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Fractional-disturbance-observer-based Sliding Mode Control for Fractional Order System with Matched and Mismatched Disturbances

  • Sheng-Li Shi
  • Jian-Xiong Li
  • Yi-Ming FangEmail author
Article
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Abstract

This paper addresses the sliding mode control for a class of fractional order systems with matched and mismatched disturbances. Firstly, fractional disturbance observer is presented to estimate both the matched and mismatched disturbances, and the boundedness of the estimation error can be guaranteed. Secondly, sliding mode surface is constructed based on the output of the observer. The bounded stability of the closed-loop system under the designed controller is revealed by theoretical analysis. Finally, simulation results show that the proposed control strategy can effectively suppress the effect of the matched and mismatched disturbances on the system.

Keywords

Fractional disturbance observer fractional order system matched and mismatched disturbances sliding mode control 

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References

  1. [1]
    S. Pashaei, and M. Badamchizadeh, “A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances,” ISA Transactions, vol. 63, pp. 39–48, July 2016.CrossRefGoogle Scholar
  2. [2]
    X. Li, K. Pan, G. Fan, R. Lu, C. Zhu, G. Rizzoni, and M. Canova, “A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis,” Journal of Power Sources, vol. 367, pp. 187–201, November 2017.CrossRefGoogle Scholar
  3. [3]
    R. Liu, Z. Nie, M. Wu, and J. She, “Robust disturbance rejection for uncertain fractional-order systems,” Applied Mathematics and Computation, vol. 322, pp. 79–88, April 2018.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Y. Chen, Y. Wei, X. Zhou, and Y. Wang, “Stability for nonlinear fractional order systems: an indirect approach,” Nonlinear Dynamics, vol. 89, no. 2, pp. 1011–1018, April 2017.CrossRefzbMATHGoogle Scholar
  5. [5]
    H. Liu, S. Li, J. Cao, G. Li, A. Alsaedi, and F. Alsaadi, “Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances,” Neurocomputing, vol. 219, no. 1, pp. 422–430, January 2017.CrossRefGoogle Scholar
  6. [6]
    S. Tabatabaei, H. Talebi, and M. Tavakoli, “An adaptive order/state estimator for linear systems with non-integer time-varying order,” Automatica, vol. 84, no. 10, pp. 1–9, October 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    C. Hua, and X. Guan, “Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties,” Automatica, vol. 68, pp. 1–8, June 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    H. Sun, Y. Li, G. Zong, L. Hou, “Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities,” Automatica, vol. 89, pp. 349–357, March 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    W. Qi, G. Zong, and H. Karimi, “ L control for positive delay systems with semi-Markov process and application to a communication network model,” IEEE Transactions on Industrial Electronics, vol. 66, no. 3, pp. 2081–2091, March 2019.CrossRefGoogle Scholar
  10. [10]
    S. Shi, K. Kang, J. Li, and Y. Fang, “Sliding mode control for continuous casting mold oscillatory system driven by servo motor,” International Journal of Control, Automation, and Systems, vol. 15, no. 4, pp. 1669–1674, June 2017.CrossRefGoogle Scholar
  11. [11]
    Z. Wang, X. Huang, and H. Shen, “Control of an uncertain fractional order economic system via adaptive sliding mode,” Neurocomputing, vol. 83, no. 6, pp. 83–88, April 2012.CrossRefGoogle Scholar
  12. [12]
    M. Aghababa, “Control of fractional-order systems using chatter-free sliding mode approach,” Journal of Computational and Nonlinear Dynamics, vol. 9, no. 3, pp. 1081–1089, February 2014.MathSciNetGoogle Scholar
  13. [13]
    M. Aghababa, “A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems,” Nonlinear Dynamics, vol. 78, no. 3, pp. 2129–2140, November 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Y. Chun, Y. Chen, and S. M. Zhong, “LMI based design of a sliding mode controller for a class of uncertain fractional-order nonlinear systems,” Proc. of American Control Conference, pp. 6511–6516, June 2013.Google Scholar
  15. [15]
    S. Dadras, S. Dadras, and H. Momeni, “Linear matrix inequality based fractional integral sliding-mode control of uncertain fractional-order nonlinear systems,” Journal of Dynamic Systems Measurement and Control, vol. 139, no. 11, pp. 111003-1-7, July 2017.CrossRefzbMATHGoogle Scholar
  16. [16]
    Z. Gao, and X. Z. Liao, “Integral sliding mode control for fractional-order systems with mismatched uncertainties,” Nonlinear Dynamics, vol. 72, no. 1-2, pp. 27–35, April 2013.MathSciNetCrossRefGoogle Scholar
  17. [17]
    L. Chen, R. Wu, Y. He, and Y. Chai, “ Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances,” Nonlinear Dynamics, vol. 80, no. 1-2, pp. 51–58, April 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Y. Guo, B. Ma, L. Chen, and R. Wu, “Adaptive sliding mode control for a class of Caputo type fractional-order interval systems with perturbation,” IET Control Theory and Applications, vol. 11, no. 1, pp. 57–65, January 2017.MathSciNetCrossRefGoogle Scholar
  19. [19]
    N. Djeghali, S. Djennoune, M. Bettayeb, M. Ghanes, and J. Barbot, “Observation and sliding mode observer for nonlinear fractional-order system with unknown input,” ISA Transactions, vol. 63, pp. 1–10, July 2016.CrossRefGoogle Scholar
  20. [20]
    S. Shao, M. Chen, and X. Yan, “Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance,” Nonlinear Dynamics, vol. 83, no. 4, pp. 1855–1866, March 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S. Shi, “Extended disturbance observer based sliding mode control for fractional-order systems,” Proc. of the 36th Chinese Control Conference, pp. 11385–11389, July 2017.Google Scholar
  22. [22]
    J. Yang, S. Li, and X. Yu, “Sliding mode control for systems with mismatched uncertainties via a disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 160–169, January 2013.CrossRefGoogle Scholar
  23. [23]
    A. Norelys, D. Manuel, and G. Javier, “Lyapunov functions for fractional order systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2951–2957, September 2014.MathSciNetCrossRefGoogle Scholar
  24. [24]
    D. Matignon, “Stability results for fractional differential equations with applications to control processing,” Computational Engineering in Systems Applications, vol. 2, pp. 963–968, 1996.Google Scholar
  25. [25]
    L. Chen, G. Chen, R. Wu, J. Machado, A. Lopes, and S. Ge, “Stabilization of uncertain multi-order fractional systems based on the extended state observer,” Asian Journal of Control, vol. 20, no. 3, pp. 1263–1273, May 2018.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    C. Li and W. Deng, “Remarks on fractional derivatives,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 777–784, April 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    A. Jmal, O. Naifar, A. Makhouf, N. Derbel, and M. Hammami, “On observer design for nonlinear Caputo fractional-order systems,” Asian Journal of Control, vol. 20, no. 4, pp. 1533–1540, July 2018.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© CROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of ScienceYanshan UniversityQinhuangdaoChina
  2. 2.Key Lab of Industrial Computer Control Engineering of Hebei ProvinceYanshan UniversityQinhuangdaoChina
  3. 3.National Engineering Research Center for Equipment and Technology of Cold Strip RollingYanshan UniversityQinhuangdaoChina

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