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On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems.
- Source :
- IEEE Transactions on Automatic Control; Apr2017, Vol. 62 Issue 4, p1700-1713, 14p
- Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 62
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 122302024
- Full Text :
- https://doi.org/10.1109/TAC.2016.2595263