Multistable Energy Shaping of Passive Linear Systems with Hybrid Mode Selector
Authors
Stefano Massaroli, Federico Califano, Angela Faragasso, Atsushi Yamashita, Hajime Asama
Abstract
This paper presents a novel control strategy for stable linear time–invariant systems operating with a finite number of set points. Inspired by the theory of passivity-based control, the proposed method aims at simultaneously and asymptotically stabilize all the desired working modes by means of a static nonlinear state feedback law. An asynchronous external signal is then employed to trigger a hybrid controller in order to switch between the different working modes. The proposed approach is validated by means of simulations performed on the ubiquitous mass-spring-damper system.
Keywords
linear systems; nonlinear control; port–Hamiltonian systems; hybrid systems; multistability; passivity–based control
Citation
- Journal: IFAC-PapersOnLine
- Year: 2020
- Volume: 53
- Issue: 2
- Pages: 9118–9124
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2020.12.2151
- Note: 21st IFAC World Congress- Berlin, Germany, 11–17 July 2020
BibTeX
@article{Massaroli_2020,
title={{Multistable Energy Shaping of Passive Linear Systems with Hybrid Mode Selector}},
volume={53},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2020.12.2151},
number={2},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Massaroli, Stefano and Califano, Federico and Faragasso, Angela and Yamashita, Atsushi and Asama, Hajime},
year={2020},
pages={9118--9124}
}
References
- Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
- Duindam, Alessandro Macchelli, Stefano Strami-gioli, and Herman Bruyninckx. (2009)
- Efimov, D. Global Lyapunov Analysis of Multistable Nonlinear Systems. SIAM Journal on Control and Optimization vol. 50 3132–3154 (2012) – 10.1137/090767509
- Goebel, R., Sanfelice, R. G. & Teel, A. R. Hybrid dynamical systems. IEEE Control Systems vol. 29 28–93 (2009) – 10.1109/mcs.2008.931718
- Maschke, Port-controlled hamiltonian systems: Modelling origins and systemthe-oretic properties. IFAC Proceedings (1992)
- Ortega, R. & Mareels, I. Energy-balancing passivity-based control. Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334) 1265–1270 vol.2 (2000) doi:10.1109/acc.2000.876703 – 10.1109/acc.2000.876703
- Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
- Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
- Pisarchik, A. N. & Feudel, U. Control of multistability. Physics Reports vol. 540 167–218 (2014) – 10.1016/j.physrep.2014.02.007
- Secchi, (2007)
- Sontag, Input to state stability: Basic concepts and results. (2008)
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
- Van Der Schaft, (2000)