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Peaking Reduction of CRM-Based Adaptive Control via a Modified Adaptive Law

  • Yafei Liu
  • Jun Yang
  • Jing NaEmail author
  • Guanbin Gao
  • Shubo Wang
  • Qiang Chen
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)

Abstract

To circumvent the oscillations induced by high-gain adaptation in the model reference adaptive control (MRAC), closed-loop reference model (CRM) based MRAC was recently proposed. However, although a fair steady-state performance can be guaranteed, the induced peaking phenomenon in the CRM based adaptive control system may deteriorate the transient tracking response. In this paper, we first analyze the peaking value based on L2 norm and Cauchy-Schwartz inequality. Then according to the analysis, a novel adaptive law containing the parameter estimation error is constructed to alleviate the peaking phenomenon. This proposed method can allow using a fairly large feedback gain in the CRM based MRAC system to achieve better transient performance. Experiment results based on a 3-DOF helicopter show that the modified CRM adaptive control system can alleviate the peaking phenomenon.

Keywords

Closed-loop reference model Adaptive control Peaking phenomenon Parameter estimation 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant 61573174 and 61922037).

References

  1. 1.
    Yucelen, T., Calise, A.J.: Kalman filter modification in adaptive control. J. Guid. Control Dyn. 33, 426–439 (2010)CrossRefGoogle Scholar
  2. 2.
    Gibson, T.E., Annaswamy, A.M., Lavretsky, E.: On adaptive control with closed-loop reference models: transients, oscillations, and peaking. IEEE Access 1, 703–717 (2013)CrossRefGoogle Scholar
  3. 3.
    Na, J., Herrmann, G., Zhang, K.: Improving transient performance of adaptive control via a modified reference model and novel adaptation. Int. J. Robust Nonlinear Control 27, 1351–1372 (2017)CrossRefGoogle Scholar
  4. 4.
    Yang, J., Liu, Y., Na, J., Gao, G.: Improving transient performance of modified model reference adaptive control. In: Innovative Techniques and Applications of Modelling, Identification and Control, pp. 331–343 (2018)Google Scholar
  5. 5.
    Xiao, L., Liu, F., Xue, L., Yu, G.: Parameter identification and optimisation for a class of fractional-order chaotic system with time delay. Int. J. Model. Ident. Control 29, 1–12 (2018)CrossRefGoogle Scholar
  6. 6.
    Lee, T.G., Huh, U.Y.: An error feedback model based adaptive controller for nonlinear systems. In: IEEE International Symposium on Industrial Electronics, pp. 1095–1100 (1997)Google Scholar
  7. 7.
    Stepanyan, V., Krishnakumar, K.: M-MRAC for nonlinear systems with bounded disturbances. In: Decision and Control and European Control Conference, Orlando, FL, USA, pp. 5419–5424 (2011)Google Scholar
  8. 8.
    Lavretsky, E.: Combined/composite model reference adaptive control. IEEE Trans. Autom. Control 54, 2692–2697 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lavretsky, E.: Reference dynamics modification in adaptive controllers for improved transient performance. In: AIAA Guidance, Navigation, and Control Conference, Portland, Oregon (2006)Google Scholar
  10. 10.
    Stepanyan, V., Krishnakumar, K.: MRAC revisited: guaranteed performance with reference model modification. In: American Control Conference, Marriott Waterfront, Baltimore, MD, USA, pp. 93–98 (2010)Google Scholar
  11. 11.
    Narendra, K.S., Annaswamy, A.M.: Stable Adaptive Systems. Prentice-Hall (1989)Google Scholar
  12. 12.
    Na, J., Mahyuddin, M.N., Herrmann, G., Ren, X.: Robust adaptive finite-time parameter estimation and control for robotic systems. Int. J. Robust Nonlinear Control 25, 3045–3071 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yang, J., Na, J., Gao, G.: Robust adaptive control with a modified controller for transient response improvement. In: 2017 9th International Conference on Modelling, Identification and Control, Kunming, China, pp. 929–934 (2017)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Yafei Liu
    • 1
  • Jun Yang
    • 1
  • Jing Na
    • 1
    Email author
  • Guanbin Gao
    • 1
  • Shubo Wang
    • 2
  • Qiang Chen
    • 3
  1. 1.Faculty of Mechanical & Electrical EngineeringKunming University of Science & TechnologyKunmingChina
  2. 2.School of AutomationQingdao UniversityQingdaoChina
  3. 3.College of Information EngineeringZhejiang University of TechnologyHangzhouChina

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