iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/S11424-020-8245-6
Output Tracking for One-Dimensional Wave Equation with Non-Collocated Control and Output Configuration | Journal of Systems Science and Complexity Skip to main content
Springer Nature Link
Log in

Output Tracking for One-Dimensional Wave Equation with Non-Collocated Control and Output Configuration

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

Abstract

This paper considers output tracking for a one-dimensional wave equation with general disturbance which includes both internal nonlinear uncertainty and external disturbance. The performance output is non-collocated to the control. The disturbance is estimated by an essentially extended state observer from active disturbance rejection control and the difficulty caused by the non-collocated configuration of control and output is overcome by a proper trajectory planning. An output feedback law is proposed to make the tracking error be convergent to zero exponentially as time goes to infinity. At the same time, all states of the closed-loop system are shown to be uniformly bounded. Numerical simulation is also presented to validate the theoretical results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Huang J, Nonlinear Output Regulation: Theory and Applications, SIAM, Philadelphia, 2004.

    Book  Google Scholar 

  2. Anantharam V and Desoer C A, Tracking and disturbance rejection of MIMO nonlinear systems with a PI or PS controller, IEEE Conference on Decision and Control, 1985, 1367–1368.

  3. Desoer C A and Lin C A, Tracking and disturbance rejection of MIMO nonlinear systems with PI controller, IEEE Trans. Automat. Control, 1985, 30(9): 861–867.

    Article  MathSciNet  Google Scholar 

  4. Francis B A and Wonham W M, The internal model principle of control theory, Automatica, 1976, 12(5): 457–465.

    Article  MathSciNet  Google Scholar 

  5. Deutscher J, Output regulation for linear distributed-parameter systems using finite-dimensional dual observers, Automatica, 2011, 47(11): 2468–2473.

    Article  MathSciNet  Google Scholar 

  6. Deutscher J, A backstepping approach to the output regulation of boundary controlled parabolic PDEs, Automatica, 2015, 57: 56–64.

    Article  MathSciNet  Google Scholar 

  7. Immonen E and Pohjolainen S, Feedback and feedforward output regulation of bounded uniformly continuous signals for infinite-dimensional systems, SIAM J. Control Optim., 2006, 45(5): 1714–1735.

    Article  MathSciNet  Google Scholar 

  8. Paunonen L and Pohjolainen S, The internal model principle for systems with unbounded control and observation, SIAM J. Control Optim., 2014, 52(6): 3967–4000.

    Article  MathSciNet  Google Scholar 

  9. Lamare P O and Bekiaris-Liberis N, Control of 2 × 2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking, Systems Control Lett., 2015, 86: 24–33.

    Article  MathSciNet  Google Scholar 

  10. Trinh N T, Andrieu V, and Xu C Z, Output regulation for a cascaded network of 2 × 2 hyperbolic systems with PI controller, Automatica, 2018, 91: 270–278.

    Article  MathSciNet  Google Scholar 

  11. Jin F F and Guo B Z, Boundary output tracking for an Euler-Bernoulli beam equation with unmatched perturbations from a known exosystem, Automatica, 2019, 109: 108507.

    Article  MathSciNet  Google Scholar 

  12. Deutscher J and Kerschbaum S, Output regulation for coupled linear parabolic PIDEs, Automatica, 2019, 100: 360–370.

    Article  MathSciNet  Google Scholar 

  13. Paunonen L, Robust controllers for regular linear systems with infinite-dimensional exosystems, SIAM J. Control Optim., 2017, 55(3): 1567–1597.

    Article  MathSciNet  Google Scholar 

  14. Xu X and Dubljevic S, Output and error feedback regulator designs for linear infinite-dimensional systems, Automatica, 2017, 83: 170–178.

    Article  MathSciNet  Google Scholar 

  15. Guo W, Guo B Z, and Jin F F, Performance output tracking and disturbance rejection for one-dimensional wave equation with boundary disturbance, IEEE Conference on Decision and Control, 2015, 1911–1916.

  16. Zhang X Y, Feng H, and Chai S G, Performance output exponential tracking for a wave equation with a general boundary disturbance, Systems Control Lett., 2016, 98: 79–85.

    Article  MathSciNet  Google Scholar 

  17. Jin F F and Guo B Z, Performance boundary output tracking for one-dimensional heat equation with boundary unmatched disturbance, Automatica, 2018, 96: 1–10.

    Article  MathSciNet  Google Scholar 

  18. Guo W and Krstic M, Finite-dimensional adaptive error feedback output regulation for 1D wave equation, IFAC papers online, 2017, 50: 9192–9197.

    Article  Google Scholar 

  19. Zhou H C and Guo B Z, Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control, Eur. J. Control, 2018, 39: 39–52.

    Article  MathSciNet  Google Scholar 

  20. Zhou H C and Guo B Z, Unknown input observer design and output feedback stabilization for multi-dimensional wave equation with boundary control matched uncertainty, J. Differential Equations, 2017, 263: 2213–2246.

    Article  MathSciNet  Google Scholar 

  21. Guo B Z and Zhao Z L, On convergence of the nonlinear active disturbance rejection control for MIMO Systems, SIAM J. Control Optim., 2013, 51(2): 1727–1757.

    Article  MathSciNet  Google Scholar 

  22. Feng H and Guo B Z, New unknown input observer and output feedback stabilization for uncertain heat equation, Automatica, 2017, 86: 1–10.

    Article  MathSciNet  Google Scholar 

  23. Pazy A, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.

    Book  Google Scholar 

  24. Weiss G, Admissibility of unbounded control operators, SIAM J. Control Optim., 1989, 27(3): 527–545.

    Article  MathSciNet  Google Scholar 

  25. Feng H and Guo B Z, A new active disturbance rejection control to output feedback stabilization for a one-dimensional anti-stable wave equation with disturbance, IEEE Trans. Automat. Control, 2017, 62(8): 3774–3787.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

    Jing Wei & Hongyinping Feng

Authors
  1. Jing Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongyinping Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongyinping Feng.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61873153 and 11671240.

This paper was recommended for publication by Editor SUN Jian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, J., Feng, H. Output Tracking for One-Dimensional Wave Equation with Non-Collocated Control and Output Configuration. J Syst Sci Complex 33, 1469–1484 (2020). https://doi.org/10.1007/s11424-020-8245-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-020-8245-6

Keywords

Search

Navigation