Modeling and control of flow with dynamical boundary actions

In this paper a flow inside a pipe is modeled by a hyperbolic system (written in terms of a partial differential equation). One boundary condition is given by the coupling with a finite-dimensional dynamic model of heating column and a static modeling of ventilator. Then, the classical finite-dimensional technique is applied for the linearization of first order hyperbolic systems with dynamics associated to the boundary conditions. The discretization of the infinite-dimensional system is used and an augmented discrete linear system with dimension depending on the step size of discretization in space is obtained. The results are illustrated on simulations considering a Poiseuille flow experimental setup.