On the synthesis of boundary control laws for distributed port-hamiltonian systems

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

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    38 Citations (Scopus)


    This paper is concerned with the energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations.

    Original languageEnglish
    Article number7524022
    Pages (from-to)1700-1713
    Number of pages14
    JournalIEEE transactions on automatic control
    Issue number4
    Publication statusPublished - 1 Apr 2017


    • Boundary control
    • Distributed port-Hamiltonian systems
    • Passivity-based control
    • Stability of pdes

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