The piston problem in a port-Hamiltonian formalism
Authors
Julien Lequeurre, Marius Tucsnak
Abstract
The aim of this paper is to write two simple fluid-structure interaction coupled systems as wellposed port-Hamiltonian systems. Moreover, we investigate the stabilization of the system Burgers/piston thanks to a very simple feedback law.
Keywords
Distributed parameters systems; port-Hamiltonian systems
Citation
- Journal: IFAC-PapersOnLine
- Year: 2015
- Volume: 48
- Issue: 13
- Pages: 212–216
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2015.10.241
- Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015
BibTeX
@article{Lequeurre_2015,
title={{The piston problem in a port-Hamiltonian formalism}},
volume={48},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2015.10.241},
number={13},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Lequeurre, Julien and Tucsnak, Marius},
year={2015},
pages={212--216}
}
References
- Cindea, N., Micu, S., Roventa, I., and Tucsnak, M. (to appear). Moving pointwise control of a simplified fluid structure system. Journal de Mathématiques Pures et Appliquées.
- Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- Lequeurre, J. and Tucsnak, M. (working paper, a). Global existence and stabilization of the one-dimensional Burgers - point mass system.
- Lequeurre, J. and Tucsnak, M. (working paper, b). Global existence and stabilization of the one-dimensional compressible Navier-Stokes equations - point mass system.
- Shelukhin, V. (1977). The unique solvability of the problem of motion of a piston in a viscous gas. Dinamika Sploshn. Sredy, 31, 132-150.
- Tucsnak, M. & Weiss, G. Well-posed systems—The LTI case and beyond. Automatica vol. 50 1757–1779 (2014) – 10.1016/j.automatica.2014.04.016
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- van der Schaft, A. (2006). Port-Hamiltonian systems: an introductory survey. In International Congress of Mathematicians. Vol. III, 1339-1365. Eur. Math. Soc., Zürich.
- Vázquez, J. L. & Zuazua, E. Large Time Behavior for a Simplified 1D Model of Fluid–Solid Interaction†. Communications in Partial Differential Equations vol. 28 1705–1738 (2003) – 10.1081/pde-120024530
- VÁZQUEZ, J. L. & ZUAZUA, E. LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID–SOLID INTERACTION. Mathematical Models and Methods in Applied Sciences vol. 16 637–678 (2006) – 10.1142/s0218202506001303
- Zwart, H., Le Gorrec, Y., Maschke, B. & Villegas, J. Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain. ESAIM: Control, Optimisation and Calculus of Variations vol. 16 1077–1093 (2009) – 10.1051/cocv/2009036