Wave motion stability for coupled canal pool-AMIL gate systems

Concerns an irrigation canal with hydromechanic AMIL gates. This gate is used for proportional control of local upstream water level. The gates are associated with upstream water distribution. The stability was studied on a coupled canal pool-AMIL gate subsystem, then on two coupled subsystems. A type turnout perturbation is supposed to be in the upstream side close to the gate. The dimensionless St Venant equations are linearized around a normal steady flow. By Laplace transform, a feasible system is established. By integration, the distributed parameter system was obtained. It represents the canal pool dynamics. The gate dynamics is supposed as succession of steady states. The transcendent transfer function is established by coupling the pool dynamics representation and the linearized discharge equation of the gate. The resulting stability condition depends on dimensionless numbers and the linearization parameters of the discharge equation. In the first case, a sufficient and necessary condition for unconditional stability is found. In the second case, a sufficient condition is found. We propose an easy-use stability sufficient condition for coupled subsystems. A general method was used in order to study the wave motion stability for simple and coupled subsystems. This method can be directly applied when studying the stability problems of all canal pool-motorized hydraulic structure (controller) system. Obtained conditions can be used like design norms of irrigation canals.