Energy shaping of boundary controlled linear port Hamiltonian systems

Yann Le Gorrec, Alessandro Macchelli, Hector Ramirez, Hans Zwart

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    Abstract

    In this paper, we consider the asymptotic stabilization of a class of one dimensional boundary controlled port Hamiltonian systems by an immersion/reduction approach and the use of Casimir invariants. We first extend existing results on asymptotic stability of linear infinite dimensional systems controlled at their boundary to the case of stable Port Hamiltonian controllers including some physical constraints as clamping. Then the relation between structural invariants, namely Casimir functions, and the controller structure is computed. The Casimirs are employed in the selection of the controllers Hamiltonian to shape the total energy function of the closed loop system and introduce a minimum in the desired equilibrium configuration. The approach is illustrated on the model of a micro manipulation process with partial-actuation on one side of the spatial domain.

    Original languageEnglish
    Title of host publication19th IFAC World Congress IFAC 2014, Proceedings
    PublisherIFAC Secretariat
    Pages1580-1585
    Number of pages6
    Volume19
    ISBN (Electronic)9783902823625
    Publication statusPublished - 2014
    Event19th IFAC World Congress 2014 - Cape Town International Convention Centre, Cape Town, South Africa
    Duration: 24 Aug 201429 Aug 2014
    Conference number: 19
    http://www.ifac2014.org/

    Conference

    Conference19th IFAC World Congress 2014
    Abbreviated titleIFAC
    CountrySouth Africa
    CityCape Town
    Period24/08/1429/08/14
    Internet address

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    Keywords

    • Asymptotic stability
    • Immersion reduction control design
    • Infinite dimensional port Hamiltonian systems

    Cite this

    Le Gorrec, Y., Macchelli, A., Ramirez, H., & Zwart, H. (2014). Energy shaping of boundary controlled linear port Hamiltonian systems. In 19th IFAC World Congress IFAC 2014, Proceedings (Vol. 19, pp. 1580-1585). IFAC Secretariat.