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Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1561–1582 | Cite as

Integral Sliding Mode Control for Singularly Perturbed Systems with Mismatched Disturbances

  • Chunyu YangEmail author
  • Zhiyuan Che
  • Linna Zhou
Article
  • 49 Downloads

Abstract

This paper presents a novel integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. A singular perturbation parameter \(\varepsilon \)-dependent disturbance observer is constructed to estimate the disturbances. An ISMC which incorporates the disturbance vector estimate is designed, such that the reachability condition is guaranteed. In order to compensate the effect of mismatched components of the disturbances extracted by the projection matrix theory, \({H_\infty }\) control theory is employed to determine the gain of ISMC by solving a set of linear matrix inequalities. As a result, the closed-loop SPSs under the ISMC are internally exponentially stable with the \({H_\infty }\) performance index guaranteed. Finally, the effectiveness and advantages of the proposed method are demonstrated by two examples.

Keywords

Singularly perturbed systems (SPSs) Mismatched disturbances Integral sliding mode control (ISMC) Linear matrix inequalities (LMIs) 

Notes

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (2017XKQY055).

References

  1. 1.
    A.E. Ahmed, H.M. Schwartz, V.C. Aitken, Sliding mode control for singularly perturbed system, in Proceedings of 5th Asian Control Conference (2004), pp. 1946–1950Google Scholar
  2. 2.
    B. Barmish, G. Leitmann, On ultimate boundedness control of uncertain systems in the absence of matching condition. IEEE Trans. Autom. Control 27(1), 153–158 (1982)zbMATHGoogle Scholar
  3. 3.
    F. Castanos, L. Fridman, Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Trans. Autom. Control 51(5), 853–858 (2006)MathSciNetzbMATHGoogle Scholar
  4. 4.
    W.H. Chen, Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. J. Guid. Control Dyn. 26(1), 161–166 (2003)Google Scholar
  5. 5.
    H.H. Choi, LMI-based sliding surface design for integral sliding model control of mismatched uncertain systems. IEEE Trans. Autom. Control 52(4), 736–742 (2007)zbMATHGoogle Scholar
  6. 6.
    B.L. Cong, Z. Chen, X.D. Liu, On adaptive sliding mode control without switching gain overestimation. Int. J. Robust Nonlinear Control 24(3), 515–531 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Z. Gao, X.Z. Liao, Integral sliding mode control for fractional-order systems with mismatched uncertainties. Nonlinear Dyn. 72(1), 27–35 (2013)MathSciNetGoogle Scholar
  8. 8.
    Y.B. Gao, G.P. Lu, Z.M. Wang, Passivity analysis of uncertain singularly perturbed systems. IEEE Trans. Circuits Syst. II Express Briefs 57(6), 486–490 (2010)Google Scholar
  9. 9.
    Y.B. Gao, B.H. Sun, G.P. Lu, Passivity-based integral sliding-mode control of uncertain singularly perturbed systems. IEEE Trans. Circuits Syst. II Express Briefs 58(6), 386–390 (2011)Google Scholar
  10. 10.
    B. Heck, Sliding-mode control for singularly perturbed systems. Int. J. Control 53(4), 985–1001 (1991)MathSciNetzbMATHGoogle Scholar
  11. 11.
    J. Hu, Z.D. Wang, H.J. Gao, L.K. Stergioulas, Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities. IEEE Trans. Ind. Electron. 59(7), 3008–3015 (2012)Google Scholar
  12. 12.
    M. Innocenti, L. Greco, L. Pollini, Sliding mode control for two-time scale systems: stability issues. Automatica 39(2), 273–280 (2003)MathSciNetzbMATHGoogle Scholar
  13. 13.
    T.H. Li, J.L. Lin, F.C. Kung, Composite sliding-mode control of singular perturbation systems, in Proceedings of American Control Conference (1995), pp. 2248–2249Google Scholar
  14. 14.
    S.H. Li, J. Yang, W.H. Chen, X.S. Chen, Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Trans. Ind. Electron. 59(12), 4792–4802 (2012)Google Scholar
  15. 15.
    S.H. Li, K. Zong, H.X. Liu, A composite speed controller based on a second-order model of permanent magnet synchronous motor system. Trans. Inst. Meas. Control 33(5), 522–541 (2011)Google Scholar
  16. 16.
    H.X. Liu, S.H. Li, Speed control for PMSM servo system using predictive function control and extended state observer. IEEE Trans. Ind. Electron. 59(2), 1171–1183 (2012)Google Scholar
  17. 17.
    W. Liu, Y.Y. Wang, Z.H. Wang, \({H_\infty }\) observer-based sliding mode control for singularly perturbed systems with input nonlinearity. Nonlinear Dyn. 85(1), 573–582 (2016)zbMATHGoogle Scholar
  18. 18.
    M. Liu, L.X. Zhang, P. Shi, H.R. Karimi, Robust control of stochastic systems against bounded disturbances with application to flight control. IEEE Trans. Ind. Electron. 61(3), 1504–1515 (2014)Google Scholar
  19. 19.
    Z. Liu, L. Zhao, H.M. Xiao, C.C. Gao, Adaptive \({H_\infty }\) integral sliding mode control for uncertain singular time-delay systems based on observer. Circuits Syst. Signal Process. 36(11), 4365–4387 (2017)MathSciNetzbMATHGoogle Scholar
  20. 20.
    X.P. Ma, Q.J. Wang, L.N. Zhou, C.Y. Yang, Controller design and analysis for singularly perturbed switched systems with actuator saturation. Int. J. Robust Nonlinear Control 26(15), 3404–3420 (2016)MathSciNetzbMATHGoogle Scholar
  21. 21.
    M. Morawiec, The adaptive backstepping control of permanent magnet synchronous motor supplied by current source inverter. IEEE Trans. Indus. Inform. 9(2), 1047–1055 (2013)Google Scholar
  22. 22.
    R.K. Munje, B.B. Musmade, J.G. Parkhe, B.M. Patre, Sliding mode control for three time scale system with matched disturbances, in Proceedings of India Conference (2012), pp. 131–136Google Scholar
  23. 23.
    R.K. Munje, B.M. Patre, S.R. Shimjith, A.P. Tiwari, Sliding mode control for spatial stabilization of advanced heavy water reactor. IEEE Trans. Nucl. Sci. 60(4), 3040–3050 (2013)Google Scholar
  24. 24.
    T. Nguyen, W.C. Su, Z. Gajic, Variable structure control for singularly perturbed linear continuous systems with matched disturbances. IEEE Trans. Autom. Control 57(3), 777–783 (2012)MathSciNetzbMATHGoogle Scholar
  25. 25.
    T. Nguyen, W.C. Su, Z. Gajic, Sliding mode control for singularly perturbed linear continuous time systems: composite control approaches, in Proceedings of IEEE International Symposium on Computer-Aided Control System Design (2010), pp. 2011–2016Google Scholar
  26. 26.
    Z.H. Shao, Robust stability of two-time-scale systems with nonlinear uncertainties. IEEE Trans. Autom. Control 49(2), 258–261 (2004)MathSciNetzbMATHGoogle Scholar
  27. 27.
    W.C. Su, Sliding surface design for singularly perturbed systems. Int. J. Control 72(11), 990–995 (1999)MathSciNetzbMATHGoogle Scholar
  28. 28.
    H.C. Ting, J.L. Chang, Y.P. Chen, Output feedback integral sliding mode controller of time-delay systems with mismatch disturbances. Asian J. Control 14(1), 85–94 (2012)MathSciNetzbMATHGoogle Scholar
  29. 29.
    S.C. Tong, Y.M. Li, Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones. IEEE Trans. Fuzzy Syst. 20(1), 168–180 (2012)Google Scholar
  30. 30.
    S.W. Wang, D.W. Yu, D.L. Yu, Compensation for unmatched uncertainty with adaptive RBF network. Int. J. Eng. Sci. Technol. 3(6), 35–43 (2011)Google Scholar
  31. 31.
    G.L. Wang, Q.L. Zhang, C.Y. Yang, Exponential stability of stochastic singular delay systems with general Markovian switchings. Int. J. Robust Nonlinear Control 25(17), 3478–3494 (2015)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Z.G. Wu, P. Shi, H.Y. Su, J. Chu, Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Trans. Cybern. 43(6), 1796–1806 (2013)Google Scholar
  33. 33.
    J. Yang, W.H. Chen, S.H. Li, Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties. IET Control Theory Appl. 5(18), 2053–2062 (2011)MathSciNetGoogle Scholar
  34. 34.
    J. Yang, S.H. Li, J.Y. Su, X.H. Yu, Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances. Automatica 49(7), 2287–2291 (2013)MathSciNetzbMATHGoogle Scholar
  35. 35.
    J. Yang, S.H. Li, C.Y. Sun, L. Guo, Nonlinear-disturbance-observer-based robust flight control for airbreathing hypersonic vehicles. IEEE Trans. Aerosp. Electron. Syst. 49(2), 1263–1275 (2013)Google Scholar
  36. 36.
    J. Yang, S.H. Li, X.H. Yu, Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans. Ind. Electron. 60(1), 160–169 (2012)Google Scholar
  37. 37.
    C.Y. Yang, T.T. Ma, Z.Y. Che, L.N. Zhou, An adaptive-gain sliding mode observer for sensorless control of permanent magnet linear synchronous. IEEE Access 6(1), 3469–3478 (2018)Google Scholar
  38. 38.
    C.Y. Yang, L. Ma, X.P. Ma, X.S. Wang, Stability analysis of singularly perturbed control systems with actuator saturation. J. Frankl. Inst. 353(6), 1284–1296 (2016)MathSciNetzbMATHGoogle Scholar
  39. 39.
    P. Yang, J.F. Ni, X. Pan, J.W. Liu, Global robust sliding mode control for time-delay systems with mismatched uncertainties. Circuits Syst. Signal Process. 35(8), 3015–3026 (2016)zbMATHGoogle Scholar
  40. 40.
    C.Y. Yang, J. Sun, X.P. Ma, Stabilization bound of singularly perturbed systems subject to actuator saturation. Automatica 49(2), 457–462 (2013)MathSciNetzbMATHGoogle Scholar
  41. 41.
    L. Yang, J.Y. Yang, Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int. J. Robust Nonlinear Control 21(16), 1865–1879 (2011)MathSciNetzbMATHGoogle Scholar
  42. 42.
    L. Yang, S. Yang, B. Richard, Modeling and robust discrete-time sliding-mode control design for a fluid power electrohydraulic actuator (EHA) system. IEEE/ASME Trans. Mechatron 18(1), 1–10 (2013)Google Scholar
  43. 43.
    C.Y. Yang, Q.L. Zhang, Multiobjective control for T–S fuzzy singularly perturbed systems. IEEE Trans. Fuzzy Syst. 17(1), 104–115 (2009)Google Scholar
  44. 44.
    C.Y. Yang, Q.L. Zhang, J. Sun, T.Y. Chai, Lur’e Lyapunov function and absolute stability criterion for Lur’e singularly perturbed systems. IEEE Trans. Autom. Control 56(11), 2666–2671 (2011)MathSciNetzbMATHGoogle Scholar
  45. 45.
    C.Y. Yang, L.N. Zhou, \({H_\infty }\) control and \(\varepsilon \)-bound estimation of discrete-time singularly perturbed systems. Circuits Syst. Signal Process. 35(7), 2640–2654 (2016)MathSciNetzbMATHGoogle Scholar
  46. 46.
    J. Yang, A. Zolotas, W.H. Chen, K. Michail, S.H. Li, Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach. ISA Trans. 50(3), 389–396 (2011)Google Scholar
  47. 47.
    J.Y. Yao, Z.X. Jiao, D.W. Ma, Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with backstepping. IEEE Trans. Ind. Electron. 61(11), 6285–6293 (2014)Google Scholar
  48. 48.
    X.H. Yu, O. Kaynak, Sliding-mode control with soft computing: a survey. IEEE Trans. Ind. Electron. 56(9), 3275–3285 (2009)Google Scholar
  49. 49.
    D. Yue, S.F. Xu Sliding mode control of singular perturbation systems, in Proceedings of the IEEE International Conference on Systems (1996), pp. 113–116Google Scholar
  50. 50.
    J.H. Zhang, G. Feng, Y.Q. Xia, Design of estimator-based sliding-mode output-feedback controllers for discrete-time systems. IEEE Trans. Ind. Electron. 61(5), 2432–2440 (2014)Google Scholar
  51. 51.
    J.H. Zhang, X.W. Liu, Y.Q. Xia, Z.Q. Zuo, Y.J. Wang, Disturbance observer based integral sliding mode control for systems with mismatched disturbances. IEEE Trans. Ind. Electron. 63(11), 7041–7047 (2016)Google Scholar
  52. 52.
    J.H. Zhang, P. Shi, Y.Q. Xia, Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties. IEEE Trans. Fuzzy Syst. 18(4), 700–711 (2010)Google Scholar
  53. 53.
    J.H. Zhang, W.X. Zheng, Design of adaptive sliding mode controllers for linear systems via output feedback. IEEE Trans. Ind. Electron. 61(7), 3553–3562 (2014)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information and Control EngineeringChina University of Mining and TechnologyXuzhouPeople’s Republic of China

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