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

A. Macchelli, Y. Le Gorrec, H. Ramirez, H. Zwart

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34 Citations (Scopus)
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Abstract

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
Volume62
Issue number4
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • Boundary control
  • distributed port-Hamiltonian systems
  • passivity-based control
  • stability of pdes

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