A constructive procedure for energy shaping of port—Hamiltonian systems
Authors
Pablo Borja, Rafael Cisneros, Romeo Ortega
Abstract
Equilibrium stabilization of nonlinear systems via energy shaping is a well-established, robust, passivity-based controller design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations, which is usually a difficult task. In this paper a new, fully constructive, procedure to shape the energy for a class of port-Hamiltonian systems that obviates the solution of partial differential equations is proposed. Proceeding from the well-known passive, power shaping output we propose a nonlinear static state-feedback that preserves passivity of this output but with a new storage function. A suitable selection of a controller gain makes this function positive definite, hence it is a suitable Lyapunov function for the closed-loop. The resulting controller may be interpreted as a classical PI—connections with other standard passivity-based controllers are also identified.
Keywords
Passivity; Nonlinear systems; Passivity-based control; Hamiltonian systems
Citation
- Journal: Automatica
- Year: 2016
- Volume: 72
- Issue:
- Pages: 230–234
- Publisher: Elsevier BV
- DOI: 10.1016/j.automatica.2016.05.028
BibTeX
@article{Borja_2016,
title={{A constructive procedure for energy shaping of port—Hamiltonian systems}},
volume={72},
ISSN={0005-1098},
DOI={10.1016/j.automatica.2016.05.028},
journal={Automatica},
publisher={Elsevier BV},
author={Borja, Pablo and Cisneros, Rafael and Ortega, Romeo},
year={2016},
pages={230--234}
}
References
- Borja, P., Cisneros, R. & Ortega, R. Shaping the energy of port-Hamiltonian systems without solving PDE’s. 2015 54th IEEE Conference on Decision and Control (CDC) 5713–5718 (2015) doi:10.1109/cdc.2015.7403116 – 10.1109/cdc.2015.7403116
- Borovic, B., Hong, C., Liu, A. Q., Xie, L. & Lewis, F. L. Control of a MEMS optical switch. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 3039-3044 Vol.3 (2004) doi:10.1109/cdc.2004.1428930 – 10.1109/cdc.2004.1428930
- Donaire, A. et al. Shaping the Energy of Mechanical Systems Without Solving Partial Differential Equations. IEEE Transactions on Automatic Control vol. 61 1051–1056 (2016) – 10.1109/tac.2015.2458091
- Duindam, (2009)
- Khalil, (2000)
- Ortega, R. & Borja, L. P. New results on Control by Interconnection and Energy-Balancing Passivity-Based Control of port-hamiltonian systems. 53rd IEEE Conference on Decision and Control 2346–2351 (2014) doi:10.1109/cdc.2014.7039746 – 10.1109/cdc.2014.7039746
- Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
- Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
- Ortega, R., Liu, Z. & Su, H. Control via interconnection and damping assignment of linear time-invariant systems: a tutorial. International Journal of Control vol. 85 603–611 (2012) – 10.1080/00207179.2012.660734
- 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
- Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
- Prajna, S., van der Schaft, A. & Meinsma, G. An LMI approach to stabilization of linear port-controlled Hamiltonian systems. Systems & Control Letters vol. 45 371–385 (2002) – 10.1016/s0167-6911(01)00195-5
- van der Schaft, (1996)
- Venkatraman, A. & van der Schaft, A. Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs. European Journal of Control vol. 16 665–677 (2010) – 10.3166/ejc.16.665-677