LMI & BMI technics for the design of a PI control for irrigation channels

Mickael Rodrigues (1) , Yongxin Wu (1) , Samir Aberkane (2) , Valérie dos Santos (1)

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 CRAN - Centre de Recherche en Automatique de Nancy

This paper considers the problem of control design for a nonlinear distributed parameter system in infinite dimension which is described by hyperbolic Partial Differential Equations (PDEs) of de Saint-Venant. For describing the dynamic of this nonlinear system over a wide operating range, the Multi-Models approach, which takes into account Linear Time Invariant (LTI) models defined around a set of operating points, has been used. By means of an Internal Model Boundary Control (IMBC), a new design of Proportional Integral (PI) feedback is performed through BilinearMatrix Inequality (BMI) and Linear Matrix Inequality (LMI) technics. The new results have been simulated and also compared to the previous results, illustrating the new theoretical contribution.

Mots clés: LMI; PI Control; Irrigation Channels; Multi-Models

Domaines: Automatique / Robotique

Mickael Rodrigues, Yongxin Wu, Samir Aberkane, Valérie dos Santos. LMI & BMI technics for the design of a PI control for irrigation channels. 12th European Control Conference, ECC'13, Jul 2013, Zürich, Switzerland. pp.CDROM. ⟨hal-00823551⟩