Improved Results for Port-Hamiltonian Systems Subjected to Actuator Saturation via Energy-Shaped

Authors

Liangcheng Cai

Abstract

The existed control methods for Port-Hamiltonian (PH) systems subjected to actuator saturation (AS) were only beneficial for the Hamiltonian function having a local minimum at its equilibrium point. Once the Hamiltonian function do not have that feature or is not positive definite, the existed methods are ineffective. To improve the defect of existed methods, this paper investigates the stabilization of PH systems subjected to AS via energy-shaped and Hoo control. Compared with the existed results, the proposed methods not only effectively deal with the Hamiltonian function having a local minimum, but also work out that the Hamiltonian function is not positive definite at the equilibrium point or not bounded from the below. Thus, the proposed methods enlarge the applications of PH systems subjected to AS. Finally, example is given to show the validity and advantage of the proposed methods.

Citation

• Journal: 2018 37th Chinese Control Conference (CCC)
• Year: 2018
• Volume:
• Issue:
• Pages: 310–315
• Publisher: IEEE
• DOI: 10.23919/chicc.2018.8482759

BibTeX

@inproceedings{Cai_2018,
  title={{Improved Results for Port-Hamiltonian Systems Subjected to Actuator Saturation via Energy-Shaped}},
  DOI={10.23919/chicc.2018.8482759},
  booktitle={{2018 37th Chinese Control Conference (CCC)}},
  publisher={IEEE},
  author={Cai, Liangcheng},
  year={2018},
  pages={310--315}
}

Download the bib file

References

• hu, Control systems with actuator saturation: analysis and design. Boston Birkhauser (2001)
• Zairong Xi, Feng, G., Daizhan Cheng & Qiang Lu. Nonlinear decentralized saturated controller design for power systems. IEEE Trans. Contr. Syst. Technol. 11, 539–547 (2003) – 10.1109/tcst.2003.813404
• Wei, A. & Wang, Y. Stabilization and \(H_{\infty}\) control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Automatica 46, 2008–2013 (2010) – 10.1016/j.automatica.2010.08.001
• cai, The Relationship between Overshoot and Damping Injection for the Port-Hamiltonian System Subject to Actuator Saturation. proceedings of the 34th Chinese Control Conference (2015)
• Zhang, M., Ortega, R., Jeltsema, D. & Su, H. Further deleterious effects of the dissipation obstacle in control-by-interconnection of port-Hamiltonian systems. Automatica 61, 227–231 (2015) – 10.1016/j.automatica.2015.08.010
• Borja, P., Cisneros, R. & Ortega, R. A constructive procedure for energy shaping of port—Hamiltonian systems. Automatica 72, 230–234 (2016) – 10.1016/j.automatica.2016.05.028
• Cai, L. & He, Y. Exponential stability of port-Hamiltonian systems via energy-shaped method. Journal of the Franklin Institute 354, 2944–2958 (2017) – 10.1016/j.jfranklin.2017.02.004
• lu, Nonlinear Control of Power System (1993)
• Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45, 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 53, 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Ramirez, H., Le Gorrec, Y., Macchelli, A. & Zwart, H. Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback. IEEE Trans. Automat. Contr. 59, 2849–2855 (2014) – 10.1109/tac.2014.2315754
• Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters 62, 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
• Schiffer, J., Fridman, E., Ortega, R. & Raisch, J. Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica 74, 71–79 (2016) – 10.1016/j.automatica.2016.07.022
• Schiffer, J., Ortega, R., Astolfi, A., Raisch, J. & Sezi, T. Conditions for stability of droop-controlled inverter-based microgrids. Automatica 50, 2457–2469 (2014) – 10.1016/j.automatica.2014.08.009
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• 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 Trans. Power Syst. 32, 1689–1700 (2017) – 10.1109/tpwrs.2016.2605007