Skip to main content
Log in

Tuning of sampled-data ADRC for nonlinear uncertain systems

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

Abstract

This paper concerns with the parameters tuning of active disturbance rejection control (ADRC) for a class of nonlinear systems with sampling rate not fast enough. The theoretical results show the quantitative relationship between the sampling rate, the parameters of ADRC, the size of uncertainties in system and the properties of the closed-loop system. Furthermore, the capability of the sampled-data ADRC under given sampling rate is quantitatively discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Nakao M, Ohnishi K, and Miyachi K, A robust decentralized joint control based on interference estimation, Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, 1987.

    Google Scholar 

  2. Schrijver E and Dijk J, Disturbance observers for rigid mechanical systems: Equivalence,stability, and design, Journal of Dynamic Systems, Measurement, and Control, 2002, 124(4): 539–548.

    Article  Google Scholar 

  3. Han J, Auto-disturbance rejection control and its applications, Control and Decision, 1998, 13(1): 19–23 (in Chinese).

    Google Scholar 

  4. Han J, From PID to active disturbance rejection control, IEEE Transactions on Industrial Electronics, 2009, 56(3): 900–906.

    Article  Google Scholar 

  5. Freidovich L B and Khalil H K, Performance recovery of feedback-linearization based designs, IEEE Transactions on Automatic Control, 2008, 53(10): 2324–2334.

    Article  MathSciNet  Google Scholar 

  6. Praly L and Jiang Z, Linear output feedback with dynamic high gain for nonlinear systems, Systems & Control Letters, 2004, 53: 53–107.

    MathSciNet  MATH  Google Scholar 

  7. Chakrabortty A and Arcak M, Time-scale separation redesigns for stabilization and performance recovery of uncertain nonlinear systems, Automatica, 2009, 45: 45–34.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yang J, Li S, and Chen W H, Nonlinear disturbance observer-based control for multi-input multioutput nonlinear systems subject to mismatching condition, International Journal of Control, 2012, 85(8): 1071–1082.

    Article  MathSciNet  MATH  Google Scholar 

  9. Yao X and Guo L, Composite anti-disturbance control for markovian jump nonlinear systems via disturbance observer, Automatica, 2013, 49(8): 2538–2545.

    Article  MathSciNet  Google Scholar 

  10. Xia Y, Zhu Z, Fu M, et al., Attitude tracking of rigid spacecraft with bounded disturbances, IEEE Transactions on Industrial Electronics, 2011, 58(2): 647–659.

    Article  Google Scholar 

  11. Wu D and Chen K, Design and analysis of precision active disturbance rejection control for noncircular turning process, IEEE Transactions on Industrial Electronics, 2009, 56(7): 2746–2753.

    Article  Google Scholar 

  12. Li S and Liu Z, Adaptive speed control for permanent-magnet synchronous motor system with variations of load inertia, IEEE Transactions on Industrial Electronics, 2009, 56(8): 3050–3059.

    Article  Google Scholar 

  13. Sun M, Wang Z, Wang Y, et al., On low-velocity compensation of brushless dc servo in the absence of friction model, IEEE Transactions on Industrial Electronics, 2013, 60(9): 3897–3905.

    Article  Google Scholar 

  14. Talole S E, Kolhe J P, and Phadke S B, Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer, IEEE Transactions on Industrial Electronics, 2010, 57(4): 1411–1419.

    Article  Google Scholar 

  15. Su J, Ma H, Qiu W, et al., Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer, IEEE Transactions on Systems, Man, And Cybernetics, Part B: Cybernetics, 2004, 34(4): 1917–1922.

    Article  Google Scholar 

  16. Zheng Q, Dong L, Lee D H, et al., Active disturbance rejection control for mems gyroscopes, IEEE Transactions on Industrial Electronics, 2009, 17(6): 1432–1438.

    Google Scholar 

  17. Vincent J, Morris D, Usher N, et al., On active disturbance rejection based control design for superconducting RF cavities, Nuclear Instruments and Methods in Physics Research A, 2011, 643: 643–11.

    Article  Google Scholar 

  18. Huang C, Li D, and Xue L, Acitve disturbance rejection control for the alstom gasifier benchmark problem, Control Engineering Practice, 2013, 21(4): 556–564.

    Article  Google Scholar 

  19. Zheng Q, Chen Z, and Gao Z, A practical approach to disturbance decoupling control, Control Engineering Practice, 2009, 17: 17–1016.

    Google Scholar 

  20. Zhao C and Huang Y, ADRC based input disturbance rejection for minimum-phase plants with unknown orders and/or uncertain relative degrees, Journal of Systems Science Complexity, 2012, 25(4): 625–640.

    Article  MathSciNet  MATH  Google Scholar 

  21. Yang R, Sun M, and Chen Z, Active disturbance rejection control on first-order plant, Journal of Systems Engineering and Electronics, 2011, 22(1): 95–102.

    Article  Google Scholar 

  22. Guo B and Zhao Z, On convergence of the nonlinear active disturbance rejection control for mimo systems, SIAM J. Control and Optimization, 2013, 51(2): 1727–1757.

    Article  MathSciNet  MATH  Google Scholar 

  23. Han J, Active Disturbance Rjection Control Technique, National Defense Industry Press, Beijing, 2008 (in Chinese).

    Google Scholar 

  24. Yoo D, Yau S S T, and Gao Z, Optimal fast tracking observer bandwidth of the linear extended state observer, International Journal of Control, 2007, 80(1): 102–111.

    Article  MathSciNet  MATH  Google Scholar 

  25. Nesic D and Grunea L, Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation, Automatica, 2005, 41: 41–1143.

    Article  MathSciNet  Google Scholar 

  26. Grunea L, Worthmanna K, and Nesic D, Continuous-time controller redesign for digital implementation: Atrajectory based approach, Automatica, 2008, 44: 44–225.

    Google Scholar 

  27. Nesic D and Laila D S, A note on input-to-state stabilization for nonlinear sampled-data systems, IEEE Transactions on Automatic Control, 2002, 47(7): 1153–1158.

    Article  MathSciNet  Google Scholar 

  28. Postoyana R, Ahmed-Alib T, and Lamnabhi-Lagarrigued F, Robust backstepping for the euler approximate model of sampled-data strict-feedback systems, Automatica, 2009, 45: 45–2164.

    Article  MathSciNet  Google Scholar 

  29. Karafyllis I and Kravaris C, Robust global stabilisability by means of sampled-data control with positive sampling rate, Automatica, 2009, 82(4): 755–772.

    MathSciNet  MATH  Google Scholar 

  30. Xie L and Guo L, How much uncertainty can be dealt with by feedback?, IEEE Transactions on Automatic Control, 2000, 45(12): 2203–2217.

    Article  MathSciNet  MATH  Google Scholar 

  31. Xue F and Guo L, On limitations of the sampled-data feedback for nonparamtric dynamical systems, Journal of Systems Science and Complexity, 2002, 15(3): 225–250.

    MathSciNet  MATH  Google Scholar 

  32. Ma H, Further results on limitations to the capability of feedback, International Journal of Control, 2008, 81(1): 21–42.

    Article  MathSciNet  MATH  Google Scholar 

  33. Li C and Guo L, On feedback capability in a class of nonlinearly parameterized uncertain systems, IEEE Transactions on Automatic Control, 2011, 56(12): 2946–2950.

    Article  MathSciNet  Google Scholar 

  34. Gao Z, Scaling and bandwidth-parameterization based controller tuning, Proceedings of the 2003 American Control Conference, Denver, Colorado, 2003.

    Google Scholar 

  35. Xue W and Huang Y, On frequency-domain analysis of ADRC for uncertain system, Proceedings of the 2013 American Control Conference, Washington, D.C., 2013.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wenchao Xue.

Additional information

This research was supported by the National Basic Research Program of China (973 Program) under Grant No. 2014CB845303 and the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences.

This paper was recommended for publication by Editor LIU Yungang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xue, W., Huang, Y. Tuning of sampled-data ADRC for nonlinear uncertain systems. J Syst Sci Complex 29, 1187–1211 (2016). https://doi.org/10.1007/s11424-016-4285-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-016-4285-3

Keywords

Navigation