Skip to main content
SpringerLink
Log in

Asymptotic stability of port-hamiltonian systems with constant inputs

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. van der Schaft, A. (2017). \(L_{2}\)-Gain and Passivity Techniques in the Nonlinear Control (3rd ed.). Berlin: Springer.

  2. Ortega, R., & Garcia-Canseco, E. (2004). Interconnection and damping assignment passivity-based control: a survey. European Journal of Control, 10(2), 432–450.

    Article  MathSciNet  Google Scholar 

  3. Ortega, R., van der Schaft, A., Castanos, F., & Astolfi, A. (2008). Control by interconnection and standard passivity-based control of port-hamiltonian systems. IEEE Transactions on Automatic Control, 53(11), 2527–2542.

    Article  MathSciNet  Google Scholar 

  4. Aranovskiy, S., Ortega, R., & Cisneros, R. (2016). Robust PI passivity-based control of nonlinear systems and its application to port-hamiltonian systems and temperature regulation. International Journal of Robust and Nonlinear Control, 26(10), 2216–2231.

    Article  MathSciNet  Google Scholar 

  5. Cai, L., He, Z., & Hu, H. (2017). 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, 32(3), 1689–1700.

    Article  Google Scholar 

  6. Yaghmaei, A., & Yazdanpanah, M. (2017). Trajectory tracking for a class of contractive port-Hamiltonian systems. Automatica, 83(9), 331–336.

    Article  MathSciNet  Google Scholar 

  7. Zhang, M., Borja, P., Ortega, R., Liu, Z., & Su, H. (2018). PID passivity-based control of port-Hamiltonian systems. IEEE Transactions on Automatic Control, 63(4), 1032–1044.

    Article  MathSciNet  Google Scholar 

  8. Benedito, E., del Puerto-Flores, D., Doria-Cerezo, A., & Scherpen, J. M. A. (2019). Port-hamiltonian based optimal power flow algorithm for multi-terminal DC networks. Control Engineering Practice, 83, 141–150.

    Article  Google Scholar 

  9. Yaghmaei, A., & Yazdanpanah, M. (2019). Structure preserving observer design for port-hamiltonian systems. IEEE Transactions on Automatic Control, 64(3), 1214–1220.

    Article  MathSciNet  Google Scholar 

  10. Jayawardhana, B., & Weiss, G. (2005). A class of port-controlled Hamiltonian systems. The 44th IEEE Conference on Decision and Control and European Control Conference, Seville, Spain (pp. 5630–5632).

  11. Jayawardhana, B., Ortega, R., Garcia-Canseco, E., & Castanos, F. (2007). Passivity of nonlinear incremental systems: application to PI stabilization of nonlinear RLC circuits. Systems & Control Letters, 56(9), 618–622.

    Article  MathSciNet  Google Scholar 

  12. Ortega, R., Monshizadeh, N., Monshiadeh, P., & Bazylev, D. (2018). Permanent magnet synchronous motors are globally asymptotically stabilizable with PI current control. Automatica, 98, 296–301.

    Article  MathSciNet  Google Scholar 

  13. Monshizadeh, N., Monshizadeh, P., Ortega, R., & van der Schaft, A. (2019). Conditions on shifted passivity of port-hamiltonian systems. Systems & Control Letters, 123(4), 55–61.

    Article  MathSciNet  Google Scholar 

  14. Monshizadeh, N., Monshizadeh, P., Ortega, R., & van der Schaft, A. (2019). Power-controlled Hamiltonian systems: application to electrical systems with constant power loads. Automatica, 109. https://doi.org/10.1016/j.automatica.2019.108527.

  15. Wang, Y., Feng, G., & Cheng, D. (2007). Simultaneous stabilization of a set of nonlinear port-controlled hamiltonian systems. Automatica, 43(7), 403–415.

    Article  MathSciNet  Google Scholar 

  16. Wei, A., & Wang, Y. (2010). Stabilization and \({\rm H}_{\infty }\) control of nonlinear port-controlled hamiltonian systems subject to actuator saturation. Automatica, 46(12), 2008–2013.

    Article  MathSciNet  Google Scholar 

  17. Cai, L., & He, Y. (2017). Exponential stability of port-Hamiltonian system via energy shaped. Journal of the Franklin Institute, 354(7), 2944–2958.

    Article  MathSciNet  Google Scholar 

  18. Donaire, A., & Junco, S. (2009). On the dddition of integral action to port-controlled hamiltonian systems. Automatica, 45(8), 1910–1916.

    Article  MathSciNet  Google Scholar 

  19. Sanchez, S., Ortega, R., Griño, R., Bergna, G., & Molinas, M. (2014). Conditions for existence of equilibria of systems with constant power loads. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(7), 2204–2211.

    Article  Google Scholar 

  20. Barabanov, N., Ortega, R., Griño, R., & Polyak, B. (2016). On existence and stability of equilibria of linear time-invariant systems with constant power loads. IEEE Transactions on Circuits and Systems I: Regular Papers, 63(1), 114–121.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Nature Science Fund of China (No. 61603311).

Author information

Authors and Affiliations

  1. School of Electric Engineer, Southwest Jiaotong University, Chengdu, Sichuan, 610031, China

    Liangcheng Cai

Authors
  1. Liangcheng Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liangcheng Cai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cai, L. Asymptotic stability of port-hamiltonian systems with constant inputs. Control Theory Technol. 19, 227–235 (2021). https://doi.org/10.1007/s11768-021-00042-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-021-00042-2

Keywords

Search

Navigation