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Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach

Le Gorrec, Yann and Matignon, Denis Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach. (2015) In: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 4 July 2015 - 7 July 2015 (Lyon, France).

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Official URL: https://doi.org/10.1016/j.ifacol.2015.10.236

Abstract

This paper discusses the passivity of the port-Hamiltonian formulation of a multivariable impedance matching boundary feedback of fractional order, expressed through diffusive representation. It is first shown in the 1D-wave equation case that the impedance matching boundary feedback can be written as a passive feedback on the boundary port variables. In the Euler-Bernoulli case, the impedance matching feedback matrix involves fractional derivatives and integrals. It is shown that the usual diffusive representation of such feedback is not formally a dissipative port-Hamiltonian system, even if from a frequency point of view this feedback proves passive.

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference without published proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Nationale Supérieure de Mécanique et des Microtechniques - ENSMM (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université de Franche-Comté (FRANCE)
Other partners > Université de Technologie de Belfort-Montbéliard - UTBM (FRANCE)
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ANR
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Deposited By: Denis Matignon
Deposited On:13 Jun 2018 10:22

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