Asymptotic stability of port-hamiltonian systems with constant inputs

Authors

Liangcheng Cai

Abstract

In this paper, the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied. Constant inputs are useful for stabilizing systems at their nonzero equilibria and can be realized by step signals. To achieve this goal, two methods based on integral action and comparison principle are presented in this paper. These methods change the convex Hamiltonian function and the restricted damping matrix of the previous results into a Hamiltonian function with a local minimum and a positive semidefinite matrix, respectively. Due to common conditions of Hamiltonian function and damping matrix, the proposed method asymptotically stabilizes more classes of PH systems with constant inputs than the existing methods. Finally, the validity and advantages of the presented methods are shown in an example.

Keywords

Port-Hamiltonian systems; Constant inputs; Integral action; Compare principle; Asymptotic stability

Citation

• Journal: Control Theory and Technology
• Year: 2021
• Volume: 19
• Issue: 2
• Pages: 227–235
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s11768-021-00042-2

BibTeX

@article{Cai_2021,
  title={{Asymptotic stability of port-hamiltonian systems with constant inputs}},
  volume={19},
  ISSN={2198-0942},
  DOI={10.1007/s11768-021-00042-2},
  number={2},
  journal={Control Theory and Technology},
  publisher={Springer Science and Business Media LLC},
  author={Cai, Liangcheng},
  year={2021},
  pages={227--235}
}

Download the bib file

References

• van der Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer International Publishing, 2017). doi:10.1007/978-3-319-49992-5 – 10.1007/978-3-319-49992-5
• 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., 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
• Aranovskiy, S., Ortega, R. & Cisneros, R. A robust PI passivity-based control of nonlinear systems and its application to temperature regulation. International Journal of Robust and Nonlinear Control vol. 26 2216–2231 (2015) – 10.1002/rnc.3404
• Cai, L., He, Z. & Hu, H. A New Load Frequency Control Method of Multi-Area Power System via the Viewpoints of Port-Hamiltonian System and Cascade System. IEEE Transactions on Power Systems vol. 32 1689–1700 (2017) – 10.1109/tpwrs.2016.2605007
• Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking for a class of contractive port Hamiltonian systems. Automatica vol. 83 331–336 (2017) – 10.1016/j.automatica.2017.06.039
• Zhang, M., Borja, P., Ortega, R., Liu, Z. & Su, H. PID Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 63 1032–1044 (2018) – 10.1109/tac.2017.2732283
• Benedito, E., del Puerto-Flores, D., Dòria-Cerezo, A. & Scherpen, J. M. A. Port-Hamiltonian based Optimal Power Flow algorithm for multi-terminal DC networks. Control Engineering Practice vol. 83 141–150 (2019) – 10.1016/j.conengprac.2018.10.018
• Yaghmaei, A. & Yazdanpanah, M. J. Structure Preserving Observer Design for Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 64 1214–1220 (2019) – 10.1109/tac.2018.2847904
• Jayawardhana, B. & Weiss, G. A class of port-controlled Hamiltonian systems. Proceedings of the 44th IEEE Conference on Decision and Control 5630–5632 doi:10.1109/cdc.2005.1583059 – 10.1109/cdc.2005.1583059
• 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
• Ortega, R., Monshizadeh, N., Monshizadeh, P., Bazylev, D. & Pyrkin, A. Permanent magnet synchronous motors are globally asymptotically stabilizable with PI current control. Automatica vol. 98 296–301 (2018) – 10.1016/j.automatica.2018.09.031
• Monshizadeh, N., Monshizadeh, P., Ortega, R. & van der Schaft, A. Conditions on shifted passivity of port-Hamiltonian systems. Systems & Control Letters vol. 123 55–61 (2019) – 10.1016/j.sysconle.2018.10.010
• Monshizadeh, P., Machado, J. E., Ortega, R. & van der Schaft, A. Power-controlled Hamiltonian systems: Application to electrical systems with constant power loads. Automatica vol. 109 108527 (2019) – 10.1016/j.automatica.2019.108527
• 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
• Wei, A. & Wang, Y. Stabilization and $H^\infty$ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica vol. 46 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
• Cai, L. & He, Y. Exponential stability of port-Hamiltonian systems via energy-shaped method. Journal of the Franklin Institute vol. 354 2944–2958 (2017) – 10.1016/j.jfranklin.2017.02.004
• 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
• Sanchez, S., Ortega, R., Grino, R., Bergna, G. & Molinas, M. Conditions for Existence of Equilibria of Systems With Constant Power Loads. IEEE Transactions on Circuits and Systems I: Regular Papers vol. 61 2204–2211 (2014) – 10.1109/tcsi.2013.2295953
• Barabanov, N., Ortega, R., Grino, R. & Polyak, B. On Existence and Stability of Equilibria of Linear Time-Invariant Systems With Constant Power Loads. IEEE Transactions on Circuits and Systems I: Regular Papers vol. 63 114–121 (2016) – 10.1109/tcsi.2015.2497559