Design of a PI Control using Operator Theory for the nonlinear de Saint-Venant equations: Some numerical extension

Valérie dos Santos Martins (1) , Mickael Rodrigues (1)

1 LAGEP - Laboratoire d'automatique et de génie des procédés

— This paper considers the control design of a nonlinear distributed parameter system in infinite dimension, described by the hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. The nonlinear system dynamic is formulated by a Multi-Models approach over a wide operating range, where each local model is defined around a set of operating regimes. A Proportional Integral (PI) feedback was designed and performed through Bilinear Operator Inequality (BOI) and Linear Operator Inequality (LOI) techniques for infinite dimensional systems. The authors propose in this paper to improve the numerical part by introducing weight µi not only equal to {0,1}, but µi ∈ [0, 1].

Mots clés: EDP de Saint-Venant; PI Control; LMI approach; Stability

Domaines: Automatique / Robotique; Automatique

Valérie dos Santos Martins, Mickael Rodrigues. Design of a PI Control using Operator Theory for the nonlinear de Saint-Venant equations: Some numerical extension. 2015 SIAM Conference on Control and Its Applications, Jul 2015, PARIS, France. ⟨hal-01177070⟩