Control by Interconnection of the Timoshenko Beam
Authors
Alessandro Macchelli, Claudio Melchiorri
Abstract
In this paper, the dynamical control of a mixed finite and infinite dimensional mechanical system is approached within the framework of port Hamiltonian systems. As an applicative example of the presented methodology, a flexible beam, modeled according to the Timoshenko theory, with a mass under gravity field connected to a free end, is considered. After the distributed port Hamiltonian (dpH) model of the beam is introduced, the control problem is discussed. The concept of structural invariant (Casimir function) is generalized to the infinite dimensional case and the so-called control by interconnection control technique is extended to the infinite dimensional case. In this way, finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy, i.e. by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipation effect is introduced
Keywords
control, distributed port hamiltonian systems, energy shaping, timoshenko beam
Citation
- Journal: IFAC Proceedings Volumes
- Year: 2003
- Volume: 36
- Issue: 2
- Pages: 153–158
- Publisher: Elsevier BV
- DOI: 10.1016/s1474-6670(17)38883-3
- Note: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control 2003, Seville, Spain, 3-5 April 2003
BibTeX
@article{Macchelli_2003,
title={{Control by Interconnection of the Timoshenko Beam}},
volume={36},
ISSN={1474-6670},
DOI={10.1016/s1474-6670(17)38883-3},
number={2},
journal={IFAC Proceedings Volumes},
publisher={Elsevier BV},
author={Macchelli, Alessandro and Melchiorri, Claudio},
year={2003},
pages={153--158}
}References
- Abraham, (1978)
- Golo, (2002)
- Golo, A hamiltonian formulation of the tim-oshenko beam model. Proc. of Mechatronics 2002 (2002)
- Macchelli, Distributed port hamiltonian formulation of the timoshenko beam: Modeling and control. (2003)
- Ortega, Energy-shaping of port-controlled hamiltonian systems by interconnection. Proc. of the 38th CDC Conference (1999)
- Rodriguez, On stabilization of non-linear distributed parameter port-controlled hamiltonian systems via energy shaping. Proc. of the 40th CDC Conference (2001)
- Stramigioli, (2001)
- Swaters, (2000)
- van der Schaft, (1999)
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics 42, 166–194 (2002) – 10.1016/s0393-0440(01)00083-3