PI simultaneous stabilization and set-point output regulation of Port-Hamiltonian systems
Authors
Meng Zhang, Zhitao Liu, Hongye Su, Jianping Cai, Longhua Ma
Abstract
This paper is concerned with the problems of simultaneous stabilization and set-point output regulation of N Port-Hamiltonian (PH) systems. First, incremental models of PH systems are constructed and the passivity of incremental systems is established with some reasonable assumptions. Then a proportional plus integral (PI) controller is proposed to simultaneously stabilize incremental systems, and the stability of the closed-loop system is proved by Lyapunov function approach. The simple case with two PH systems is studied emphatically, and the obtained results are also naturally extended to the general case of N PH systems. Finally, the validity and applicability of the proposed PI controller is verified through an illustrative example.
Citation
- Journal: Journal of the Franklin Institute
- Year: 2017
- Volume: 354
- Issue: 18
- Pages: 8283–8292
- Publisher: Elsevier BV
- DOI: 10.1016/j.jfranklin.2017.10.020
BibTeX
@article{Zhang_2017,
title={{PI simultaneous stabilization and set-point output regulation of Port-Hamiltonian systems}},
volume={354},
ISSN={0016-0032},
DOI={10.1016/j.jfranklin.2017.10.020},
number={18},
journal={Journal of the Franklin Institute},
publisher={Elsevier BV},
author={Zhang, Meng and Liu, Zhitao and Su, Hongye and Cai, Jianping and Ma, Longhua},
year={2017},
pages={8283--8292}
}
References
- Maschke, Port-controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
- Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
- 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
- Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters vol. 62 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
- Rodriguez, H., Ortega, R., Escobar, G. & Barabanov, N. A robustly stable output feedback saturated controller for the boost DC-to-DC converter. Systems & Control Letters vol. 40 1–8 (2000) – 10.1016/s0167-6911(99)00113-9
- Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
- Fiaz, S., Zonetti, D., Ortega, R., Scherpen, J. M. A. & van der Schaft, A. J. A port-Hamiltonian approach to power network modeling and analysis. European Journal of Control vol. 19 477–485 (2013) – 10.1016/j.ejcon.2013.09.002
- Zhang, M., Ortega, R., Jeltsema, D. & Su, H. Further deleterious effects of the dissipation obstacle in control-by-interconnection of port-Hamiltonian systems. Automatica vol. 61 227–231 (2015) – 10.1016/j.automatica.2015.08.010
- Yong-Yan Cao, You-Xian Sun & Lam, J. Simultaneous stabilization via static output feedback and state feedback. IEEE Transactions on Automatic Control vol. 44 1277–1282 (1999) – 10.1109/9.769390
- HOWITT, G. D. & LUUS, R. Simultaneous stabilization of linear single-input systems by linear state feedback control. International Journal of Control vol. 54 1015–1030 (1991) – 10.1080/00207179108934197
- Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica vol. 43 403–415 (2007) – 10.1016/j.automatica.2006.09.008
- Perez, M., Ortega, R. & Espinoza, J. Passivity-Based PI Control of Switched Power Converters. IEEE Transactions on Control Systems Technology vol. 12 881–890 (2004) – 10.1109/tcst.2004.833628
- Yu, Speed regulation of PMSM based on port-controlled Hamiltonian systems and PI control principle. (2009)
- van der Schaft, (1999)
- Zhang, M., Ortega, R., Liu, Z. & Su, H. A new family of interconnection and damping assignment passivity-based controllers. International Journal of Robust and Nonlinear Control vol. 27 50–65 (2016) – 10.1002/rnc.3557
- Zhang, PID passivity-based control of port-Hamiltonian systems. IEEE Trans. Autom. Control (2017)
- 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
- Jayawardhana, B., Ortega, R., García-Canseco, E. & Castaños, F. Passivity of nonlinear incremental systems: Application to PI stabilization of nonlinear RLC circuits. Systems & Control Letters vol. 56 618–622 (2007) – 10.1016/j.sysconle.2007.03.011
- Khalil, (2002)