Some Properties of Conservative Port Contact Systems

Favache, Audrey; Martins, V.S. dos Santos; Dochain, Denis; Maschke, Bernhard

doi:10.1109/tac.2009.2028973

Cited by 44 publications

(37 citation statements)

References 21 publications

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“…Several other examples, concerning also the generalization to open systems (called control contact systems) can be found in [28] and also in subsequent works, e.g., [29][30][31][32][33][34]. Further (and different) approaches to the use of contact Hamiltonian dynamics in irreversible thermodynamics can be found in [12,15,16,[35][36][37].…”

Section: The Work Of Eberard Maschke and Van Der Schaft On Conservatmentioning

confidence: 99%

Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti

2017

Entropy

130

100

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Section: The Work Of Eberard Maschke and Van Der Schaft On Conservatmentioning

confidence: 99%

Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti

2017

Entropy

130

100

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“…Controlled contact systems are defined on the Thermodynamic Phase Space consisting of n + 1 extensive variables and n intensive variables and endowed with a contact structure associated with Gibbs' relation defining the thermodynamic properties of the system. On the Thermodynamic Phase Space, one may then define controlled contact systems which are the analogue of control Hamiltonian systems and have been introduced in [1] and further developed in [2,9,8]. After the introductory example of a 2-compartment heat exchange system we shall recall the precise definitions needed in this paper.…”

Section: On Controlled Contact Systemsmentioning

confidence: 99%

“…Such systems are defined on the Thermodynamic Phase Space which is endowed with a contact structure (or a contact form) which is canonically associated with Gibbs' relation defining the Thermodynamic Equilibrium properties of physical systems [3,4,5,6]. Extending the work on reversible thermodynamical transformations in [7] to irreversible transformation of open thermodynamical systems leads to the definition of control contact systems [1,2] which are a strict extension of control Hamiltonian and portHamiltonian systems [8], and to the analysis of some of their dynamic properties [2,9].…”

Section: Introductionmentioning

confidence: 99%

Feedback equivalence of input–output contact systems

Ramírez

Maschke

Sbárbaro

2013

Systems & Control Letters

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Control contact systems represent controlled (or open) irreversible processes which allow to represent simultaneously the energy conservation and the irreversible creation of entropy. Such systems systematically arise in models established in Chemical Engineering. The differential-geometric of these systems is a contact form in the same manner as the symplectic 2-form is associated to Hamiltonian models of mechanics. In this paper we study the feedback preserving the geometric structure of controlled contact systems and renders the closed-loop system again a contact system. It is shown that only a constant control preserves the canonical contact form, hence a state feedback necessarily changes the closed-loop contact form. For strict contact systems, arising from the modelling of thermodynamic systems, a class of state feedback that shapes the closed-loop contact form and contact Hamiltonian function is proposed. The state feedback is given by the composition of an arbitrary function and the control contact Hamiltonian function. The similarity with structure preserving feedback of input-output Hamiltonian systems leads to the definition of inputoutput contact systems and to the characterization of the feedback equivalence of input-output contact systems. An irreversible thermodynamic process, namely the heat exchanger, is used to illustrate the results.

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“…In this section we shall briefly recall the definition and main properties of a class of nonlinear control systems, called input-output contact systems, that arise when modelling control systems in chemical engineering or any process where the internal energy (or entropy) balance equation is written (Eberard et al, 2007;Favache et al, 2009Favache et al, , 2010Ramirez, 2012).…”

Section: Input-output Contact Systemsmentioning

confidence: 99%

“…Few papers exist on the dynamic properties of contact vector fields. Using linearisation techniques, a local stability study of dynamical systems defined by contact vector fields has been performed in Favache et al (2009) in the case when these vector field leaves invariant some Legendre submanifolds. In the sequel, we show that it is impossible, by output feedback, to achieve the asymptotic stabilization of an equilibrium point but only stability with respect to some Legendre submanifold rendered invariant by feedback.…”

Section: Controlled Control Systems Have Been Introduced Inmentioning

confidence: 99%

Control of input-output contact systems

Ramírez

Maschke

Sbárbaro

2013

IFAC Proceedings Volumes

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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.

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Some Properties of Conservative Port Contact Systems

Cited by 44 publications

References 21 publications

Contact Hamiltonian Dynamics: The Concept and Its Use

Contact Hamiltonian Dynamics: The Concept and Its Use

Feedback equivalence of input–output contact systems

Control of input-output contact systems

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