INTERNAL MODEL BOUNDARY CONTROL OF HYPERBOLIC SYSTEM : APPLICATION TO THE REGULATION OF CHANNELS

V Dos Santos (1) , Youssoufi Touré (1)

1 LVR - Laboratoire Vision et Robotique

This paper deals with the regulation problem of irrigation channels using a particular form of control by internal model (IMC). 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 spatial dependency of the operator parameters 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. In this paper previous stability results are generalized using perturbation theory in infinite dimensional Hilbert space, including more general hyperbolic systems and sufficient conditions for the closed loop stability are given explicitely by the spectrum calculation e.g.. Simulation and experimental results from Valence experimental micro-channel show that this approach shoud be suitable for more realistic situations.

Mots clés: Shallow water equations; infinite dimensional perturbation theory; stabilization; multivariable internal model boundary control; hyperbolic PDE

Domaines: Automatique; Automatique / Robotique

V Dos Santos, Youssoufi Touré. INTERNAL MODEL BOUNDARY CONTROL OF HYPERBOLIC SYSTEM : APPLICATION TO THE REGULATION OF CHANNELS. 7th Portuguese Conference on Automatic Control (CONTROLO’2006), Sep 2006, Lisbonne, Portugal. ⟨hal-02025566⟩