Distributed Control for Infinite Dimensional Port-Hamiltonian Systems
Authors
Abstract
The aim of the paper is twofold. At first, a class of autonomous port-Hamiltonian systems whose dynamic is described by coupled PDEs and (nonlinear) ODEs is presented, and some properties (i.e., well-posedness and asymptotic stability of the origin) investigated. Secondly, an energy-based control design methodology is discussed. The finite-dimensional subsystem is equipped with an input, and a procedure for designing a state-feedback control action that maps the open-loop dynamic to a target one still in port-Hamiltonian form is illustrated. The idea is that the corresponding error system meets the requirements regarding the asymptotic stability of the origin stated in the first part of the paper. In this way, asymptotic convergence of the trajectories to the desired equilibrium configuration can be proved.
Keywords
port-Hamiltonian systems; passivity-based control; stability analisys
Citation
- Journal: IFAC-PapersOnLine
- Year: 2021
- Volume: 54
- Issue: 19
- Pages: 52–57
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2021.11.054
- Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021
BibTeX
@article{Macchelli_2021,
title={{Distributed Control for Infinite Dimensional Port-Hamiltonian Systems}},
volume={54},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2021.11.054},
number={19},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Macchelli, Alessandro},
year={2021},
pages={52--57}
}
References
- Curtain, (1995)
- Jacob, (2012)
- 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
- Luo, (1999)
- Maschke, B. M. & van der Schaft, A. J. PORT-CONTROLLED HAMILTONIAN SYSTEMS: MODELLING ORIGINS AND SYSTEMTHEORETIC PROPERTIES. Nonlinear Control Systems Design 1992 359–365 (1993) doi:10.1016/b978-0-08-041901-5.50064-6 – 10.1016/b978-0-08-041901-5.50064-6
- Mattioni, A., Wu, Y., Ramirez, H., Gorrec, Y. L. & Macchelli, A. Modelling and control of a class of lumped beam with distributed control. IFAC-PapersOnLine vol. 51 217–222 (2018) – 10.1016/j.ifacol.2018.06.057
- Olver, (1993)
- Ortega, Putting energy back in control. (2001)
- Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
- Ramirez, H., Zwart, H. & Le Gorrec, Y. Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control. Automatica vol. 85 61–69 (2017) – 10.1016/j.automatica.2017.07.045
- 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