Stabilization of Port-Controlled Hamiltonian systems subject to exogenous disturbances via compensation control approach

Authors

Baozeng Fu, Qingzhi Wang, Yongchao Liu

Abstract

The stabilization of Port-Controlled Hamiltonian (PCH) systems under exogenous disturbances by designing a compensation control approach is studied in the paper. Firstly, a baseline feedback control is proposed utilizing the damping injection method. To estimate disturbances, then a novel exogenous disturbance observer is constructed, based on which a feedforward compensation control is developed. Next, a composite control law is proposed based on the feedforward compensation and the feedback control. For the Hamiltonian system, an asymptotic stability analysis is followed finally. The feasibility of the compensation control strategy is revealed by a numerical simulation example.

Citation

• Journal: 2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)
• Year: 2023
• Volume:
• Issue:
• Pages: 1756–1760
• Publisher: IEEE
• DOI: 10.1109/ddcls58216.2023.10165926

BibTeX

@inproceedings{Fu_2023,
  title={{Stabilization of Port-Controlled Hamiltonian systems subject to exogenous disturbances via compensation control approach}},
  DOI={10.1109/ddcls58216.2023.10165926},
  booktitle={{2023 IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)}},
  publisher={IEEE},
  author={Fu, Baozeng and Wang, Qingzhi and Liu, Yongchao},
  year={2023},
  pages={1756--1760}
}

Download the bib file

References

• Yang, R., Sun, L., Zhang, G. & Zhang, Q. Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method. Journal of the Franklin Institute 356, 5961–5992 (2019) – 10.1016/j.jfranklin.2019.04.033
• Lv, X., Niu, Y. & Song, J. Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach. Nonlinear Dyn 104, 497–507 (2021) – 10.1007/s11071-021-06292-8
• Maschke, Port-controlled Hamiltonian systems: Modeling origins and system theoretic properties. Proc. the IFAC symposium Nonlin. Control Syst. Design
• Vander Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Archive fr Elektronik und bertragungstechnik (1995)
• Transient stabilization of multimachine power systems with nontrivial transfer conductances. IEEE Trans. Automat. Contr. 50, 60–75 (2005) – 10.1109/tac.2004.840477
• Shen, T., Mei, S., Lu, Q., Hu, W. & Tamura, K. Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems. Automatica 39, 81–89 (2003) – 10.1016/s0005-1098(02)00175-9
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
• Haddad, W. M., Rajpurohit, T. & Jin, X. Energy-based feedback control for stochastic port-controlled Hamiltonian systems. Automatica 97, 134–142 (2018) – 10.1016/j.automatica.2018.07.031
• Cupelli, M. et al. Port Controlled Hamiltonian Modeling and IDA-PBC Control of Dual Active Bridge Converters for DC Microgrids. IEEE Trans. Ind. Electron. 66, 9065–9075 (2019) – 10.1109/tie.2019.2901645
• Zhou, P., Yang, R., Zhang, G. & Han, Y. Adaptive Robust Simultaneous Stabilization of Two Dynamic Positioning Vessels Based on a Port-Controlled Hamiltonian (PCH) Model. Energies 12, 3936 (2019) – 10.3390/en12203936
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• Zhao, Z., Yang, J., Li, S., Zhang, Z. & Guo, L. Finite-time super-twisting sliding mode control for Mars entry trajectory tracking. Journal of the Franklin Institute 352, 5226–5248 (2015) – 10.1016/j.jfranklin.2015.08.022
• Fu, B., Li, S., Yang, J. & Guo, L. Global output regulation for a class of single input Port-controlled Hamiltonian disturbed systems. Applied Mathematics and Computation 325, 322–331 (2018) – 10.1016/j.amc.2017.12.046
• Wang, Z.-M., Wei, A., Zong, G., Zhao, X. & Li, H. Finite-time stabilization and\(\boldsymbol{\mathcal{H}}_{\infty}\)control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Journal of the Franklin Institute 357, 11807–11829 (2020) – 10.1016/j.jfranklin.2019.11.055
• Sun, W., Wang, Y. & Yang, R. L 2 disturbance attenuation for a class of time-delay Hamiltonian systems. J Syst Sci Complex 24, 672–682 (2011) – 10.1007/s11424-011-8368-x
• Zhang, M., Borja, P., Ortega, R., Liu, Z. & Su, H. PID Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 63, 1032–1044 (2018) – 10.1109/tac.2017.2732283
• Ferguson, J., Middleton, R. H. & Donaire, A. Disturbance rejection via control by interconnection of port-Hamiltonian systems. 2015 54th IEEE Conference on Decision and Control (CDC) 507–512 (2015) doi:10.1109/cdc.2015.7402279 – 10.1109/cdc.2015.7402279
• Wu, C., Yang, J., Li, S., Li, Q. & Guo, L. Disturbance observer based model predictive control for accurate atmospheric entry of spacecraft. Advances in Space Research 61, 2457–2471 (2018) – 10.1016/j.asr.2018.02.010
• Li, S., Yang, J., Chen, W.-H. & Chen, X. Disturbance Observer-Based Control. (2016) doi:10.1201/b16570 – 10.1201/b16570