Port-Hamiltonian systems: network modeling and control of nonlinear physical systems

A.J. van der Schaft

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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    Abstract

    It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamiltonian function given by the total stored energy. The structural properties of port-Hamiltonian systems are discussed, in particular the existence of Casimir functions and its implications for stability and stabilization. Furthermore it is shown how passivity-based control results from interconnecting the plant port-Hamiltonian system with a controller port-Hamiltonian system, leading to a closed-loop port-Hamiltonian system. Finally, extensions to the distributed-parameter case are provided by formulating boundary control systems as infinite-dimensional port-Hamiltonian systems.
    Original languageEnglish
    Title of host publicationAdvanced Dynamics and Control of Structures and Machines
    EditorsHans Irshik, Kurt Schlacher
    Place of PublicationWien, New York
    PublisherSpringer
    Pages127-168
    Number of pages41
    ISBN (Electronic)978-3-7091-2774-2
    ISBN (Print)978-3-211-22867-8
    DOIs
    Publication statusPublished - 2004

    Publication series

    NameCISM Courses and Lectures
    Volume444
    ISSN (Print)0254-1971
    ISSN (Electronic)2309-3706

    Fingerprint

    Hamiltonians
    Structural properties
    Stabilization
    Control systems
    Controllers
    Networks (circuits)

    Keywords

    • METIS-223799
    • Hamiltonian System
    • Multibody System
    • Kinematic Constraint
    • Dirac Structure
    • Bond Graph

    Cite this

    van der Schaft, A. J. (2004). Port-Hamiltonian systems: network modeling and control of nonlinear physical systems. In H. Irshik, & K. Schlacher (Eds.), Advanced Dynamics and Control of Structures and Machines (pp. 127-168). (CISM Courses and Lectures; Vol. 444). Wien, New York: Springer. https://doi.org/10.1007/978-3-7091-2774-2_9
    van der Schaft, A.J. / Port-Hamiltonian systems : network modeling and control of nonlinear physical systems. Advanced Dynamics and Control of Structures and Machines. editor / Hans Irshik ; Kurt Schlacher. Wien, New York : Springer, 2004. pp. 127-168 (CISM Courses and Lectures).
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    van der Schaft, AJ 2004, Port-Hamiltonian systems: network modeling and control of nonlinear physical systems. in H Irshik & K Schlacher (eds), Advanced Dynamics and Control of Structures and Machines. CISM Courses and Lectures, vol. 444, Springer, Wien, New York, pp. 127-168. https://doi.org/10.1007/978-3-7091-2774-2_9

    Port-Hamiltonian systems : network modeling and control of nonlinear physical systems. / van der Schaft, A.J.

    Advanced Dynamics and Control of Structures and Machines. ed. / Hans Irshik; Kurt Schlacher. Wien, New York : Springer, 2004. p. 127-168 (CISM Courses and Lectures; Vol. 444).

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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    AB - It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamiltonian function given by the total stored energy. The structural properties of port-Hamiltonian systems are discussed, in particular the existence of Casimir functions and its implications for stability and stabilization. Furthermore it is shown how passivity-based control results from interconnecting the plant port-Hamiltonian system with a controller port-Hamiltonian system, leading to a closed-loop port-Hamiltonian system. Finally, extensions to the distributed-parameter case are provided by formulating boundary control systems as infinite-dimensional port-Hamiltonian systems.

    KW - METIS-223799

    KW - Hamiltonian System

    KW - Multibody System

    KW - Kinematic Constraint

    KW - Dirac Structure

    KW - Bond Graph

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    T3 - CISM Courses and Lectures

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    BT - Advanced Dynamics and Control of Structures and Machines

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    van der Schaft AJ. Port-Hamiltonian systems: network modeling and control of nonlinear physical systems. In Irshik H, Schlacher K, editors, Advanced Dynamics and Control of Structures and Machines. Wien, New York: Springer. 2004. p. 127-168. (CISM Courses and Lectures). https://doi.org/10.1007/978-3-7091-2774-2_9