Skip to main content
SpringerLink
Log in

Parallel simultaneous stabilization of a set of Port-Controlled Hamiltonian systems subject to actuator saturation

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper investigates parallel simultaneous stabilization (PSS) of a set of multi-input nonlinear Port-Controlled Hamiltonian (PCH) systems subject to actuator saturation (AS), and proposes a number of results on the design of PSS controllers for the PCH systems with AS. Firstly, the case of two PCH systems with AS is studied. Exploring the special property of the saturation nonlinearity and the structural properties of dissipative Hamiltonian system, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. When there are external disturbances in the two systems, a robust PSS controller is designed for the systems. Secondly, the case of more than two PCH systems with AS is investigated, and several new results are proposed for the PSS problem. Finally, two illustrative examples are presented to show that the stabilization controllers obtained in this paper work very well.

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

Similar content being viewed by others

References

  1. D. S. Berntein, and A. N. Michel, A chronological bibliography on saturating actuators, Int. J. of Robust and Nonlinear Control, 1995, 5(5): 375–380.

    Article  Google Scholar 

  2. G. Garcia, S. Tarbouriech, and J. M. Gomes da Silva Jr, Dynamic output controller design for linear systems with actuator and sensor saturation, Proc. of the 2007 American Control Conference, New York, 2007: 5834–5839.

  3. T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design, Bikhäuser, Boston, 2001.

    MATH  Google Scholar 

  4. A. Saberi, Z. Lin, and A. R. Teel, Control of linear systems with saturating actuators, IEEE Trans. on Automatic Control, 1996, 41(3): 368–378.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. A. Stoorvogel, A. Saberi, and S. Weiland, On external semi-global stochastic stabilization of linear systems with input saturation, Proc. of the 2007 American Control Conference, New York, 2007, 5845–5850.

  6. S. Tarbouriech, G. Garcia, and H. Glattfelder, Advanced strategies in control systems with input and output contraints, Lecture Notes in Control and Information Sciences, 346, Springer-Verlag, Berlin, 2007.

    Book  Google Scholar 

  7. E. Castelan, S. Tarbouriech, and I. Queinnec, Stability and stabilization of a class of nonlinear systems with saturating actuators, Proc. of the 16th IFAC World Congress, Pargue, 2005.

  8. D. F. Coutinho, and J. M. Gomes da Silva Jr, Estimating the region of attraction of nonlinear control systems with saturating actuators, Proc. of the 2007 American Control Conference, New York, 2007: 4715–4720.

  9. R. Ortega, A. J. Van der Schaft, B. M. Maschke, and G. Escobar, Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, 2002, 38(4):585–596.

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. Wang, D. Cheng, C. Li, and Y. Ge, Dissipative Hamiltonian realization and energy-based L 2-disturbance attenuation control of multi-machine power systems, IEEE Trans. on Autom. Contr., 2003, 48(8): 1428–1433.

    Article  MathSciNet  Google Scholar 

  11. D. Cheng, A. Astolfi, and R. Ortega, On feedback equivalence to port controlled Hamiltonian systems, Systems & Control Letters, 2005, 54(9): 911–917.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Cheng and Z. Xi, Feedback realization of Hamiltonian systems, Journal of Systems Science and Complexity, 2002, 15(1): 61–68.

    MATH  MathSciNet  Google Scholar 

  13. M. Dalsmo and A. J. Van der Schaft, On representations and integrability of mathematical structures in energy-conserving physical systems, SIAM Journal on Contr. Optim., 1999 37(1): 54–91.

    Article  MATH  Google Scholar 

  14. K. Fujimoto, K. Sakurama, and T. Sugie, Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations, Automatica, 2003 39(12): 2059–2069.

    Article  MATH  MathSciNet  Google Scholar 

  15. K. Fujimoto and T. Sugie, Canonical transformations and stabilization of generalized Hamiltonian systems, Systems and Control Letters, 2001, 42(3): 217–227.

    Article  MathSciNet  Google Scholar 

  16. Y. Wang, C. Li, and D. Cheng, Generalized Hamiltonian realization of time-invariant nonlinear systems, Automatica, 2003, 39(8): 1437–1443.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Cheng, Z. Xi, and Q. Lu, Geometric structure of generalized controlled Hamiltonian systems and its application, Science in China Ser. E-Engineering & Materials Science, 2000, 43(4): 365–379.

    Article  MATH  MathSciNet  Google Scholar 

  18. T. Shen, R. Ortega, Q. Lu, et al., Adaptive L 2 disturbance attenuation of Hamiltonian systems with parameter perturbations and application to power systems, Proc. of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000: 4939–4944.

  19. Z. Xi and D. Cheng, Passivity-based stabilization and H ∞ control of the Hamiltonian control systems with dissipation and its application to power systems, Int. J. of Control, 2000, 73(18):1686–1691.

    Article  MATH  MathSciNet  Google Scholar 

  20. Z. Xi, D. Cheng, and Q. Lu, Nonlinear decentralized controller design for multi-machine power systems using Hamiltonian function method, Automatica, 2002, 38(3): 527–534.

    Article  MATH  Google Scholar 

  21. B. Ho-Mock-Qai and W. P. Dayawansa, Simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback, SIAM J. Control Optim., 1999, 37: 1701–1725.

    Article  MATH  MathSciNet  Google Scholar 

  22. J. Wu, Simultaneous stabilization for a collection of single-input nonlinear systems, IEEE Trans. Autom. Control, 2005, 50(3): 328–337.

    Article  Google Scholar 

  23. V. Blondel, Simultaneous Stabilization of Linear Systems, Springer-Verlag, New York, 1994.

    MATH  Google Scholar 

  24. P. T. Kabamba, and C. Yang, Simultaneous controller design for linear time-invariant systems, IEEE Trans. Autom. Control, 1991, 36(1): 106–110.

    Article  MATH  MathSciNet  Google Scholar 

  25. D. E. Miller and T. Chen, Simultaneous stabilization with near-optimal H ∞ performance, IEEE Trans. Autom. Control, 2002, 47(12): 1986–1998.

    Article  MathSciNet  Google Scholar 

  26. W. E. Schmitendorf and C. C. Hollot, Simultaneous stabilization via linear state feedback control, IEEE Trans. Autom. Control, 1989, 34(9): 1001–1005.

    Article  MATH  MathSciNet  Google Scholar 

  27. Y. Wang, G. Feng, and D. Cheng, Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems, Automatica, 2007, 43(3): 403–415.

    Article  MATH  MathSciNet  Google Scholar 

  28. A. J. Van der Schaft, L 2-Gain and Passivity Techniques in Nonlinear Control, Springer, Berlin, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Airong Wei & Yuzhen Wang

  2. Optimization and Systems Theory, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Airong Wei & Xiaoming Hu

  3. ACCESS Linnaeus Center, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Xiaoming Hu

Authors
  1. Airong Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuzhen Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoming Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Airong Wei.

Additional information

This research is supported by the National Nature Science Foundation of China under Grant Nos. 60774009, 61074068, 61034007, the Research Fund the Doctoral Program of Chinese Higher Education under Grant No. G200804220028, the Independent Innovation Foundation of Shandong University under Grant No. 2010TS078, and the Nature Science Foundation of Shandong Province under Grant No. ZR2010FM013.

This paper was recommended for publication by Editor Yiguang HONG.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wei, A., Wang, Y. & Hu, X. Parallel simultaneous stabilization of a set of Port-Controlled Hamiltonian systems subject to actuator saturation. J Syst Sci Complex 24, 120–139 (2011). https://doi.org/10.1007/s11424-011-8177-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8177-2

Key words

Search

Navigation