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Journal of Systems Science and Complexity

, Volume 29, Issue 5, pp 1187–1211 | Cite as

Tuning of sampled-data ADRC for nonlinear uncertain systems

  • Wenchao Xue
  • Yi Huang
Article

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.

Keywords

Active disturbance rejection control (ADRC) extended state observer nonlinear uncertain systems parameters tuning sampled-data control 

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References

  1. [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. [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.CrossRefGoogle Scholar
  3. [3]
    Han J, Auto-disturbance rejection control and its applications, Control and Decision, 1998, 13(1): 19–23 (in Chinese).Google Scholar
  4. [4]
    Han J, From PID to active disturbance rejection control, IEEE Transactions on Industrial Electronics, 2009, 56(3): 900–906.CrossRefGoogle Scholar
  5. [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.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Praly L and Jiang Z, Linear output feedback with dynamic high gain for nonlinear systems, Systems & Control Letters, 2004, 53: 53–107.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Chakrabortty A and Arcak M, Time-scale separation redesigns for stabilization and performance recovery of uncertain nonlinear systems, Automatica, 2009, 45: 45–34.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Yao X and Guo L, Composite anti-disturbance control for markovian jump nonlinear systems via disturbance observer, Automatica, 2013, 49(8): 2538–2545.MathSciNetCrossRefGoogle Scholar
  10. [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.CrossRefGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [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.CrossRefGoogle Scholar
  13. [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.CrossRefGoogle Scholar
  14. [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.CrossRefGoogle Scholar
  15. [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.CrossRefGoogle Scholar
  16. [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. [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.CrossRefGoogle Scholar
  18. [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.CrossRefGoogle Scholar
  19. [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. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [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.CrossRefGoogle Scholar
  22. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Han J, Active Disturbance Rjection Control Technique, National Defense Industry Press, Beijing, 2008 (in Chinese).Google Scholar
  24. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Nesic D and Grunea L, Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation, Automatica, 2005, 41: 41–1143.MathSciNetCrossRefGoogle Scholar
  26. [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. [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.MathSciNetCrossRefGoogle Scholar
  28. [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.MathSciNetCrossRefGoogle Scholar
  29. [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.MathSciNetzbMATHGoogle Scholar
  30. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [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.MathSciNetzbMATHGoogle Scholar
  32. [32]
    Ma H, Further results on limitations to the capability of feedback, International Journal of Control, 2008, 81(1): 21–42.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [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.MathSciNetCrossRefGoogle Scholar
  34. [34]
    Gao Z, Scaling and bandwidth-parameterization based controller tuning, Proceedings of the 2003 American Control Conference, Denver, Colorado, 2003.Google Scholar
  35. [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

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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