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Sliding Mode Control for Nonlinear Discrete Time Systems with Matching Perturbations

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Applied Methods and Techniques for Mechatronic Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 452))

Abstract

This chapter considers sliding mode control of nonlinear discrete time systems with matching perturbations. The nonlinear sliding mode controller, whose parameters assure the closed-loop system stable, is designed in order to drive the state trajectories toward to a small bounded region. The controller is approximated by a polynomial equation in current control term \(u(k)\) according to Taylor series expansion. The algebraic solutions can be obtained by resolving a polynomial equation in the latest control term \(u(k)\). The integrated procedure provides a straightforward methodology to apply sliding mode control design technique for nonlinear systems. The simulation results are provided to illustrate the effectiveness of the proposed scheme.

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References

  1. Gao W, Wang Y, Homaifa A (1995) Discrete-time variable structure control systems. IEEE Trans Ind Electron 42(2):117–122

    Article  Google Scholar 

  2. Milosavljevic D (1985) General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems. Autom Remote Control 46(30):307–314

    MATH  Google Scholar 

  3. Sarpturk SZ, Istefanopulos Y, Kaynak O (1987) On the stability of discrete variable structure systems. IEEE Trans Autom Control 32(10):930–932

    Article  MATH  Google Scholar 

  4. Furuta K (1990) Sliding mode control of a discrete system. Syst Control Lett 14:145–152

    Article  MATH  MathSciNet  Google Scholar 

  5. Wang WJ, Wu GH, Yang DC (1994) Variable structure control design for uncertain discrete time systems. IEEE Trans Autom Control 39(1):99–102

    Article  MATH  MathSciNet  Google Scholar 

  6. Utkin V, Drakunov S (1989) On discrete-time sliding mode control. In: Proceedings of IFAC symposium on nonlinear control system, Capri, Italy, pp 484–489

    Google Scholar 

  7. Su WC, Drakunov SV, Üzgüner Ü (2000) An \(O\left( T^{2} \right)\) boundary layer in sliding mode for sampled-data systems. IEEE Trans Autom Control 45(3):482–485

    Article  MATH  Google Scholar 

  8. Cheng C-C, Lin M-H, Hsiao J-M (2000) Sliding mode controllers design for linear discrete-time systems with matching perturbations. Automatica 36(8):1205–1211

    Article  MathSciNet  Google Scholar 

  9. Corradini ML, Orlando G (1998) Variable structure control of discretized continuous-time systems. IEEE Trans Autom Control 43:1329–1334

    Article  MATH  MathSciNet  Google Scholar 

  10. Utkin V, Gulder J, Shi J (2009) Sliding mode control in electro-mechanical systems, 2nd edn. Taylor and Francis, London

    Google Scholar 

  11. Zhu QM, Guo LZ (2010) A pole placement controller for non-linear dynamic plants. Proc Instn Mech Eng Part I: J Syst Control Eng 216:467–476

    Google Scholar 

  12. Taylora CJ, Chotaib A, Young PC (2009) Non-linear control by input-output state variable feedback pole assignment. Int J Control 82(6):1029–1044

    Article  Google Scholar 

  13. Apostol TM (1963) Mathematical analysis. Addison-Wesley, Reading

    Google Scholar 

  14. Pan Y, Furuta K (1994) Vss control design for discrete-time system. Control-Theory Adv Technol, Part 1 10(4):669–687

    Google Scholar 

  15. El-Ghezawi ME, Zinober ASI, Billings SA (1983) Analysis and design of variable structure systems using a geometric approach. Int J Control 38(3):657–671

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang J, Li H, Guan X, Wu X (2010) Stability of cellular neural networks with time varying delay. Int J Model Identif Control 9(1/2):59–64

    Google Scholar 

  17. Wu X, Zhang J, Zhu Q (2010) A generalized procedure in designing recurrent neural network identification and control of time-varying-delayed nonlinear dynamic systems. Neurocomputing 73:1376–13833

    Google Scholar 

  18. Wu XL, Zhang JH, Guan XP (2010) Delay-dependent asymptotic stability of BAM neural networks with time delay. Kybernetes 39(8):1313–1321

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhang J, Zhu Q, Wu X, Li Y (2013) A generalized indirect adaptive neural networks backstepping control procedure for a class of non-affine nonlinear systems with pure-feedback prototype. Neurocomputing (in press)

    Google Scholar 

  20. Wu X, Yang L, Zhang J (2012) Synchronisation of unified chaotic systems with uncertain parameters in finite time. Int J Model Identif Control 17(4):295–301

    Google Scholar 

  21. Furze JM, Zhu QM, Qiao F, Hill J (2013) Linking and implementation of fuzzy logic control to ordinate plant strategies. Int J Model Identif Control (in press)

    Google Scholar 

  22. Yoshimura T (2012) Adaptive sliding mode control for uncertain discrete-time systems using an improved reaching law. Int J Model Identif Control 16(4):380–391

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the support from the National Natural Science Foundation of China (Grant No. 61273188) and National Natural Science Foundation of Hebei Province (F2012208075) and Taishan Scholar Construction Engineering Special Funding. The authors, hereby, gratefully acknowledge this support.

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Authors and Affiliations

  1. Hebei University of Science and Technology, Shijiazhuang, 050054, China

    Xueli Wu & Jianhua Zhang

  2. Yanshan University, Qinhuangdao, 066004, China

    Yang Li & Xueli Wu

  3. University of the West of England, Coldharbour Lane, Bristol, BS16 1QY, UK

    Quanmin Zhu

Authors
  1. Yang Li
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  2. Quanmin Zhu
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  3. Xueli Wu
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  4. Jianhua Zhang
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Corresponding author

Correspondence to Yang Li .

Editor information

Editors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan, People's Republic of China

    Lei Liu

  2. University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

  3. Wuhan University of Science and Technology, Wuhan, People's Republic of China

    Lei Cheng

  4. Huazhong University of Science and Technology, Wuhan, People's Republic of China

    Yongji Wang

  5. China University of Petroleum, Qingdao, People's Republic of China

    Dongya Zhao

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Li, Y., Zhu, Q., Wu, X., Zhang, J. (2014). Sliding Mode Control for Nonlinear Discrete Time Systems with Matching Perturbations. In: Liu, L., Zhu, Q., Cheng, L., Wang, Y., Zhao, D. (eds) Applied Methods and Techniques for Mechatronic Systems. Lecture Notes in Control and Information Sciences, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36385-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-36385-6_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36384-9

  • Online ISBN: 978-3-642-36385-6

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