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11. Approximation of linear distributed parameter systems by delay systems

Author

Michael Di Loreto, Damien Eberard, Xavier Brun, Sérine Damak, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and ANR-11-JS03-0004,AIDS,Approximation des Systèmes de Dimension Infinie(2011)

Subjects
Time-delay systems, 0209 industrial biotechnology, Work (thermodynamics), Partial differential equation, Numerical analysis, 010102 general mathematics, 02 engineering and technology, 01 natural sciences, Constructive, Stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Coprime factorization, Control and Systems Engineering, Distributed parameter system, Control theory, Distributed parameter systems, Topological graph theory, Applied mathematics, 0101 mathematics, Electrical and Electronic Engineering, Approximation, Realization (systems), Mathematics
Abstract

International audience; The present work addresses continuous-time approximation of distributed parameter systems governed by linear one-dimensional partial differential equations. While approximation is usually realized by lumped systems, that is finite dimensional systems, we propose to approximate the plant by a time-delay system. Within the graph topology, we prove that, if the plant admits a coprime factorization in the algebra of BIBO-stable systems, any linear distributed parameter plant can be approximated by a time-delay system, governed by coupled differential–difference equations. Considerations on stabilization and state- space realization are carried out. A numerical method for constructive approximation is also proposed and illustrated.

Published
2016
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12. An Energy-Based Approach for n -d.o.f. Passive Dual-User Haptic Training Systems.

Author

Liu, Fei, Licona, Angel Ricardo, Lelevé, Arnaud, Eberard, Damien, Pham, Minh Tu, and Redarce, Tanneguy

Subjects
MINIMALLY invasive procedures, HAPTIC devices, DEGREES of freedom
Abstract

SUMMARY: This paper introduces a dual-user training system whose design is based on an energetic approach. This kind of system is useful for supervised hands-on training where a trainer interacts with a trainee through two haptic devices, in order to practice on a manual task performed on a virtual or teleoperated robot (e.g., for an Minimally Invasive Surgery (MIS) task in a surgical context). This paper details the proof of stability of an Energy Shared Control (ESC) architecture we previously introduced for one degree of freedom (d.o.f.) devices. An extension to multiple degrees of freedom is proposed, along with an enhanced version of the Adaptive Authority Adjustment function. Experiments are carried out with 3 d.o.f. haptic devices in free motion as well as in contact contexts in order to show the relevance of this architecture. [ABSTRACT FROM AUTHOR]

Published
2020
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13. An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes

Author

D. Eberard, van der Arjan Schaft, and Bernhard Maschke

Subjects
Hamiltonian mechanics, Dynamical systems theory, Contact geometry, Physical system, Statistical and Nonlinear Physics, Geometry, Manifold, Hamiltonian system, symbols.namesake, Classical mechanics, Phase space, symbols, Vector field, Mathematical Physics, Mathematics
Abstract

It is shown that the intrinsic geometry associated with equilibrium thermodynamics, namely the contact geometry, provides also a suitable framework in order to deal with irreversible thermodynamical processes. Therefore we introduce a class of dynamical systems on contact manifolds, called conservative contact systems, defined as contact vector fields generated by some contact Hamiltonian function satisfying a compatibility condition with some Legendre submanifold of the contact manifold. Considering physical systems' modeling, the Legendre submanifold corresponds to the definition of the thermodynamical properties of the system and the contact Hamiltonian function corresponds to the definition of some irreversible processes taking place in the system. Open thermodynamical systems may also be modeled by augmenting the conservative contact systems with some input and output variables (in the sense of automatic control) and so-called input vector fields and lead to the definition of port contact systems. Finally complex systems consisting of coupled simple thermodynamical or mechanical systems may be represented by the composition of such port contact systems through algebraic relations called interconnection structure. Two examples illustrate this composition of contact systems: a gas under a piston submitted to some external force and the conduction of heat between two media with external thermostat.

Published
2007
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14. Selective targeting of PARP-1 zinc finger recognition domains with Au(iii) organometallics.

Author

Wenzel, Margot N., Meier-Menches, Samuel M., Williams, Thomas L., Rämisch, Eberard, Barone, Giampaolo, and Casini, Angela

Subjects
ZINC-finger proteins, METAL-binding peptides, ORGANOMETALLIC compounds
Abstract

The binding of Au(iii) complexes to the zinc finger domain of the anticancer drug target PARP-1 was studied using a hyphenated mass spectrometry approach combined with quantum mechanics/molecular mechanics (QM/MM) studies. Competition experiments were carried out, whereby each Au complex was exposed to two types of zinc fingers. Notably, the cyclometallated Au-C^N complex was identified as the most selective candidate to disrupt the PARP-1 zinc finger domain, forming distinct adducts compared to the coordination compound Auphen. [ABSTRACT FROM AUTHOR]

Published
2018
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23. Port-based modelling of mass transport phenomena.

Author

Baaiu, A., Couenne, F., Eberard, D., Jallut, C., Lefevre, L., Legorrec, Y., and Maschke, B.

Subjects
BOND graphs, MASS transfer, METHODOLOGY, CONSERVATION laws (Mathematics), GEOMETRY
Abstract

The goal of this article is to present an extension of the port-based modelling approach (bond graphs) which applies to systems subject to heat and mass transfer. The methodology is based on the first principle, conservation laws and constitutive closure relations. The latter are the phenomenological laws relating fluxes and thermodynamic forces. Then instantaneous power conservation appears naturally as a geometric interconnection structure called Dirac structure. The multi-level case (several macroscopic spatial scales) is investigated with the assumption that the spatial scales are separated and may be considered as two distinct phases. In this case, it is shown that both the interconnection coupling within a phase and the multi-level interconnection coupling are Dirac structures. [ABSTRACT FROM AUTHOR]

Published
2009
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