Control of input-output contact systems.

Héctor Ramirez Estay (1) , Bernhard Maschke (2) , Daniel Sbarbaro (3)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 LAGEP - Laboratoire d'automatique et de génie des procédés
3 DIE - Departamento de Ingenieria Eléctrica

Control input-output contact systems are the representation of open irreversible Thermodynamic systems whose geometric structure is defined by Gibbs' relation. These systems are called conservative if furthermore they leave invariant a particular Legendre submanifold defining their thermodynamic properties. In this paper we address the stabilization of controlled input-output contact systems. Firstly it is shown that it is not possible to achieve stability on the complete Thermodynamic Phase Space. As a consequence, the stabilization is addressed on some invariant Legendre submanifold of the closed-loop system. For structure preserving feedback of input-output contact systems, i.e., for the class of feedback that renders the closedloop system again a contact system, the closed-loop invariant Legendre submanifolds have been characterized. The stability of the closed-loop system has then been proved using Lyapunov's second method. The results are illustrated on the classical thermodynamic process of heat transfer between two compartments and an exterior control.

Domaines: Micro et nanotechnologies/Microélectronique

Héctor Ramirez Estay, Bernhard Maschke, Daniel Sbarbaro. Control of input-output contact systems.. IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, TFMST'13., Jan 2013, France. pp.1-6. ⟨hal-00872230⟩