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Rejection and Attenuation of Multiple Disturbances for a Class of Uncertain Systems

  • Control Theory and Applications
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Abstract

A novel anti-disturbance strategy for a class of uncertain systems is investigated. Besides the unknown frequency sinusoidal, the controlled plant is subjected to bounded noise and unknown nonlinear term simultaneously. Through the construction of auxiliary observer, the sinusoidal is represented in a parametric uncertainty form. Only one unknown scalar needs estimating to construct compensation signal, meanwhile the unwanted nonlinear operation between frequency and equivalent disturbance can be removed. By integrating a feedback control law, all the unexpected dynamics can be rejected and attenuated respectively, where the conditions on the stability and optimal performance are also provided. Finally, a computer simulation example is presented to illustrate the effectiveness and the applicability of the suggested method.

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References

  1. K. K. Chew and M. Tomizuka, “Digital control of repetitive errors in disk drive systems,” IEEE Control Syst. Mag, vol. 10, no. 1, pp. 16–20, January 1990.

    Article  Google Scholar 

  2. W. H. Chen, “A nonlinear disturbance observer for robotic manipulators,” IEEE Transactions on Industrial Electronics, vol. 47, no. 4, pp. 932–938, August 2000.

    Article  Google Scholar 

  3. M. Bodson, J. S. Jensen, and S. C. Douglas, “Active noise control for periodic disturbances,” IEEE Transactions on Control Systems Technology, vol. 9, no. 1, pp. 200–205, January 2001.

    Article  Google Scholar 

  4. B. Xian and N. Jalili, “Adaptive tracking control of linear uncertain mechanical systems subjected to unknown sinusoidal disturbances,” Journal of Dynamic Systems, Measurement, and Control, vol. 125, no. 3, pp. 129–134, March 2003.

    Article  Google Scholar 

  5. X. K. Chen, C. Y. Su, and T. Fukuda, “A nonlinear disturbance observer for multivariable systems and its application to magnetic bearing systems,” IEEE Transactions on Control Systems Technology, vol. 312, no. 4, pp. 569–577, August 2004.

    Article  Google Scholar 

  6. H. Pham, H. Jung, and T. Hu, “State-space approach to modeling and ripple reduction in AC-DC converters,” IEEE Trans. Control Sys. Tech, vol. 21, no. 5, pp. 1949–1955, September 2013.

    Article  Google Scholar 

  7. J. Yang, J. Sun, W. Zheng, and S. Li, “Periodic event-triggered robust output feedback control for nonlinear uncertain systems with timevarying disturbance,” Automatica, vol. 94, no. 8, pp. 324–333, August 2018.

    Article  MathSciNet  Google Scholar 

  8. V. Nikiforov, “Nonlinear servocompensation of unknown external disturbances,” Automatica, vol. 37, no. 10, pp. 1647–1653, October 2001.

    Article  Google Scholar 

  9. Z. Ding, “Universal disturbance rejection for nonlinear systems in output feedback form,” IEEE Transactions on Automatic Control, vol. 48, no. 7, pp. 1222–1226, July 2003.

    Article  MathSciNet  Google Scholar 

  10. W. H. Chen, “Disturbance observer based control for nonlinear systems,” IEEE/ASME Transactions on Mechatronics, vol. 9, no. 4, pp. 706–710, December 2004.

    Article  Google Scholar 

  11. R. Marino and P. Tomei, “Adaptive tracking and disturbance rejection for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 90–95, Jan. 2005.

    Article  MathSciNet  Google Scholar 

  12. L. Guo and W. H. Chen, “Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach,” International Journal of Robust Nonlinear Control, vol. 15, no. 3, pp. 109–125, February 2005.

    Article  MathSciNet  Google Scholar 

  13. D. Karagiannis, M. Sassano, and A. Astolfi, “Dynamic scaling and observer design with application to adaptive control,” Automatica, vol. 45, no. 9, pp. 2883–2889, December 2009.

    Article  MathSciNet  Google Scholar 

  14. G. Fedele and A. Ferrise, “Biased sinusoidal disturbance compensation with unknown frequency,” IEEE Transactions on Automatic Control, vol. 8, no. 5, pp. 3207–3212, December 2013.

    Article  MathSciNet  Google Scholar 

  15. S. Jafari, P. Ioannou, B. Fitzpatrick, and Y. Wang, “Robustness and performance of adaptive suppression of unknown periodic disturbances,” IEEE Transactions on Automatic Control, pp. 2166–2171, August 2015.

  16. J. Yang, W. X. Zheng, and S. H. Li, “Design of a prediction accuracy enhanced continuous-time MPC for disturbed systems via a disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 62, pp. 5807–5816, September 2015.

    Article  Google Scholar 

  17. W. J. Qing, “Disturbance rejection through disturbance observer with adaptive frequency estimation,” IEEE Transactions on Magnetics, vol. 45, no. 6, pp. 2675–2678, July 2009.

    Article  Google Scholar 

  18. M. Hou, “Parameter identification of sinusoids,” IEEE Transactions on Automatic Control, vol. 57, no. 2, pp. 467–472, February 2012.

    Article  MathSciNet  Google Scholar 

  19. J. Na, J. Yang, X. Wu, and Y. Guo, “Robust adaptive parameter estimation of sinusoidal signals,” Automatica, vol. 53, pp. 376–384, March 2015.

    Article  MathSciNet  Google Scholar 

  20. J. Yang, Z. Ding, W. H. Chen, and S. H. Li, “Output-based disturbance rejection control for non-linear uncertain systems with unknown frequency disturbances using an observer backstepping approach,” IET Control Theory & Applications, vol. 10, no. 9, pp. 1052–1060, June 2016.

    Article  MathSciNet  Google Scholar 

  21. B. L. Chen, P. Li, G. Pin, G. Fedele, and T. Parisini, “Finite-time estimation of multiple exponentially-damped sinusoidal signals: A kernel-based approach,” Automatica, vol. 106, pp. 1–7, August 2019.

    Article  MathSciNet  Google Scholar 

  22. X. Y. Wen and P. Yan, “Two-layer observer based control for a class of uncertain systems with multifrequency disturbances,” ISA Transactions, vol. 63, no. 7, pp. 84–92, July 2016.

    Article  Google Scholar 

  23. L. Guo and X. Y. Wen, “Hierarchical anti-distance adaptive control for nonlinear systems with composite disturbances,” Transaction of the Institute of Measurement and Control, vol. 32, no. 2, pp. 942–956, December 2011.

    Article  Google Scholar 

  24. X. Y. Wen, L. Guo, and P. Yan, “Hierarchical anti-distance adaptive control for nonlinear systems with composite disturbances,” International Journal of Control, Automation, and Systems, vol. 12, no. 3, pp. 541–551, May 2014.

    Article  Google Scholar 

  25. X. J. Wei, Z. J. Wu, and R. K. Hamid, “Disturbance observer-based disturbance attenuation control for a class of stochastic systems,” Automatica, vol. 63, no. 1, pp. 21–25, January 2016.

    Article  MathSciNet  Google Scholar 

  26. Y. K. Zhu, J. Z. Qiao, and L. Guo, “Adaptive sliding mode disturbance observer-based composite control with prescribed performance of space manipulators for target capturing,” IEEE Transactions on Industrial Electronics, vol. 66, no. 3, pp. 1973–1983, March 2019.

    Article  Google Scholar 

  27. K. Hamed and G. Hamid, “Fuzzy logic self-tuning PID controller design for ball mill grinding circuits using an improved disturbance observer,” Mining Engineering, vol. 72, no. 2, pp. 58–59, February 2020.

    Google Scholar 

  28. M. Chen, W. H. Chen, and Q. X. Wu, “Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer,” Science China Information Sciences, vol. 57, no. 1, pp. 1–13, January 2014.

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Xin-Yu Wen & Ruo-Fan Li

  2. College of information Engineering, Yangzhou University, Yangzhou, 225009, China

    Song-Yin Cao

Authors
  1. Xin-Yu Wen
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  2. Ruo-Fan Li
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  3. Song-Yin Cao
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Correspondence to Xin-Yu Wen.

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Declaration of Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The project was supported by the National Science Foundation of China (61203049,61873346), Shanxi Province Natural Science Foundation(201801D121132), Shanxi Province Innovation Program for Postgraduates (2019SY489,2020SY424). Key R & D Program of Shanxi Province (International Cooperation, Grant 201903D421045), the Qinglan Project of Yangzhou University.

Xin-Yu Wen received his Ph.D. degree from the School of Automation, Southeast University in 2011. His research interests include nonlinear system control design, disturbance observer based control, sinusoidal signal estimation and rejection.

Ruo-Fan Li is now studying for a master’s degree at Taiyuan University of Science and Technology. Her research interests include sinusoidal signal estimation and rejection, disturbance observer based control.

Song-Yin Cao received his Ph.D. degree from the School of Automation, Southeast University, China, in 2011. Now, he is an associate professor at Yangzhou University. His current research interests include anti-disturbance control and estimation, fault-tolerant control, and inertial navigation system.

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Wen, XY., Li, RF. & Cao, SY. Rejection and Attenuation of Multiple Disturbances for a Class of Uncertain Systems. Int. J. Control Autom. Syst. 19, 2511–2518 (2021). https://doi.org/10.1007/s12555-020-0172-8

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  • DOI: https://doi.org/10.1007/s12555-020-0172-8

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