Irrigation Multireaches Regulation Problem by Internal Model Boundary Control

This paper deals with the regulation problem of irrigation canals and the multireaches case is considered. The control problem is stated as a boundary control of hyperbolic Saint-Venant Partial Differential Equations (pde). Regulation is done around an equilibrium state and the operator parameters spatial dependency is taken into account in the linearized model. The Internal Model Boundary Control (IMBC) used in a direct approach allows to make a control parameters synthesis by semigroup conservation properties, like the exponential stability. In this paper sufficient conditions are given more explicitely by the resolvent calculation using perturbations theory, in infinite dimensional Hilbert space, so the results can be used for more general hyperbolic systems. Simulation and experimental results from Valence experimental micro-channel show that this approach shoud be suitable for more realistic situations.