations are considered.

Investigation of the Ripa Model via NHRS Scheme with Its Wide-Ranging Applications

“…We consider the Ripa model with the discontinuous topography with the following initial conditions: (25,10,5,3)…”

“…There are many studies of conservation laws in which the velocity depends nonlocally on the solution, not in real time but in a time-delayed manner [9]. A time-delay system for fluid flow networks was developed by the authors of [10], which resulted in a traditional state-space representation with delays to take network transport phenomena into consideration. The authors in [10] considered analytical and numerical features of the Lighthill-Whitham-Richards traffic flow model though time delay.…”

Physical Modeling and Structural Properties of Small-Scale Mine Ventilation Networks

“…With a different perspective, the 1D pressure transport phenomena (advection and sink) is approximated by a ordinary differential equation with time-delay in [9,10] to be used as reference model in the controller design of the large advective flows appearing in the mining ventilation problem. The relationship between hyperbolic conservation laws in fluid networks and time-delay systems is further studied in [11].…”