Design of a PI Control using Operator Theory for Infinite Dimensional Hyperbolic Systems

Valérie dos Santos (1) , Yongxin Wu (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 new Proportional Integral (PI) feedback is designed and performed through Bilinear Operator Inequality (BOI) and Linear Operator Inequality (LOI) techniques for infinite dimensional systems. The new results have been simulated and also compared to previous results in finite and infinite dimension, in order to illustrate the new theoretical contribution.

Mots clés: semigroup theory; partial differential equations (PDEs); multimodels; De Saint-Venant equations; internal model boundary control (IMBC)

Domaines: Automatique / Robotique; Automatique

Valérie dos Santos, Yongxin Wu, Mickael Rodrigues. Design of a PI Control using Operator Theory for Infinite Dimensional Hyperbolic Systems. IEEE Transactions on Control Systems Technology, 2014, 22 (5), pp.2024 - 2030. ⟨10.1109/TCST.2014.2299407⟩. ⟨hal-00936398⟩