Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems

Romeo Ortega, Arjan van der Schaft, Bernard Maschke, Gerardo Escobar

    Research output: Contribution to journalArticleAcademicpeer-review

    1092 Citations (Scopus)

    Abstract

    Passivity-based control (PBC) is a well-established technique that has shown to be very powerful to design robust controllers for physical systems described by Euler-Lagrange (EL) equations of motion. For regulation problems of mechanical systems, which can be stabilized "shaping" only the potential energy, PBC preserves the EL structure and furthermore assigns a closed-loop energy function equal to the difference between the energy of the system and the energy supplied by the controller. Thus, we say that stabilization is achieved via energy balancing. Unfortunately, these nice properties of EL-PBC are lost when used in other applications which require shaping of the total energy, for instance, in electrical or electromechanical systems, or even some underactuated mechanical devices. Our main objective in this paper is to develop a new PBC theory which extends to a broader class of systems the aforementioned energy-balancing stabilization mechanism and the structure invariance. Towards this end, we depart from the EL description of the systems and consider instead port-controlled Hamiltonian models, which result from the network modelling of energy-conserving lumped-parameter physical systems with independent storage elements, and strictly contain the class of EL models.
    Original languageEnglish
    Pages (from-to)585-596
    Number of pages12
    JournalAutomatica
    Volume38
    Issue number4
    DOIs
    Publication statusPublished - 2002

    Keywords

    • Hamiltonian systems
    • Passivity
    • Stabilization of nonlinear systems
    • Non-linear control

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