Port-Based modelling for open channel irrigation systems
Résumé
A port-based model for the water flow and level dynamics in open channel systems is derived. It is structured into dissipative and conservative sub-systems related through a symplectic geometric structure which expresses instantaneous power conservation. This model is equivalent to the classical Saint-Venant equations (nonlinear PDEs also called shallow water equations) but trivially exhibits some interesting properties (passivity, stability, stored energy, entropy production) which may be useful for analysis or control purposes. The use of a geometric reduction leads to a reduced port-controlled hamiltonian (PCH) system. A Comparison between simulation results and experimental ones, obtained on an experimental micro-channel, demonstrates the effectiveness of the reduced model.