Bond graph modelling for chemical reactors

Couenne, Françoise; Jallut, Christian; Maschke, Bernhard; Breedveld, Pieter C.; Tayakout, M.

doi:10.1080/13873950500068823

Cited by 80 publications

(52 citation statements)

References 11 publications

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“…c i , where T 0 and c i are constants [14]. The state space of the heat exchanger is then defined as the following submanifold L U of the Thermodynamic Phase Space where Gibbs' equation is satisfied…”

Section: The Example Of the Heat Exchangermentioning

confidence: 99%

“…Let us now express the matching equation (13) with θ d defined by (14) in terms of a matching equation in the function F and the feedback α. The Lie derivatives in (13) may be developed as…”

Section: Proposition 41 the 1-form (14) Is A Contact Formmentioning

confidence: 99%

“…where , denotes the pairing between vector fields and 1-forms on M. It appears then clearly that the matching equation defines a linear first-order PDE in the function F defining the modified contact form θ d in (14). In the canonical coordinates of θ this PDE may be written as…”

Section: Some Remarks On Control Synthesismentioning

confidence: 99%

See 2 more Smart Citations

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: The Example Of the Heat Exchangermentioning

confidence: 99%

Section: Proposition 41 the 1-form (14) Is A Contact Formmentioning

confidence: 99%

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Feedback equivalence of input–output contact systems

Ramírez

Maschke

Sbárbaro

2013

Systems & Control Letters

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“…where the state variable x = (x 1 , x 2 ) ⊤ ∈ R 2 is the vector of the entropies x 1 and x 2 of subsystem 1 and 2, U (x 1 , x 2 ) = U 1 (x 1 ) + U 2 (x 2 ) is the internal energy of the overall system composed of the addition of the internal energies of each subsystem, the gradient of the total internal energy ∂U ∂xi = T i (x i ) being the temperatures of each compartment with T (x i ) = T 0 exp xi ci , where T 0 and c i are constants (Couenne et al, 2006), λ, λ e > 0 denote Fourier's heat conduction coefficients of the internal and external walls respectively and the controlled input u(t) is the temperature of the external heat source. The Thermodynamic Phase Space is R 5 ∋ (x 0 , x 1 , x 2 , p 1 , p 2 ) ⊤ and its elements correspond respectively to the total internal energy, the entropies and the temperatures.…”

Section: Example: the Heat Exchangermentioning

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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“…where is the number of vertices of the graph, and ℓ is equal to the number of components 3 of the complex graph 4 , the linkage classes in the terminology of [11], [7], [8].…”

Section: The Linkage Classes Of the Complex Graphmentioning

confidence: 99%

On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics

Rao

Jayawardhana

Schaft

2012

2012 American Control Conference (ACC)

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Abstract-Motivated by the recent progresses on the interplay between the graph theory and systems theory, we revisit the analysis of reversible chemical reaction networks described by mass action kinetics by reformulating it using the graph knowledge of the underlying networks. Based on this formulation, we can characterize the space of equilibrium points and provide simple dynamical analysis on the state space modulo the space of equilibrium points.

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Bond graph modelling for chemical reactors

Cited by 80 publications

References 11 publications

Feedback equivalence of input–output contact systems

Feedback equivalence of input–output contact systems

Control of input-output contact systems

On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics

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