An entropy-based formulation of irreversible processes based on contact structures

Favache, Audrey; Dochain, Denis; Maschke, Bernhard

doi:10.1016/j.ces.2010.06.019

Cited by 65 publications

(63 citation statements)

References 38 publications

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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%

“…where I n denotes the identity matrix of order n. With this definition of contact vector fields, one may define control contact systems according to [1,2] which represent the dynamics of irreversible Thermodynamic systems [8] such as the Continuous Stirred Tank Reactor [17,18]. …”

Section: Proposition 22 [16]mentioning

confidence: 99%

“…the thermodynamic properties). Using (8) it is computed that its restriction to L U is equivalent to the system equations (2).…”

Section: The Example Of the Heat Exchanger (Continued)mentioning

confidence: 99%

“…In canonical coordinates this means that they do not depend on the x 0 coordinate associated with the Reeb vector field. For models of physical systems where the x 0 coordinate represents the generating potential of the thermodynamic system (the total energy or the total entropy), this is in general the case [2,8]. Under Assumption 2, the matching equation (12) is reduced to a relation on the feedback α and the closed-loop contact form θ d…”

Section: Feedback Equivalence With Respect To a Modified Contact Formmentioning

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%

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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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Section: On Controlled Contact Systemsmentioning

confidence: 99%

Section: Proposition 22 [16]mentioning

confidence: 99%

“…the thermodynamic properties). Using (8) it is computed that its restriction to L U is equivalent to the system equations (2).…”

Section: The Example Of the Heat Exchanger (Continued)mentioning

confidence: 99%

Section: Feedback Equivalence With Respect To a Modified Contact Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Feedback equivalence of input–output contact systems

Ramírez

Maschke

Sbárbaro

2013

Systems & Control Letters

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About Some System-Theoretic Properties of Port-Thermodynamic Systems

Schaft¹,

Maschke²

2019

Lecture Notes in Computer Science

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About the Definition of Port Variables for Contact Hamiltonian Systems

Maschke

Schaft

2017

Lecture Notes in Computer Science

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Extending the formulation of reversible thermodynamical transformations to the formulation of irreversible transformations of open thermodynamical systems different classes of nonlinear control systems has been defined in terms of control Hamiltonian systems defined on a contact manifold. In this paper we discuss the relation between the definition of variational control contact systems and the input-output contact systems. We have first given an expression of the variational control contact systems in terms of a nonlinear control systems. Secondly we have shown that the conservative input-output contact systems are a subclass of the contact variational systems with integrable output dynamics.

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An entropy-based formulation of irreversible processes based on contact structures

Cited by 65 publications

References 38 publications

Feedback equivalence of input–output contact systems

Feedback equivalence of input–output contact systems

About Some System-Theoretic Properties of Port-Thermodynamic Systems

About the Definition of Port Variables for Contact Hamiltonian Systems

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