Boundary energy shaping of linear distributed port-Hamiltonian systems
Authors
Abstract
This paper deals with the energy-balancing passivity-based control of linear, lossless, distributed port-Hamiltonian systems. Once inputs and outputs have been chosen to obtain a well-defined boundary control system, the problem is tackled by determining, at first, the class of energy functions that can be employed in the energy-shaping procedure, together with the corresponding boundary state-feedback control actions. To verify the existence of solutions for the closed-loop system, the equivalence between energy-balancing and energy-Casimir methods is shown. For the latter approach, the conditions for having a particular set of Casimir functions in closed-loop are given, and then the existence of the associated semigroup is studied. Since both the methods provide the same control action, the existence result determined for the energy-Casimir method is valid also for the energy-balancing controller. Simple stability is obtained by shaping the open-loop Hamiltonian, while asymptotic stability is ensured if proper “pervasive” (boundary) damping is present. In this respect, a stability criterion is discussed. The methodology is illustrated with the help of a simple example, i.e. a Timoshenko beam with full-actuation on one side, and an inertia on the other side.
Keywords
Distributed port-Hamiltonian systems; Passivity-based control; Energy-Casimir method; Stabilisation
Citation
- Journal: European Journal of Control
- Year: 2013
- Volume: 19
- Issue: 6
- Pages: 521–528
- Publisher: Elsevier BV
- DOI: 10.1016/j.ejcon.2013.10.002
- Note: Lagrangian and Hamiltonian Methods for Modelling and Control
BibTeX
@article{Macchelli_2013,
title={{Boundary energy shaping of linear distributed port-Hamiltonian systems}},
volume={19},
ISSN={0947-3580},
DOI={10.1016/j.ejcon.2013.10.002},
number={6},
journal={European Journal of Control},
publisher={Elsevier BV},
author={Macchelli, Alessandro},
year={2013},
pages={521--528}
}
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