Réduction des systèmes à paramètres distribués. Application à la commande optimale robuste des canaux d'irrigation

Abstract : This work deals with the robust optimal control problem of open-channel hydraulic system.
Two approaches of this problem are developed. The first one is based on a reduced lumped
parameters model obtained through an orthogonal collocation method applied to the linearized
Saint-Venant model of the hydrodynamics within a reach. An optimal H2 control law is
designed to be robust to the reduction error with the help of a frequency loop shaping
approach. Using a loop transfer recovery technique, an observer is proposed to estimate the
state from the measured water levels and flows at the ends of the channel reach. The whole
control structure is then applied on various reference models as well as on an experimental
small canal. Results are compared with those obtained from classical control strategies. The
second approach is based on the semigroup theory for distributed parameter linear system. An
optimal control law which minimizes the same criterion is computed on the linearized partial
equations model. This infinite dimensional control law is then finally reduced using the same
basis functions as in the first approach. We present results related to the optimal boundary
control problem as exponential stabilizability and detectability and finally show the way to get
a finite dimensional approximation of the optimal control law using a discretization of the
associated operator-valued Riccati equation.
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Hicham Ouarit. Réduction des systèmes à paramètres distribués. Application à la commande optimale robuste des canaux d'irrigation. Automatique / Robotique. Institut National Polytechnique de Grenoble - INPG, 2004. Français. ⟨tel-00169967⟩

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