Simplified Modeling of Irrigation Canals for Controller Design

Linear parameter varying modeling and identification for real-time control of open-flow irrigation canals

“…They are large distributed parameter systems described by Saint-Venant's partial-differential equations (Chow, 1959) (Litrico, 2004) which are nonlinear partial derivative hyperbolic equations (distributed model). There is no known analytical solution in real geometry and these equations have to be solved numerically.…”

“…Such models would allow handling the dynamics of the system with few parameters; understanding the impact of physical parameters on the dynamics; and facilitating the development of a systematic design method (Litrico 2004). Then, for control purposes, the used models should be precise but simpler.…”

“…This is the case of the models as the integrator delay (ID) model (Schuurmans. 1999); the Hayami model (Litrico, 1999); the Muskingum model (Gomez, 2002); the integrator delay zero (IDZ) model (Litrico, 2004) that extends the ID model by adding a zero in the high frequencies range leading to a better fit in high frequencies and increasing the accuracy of the time-domain simulations; or black-box models identified using parameter estimation (Weyer, 2001) (Euren and Weyer 2007).…”

“…As a result, a gray-box modeling approach for obtaining an LPV canal control model based on the IDZ model (Litrico, 2004) is introduced. The IDZ model is nowadays a widely accepted model in the canal control community that has been rigorously derived by approximating the Saint-Venant's equations around a given operating point.…”

Gray-Box Model of Inland Navigation Channel: Application to the Cuinchy–Fontinettes Reach

“…Consider two points along the canal, separated by a distance D: upstream and downstream points. According to (21), the theoretical value of the upstream time delay between these two points is evaluated by computing the integral:…”