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Multirate Functional Observer Based Discrete-Time Sliding Mode Control

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Advances in Sliding Mode Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 440))

Abstract

In this chapter, a brief introduction to the functional observer, multirate output sampling and discrete-time sliding mode control will be given. Using the concept of multirate sampling of plant output, a functional observer based sliding model controller has been designed for systems with uncertainty. The necessary and sufficient conditions are given for the design of the proposed controller using the minimal number of output samples. A numerical example is considered to demonstrate the procedure and efficacy of the approach.

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References

  1. Luenberger, D.G.: Observing the state of a linear system. IEEE Tran. Mil. Elecrron. MIL-8, 74–80 (1964)

    Article  Google Scholar 

  2. Luenberger, D.G.: An introduction to observer. IEEE Tran. Autom. Contr. 16, 596–602 (1971)

    Article  Google Scholar 

  3. Cumming, S.D.G.: Design of observers of reduced.order. Elecrron. Letters 5, 213–214 (1969)

    Article  Google Scholar 

  4. Gopinath, B.: On the control of linear multiple input-output systems. Bell Syst. Tech. J. 50, 1063–1081 (1971)

    MathSciNet  MATH  Google Scholar 

  5. Wonham, W.M., Morse, A.S.: Feedback invariants of linear multivariable systems. Automatica 8, 93–100 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  6. Emre, E.: Pole assignment by dynamic feedback. Inr. J. Contr. 33(2), 381–394 (1981)

    Google Scholar 

  7. Syrmos, V.L., Syrmos, G.L.: Computational design techniques for reduced-order compensators. IEEE Tran. Autom. Control 37(11) (November 1992)

    Google Scholar 

  8. Fortmann, T.E., Williamson, D.: Design of low-order observers for linear feedback control laws. IEEE Trans. Autom.Control AC-17, 301–308 (1972)

    Article  MathSciNet  Google Scholar 

  9. Murdoch, P.: Design of degenerate observers. IEEE Trans. Autom. Control AC-19, 441–442 (1974)

    Article  MathSciNet  Google Scholar 

  10. Gupta., R.M., et al.: A direct procedure for the design of single functional observers. IEEE Trans. Circuits and Systems cas-28(4) (April 1981)

    Google Scholar 

  11. Kondo, E., Takata, M.: Design of multi-linear functional observers. JSME 20 (April 1977)

    Google Scholar 

  12. Tsui, C.-C.: A new algorithm for the design of multifunctional observers. IEEE Trans. Autom. Contr. 30, 89–93 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  13. Aldeen, M., Trinh, H.: Reduced-order linear functional observer for linear systems. IEE Proc. Control Theory Appl. 146, 399–405 (1999)

    Article  Google Scholar 

  14. Darouach, M.: Existence and design of functional observers for linear systems. IEEE Trans. Autom. Contr. 45, 940–943 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rotella, F., Zambettakis, I.: Minimal single linear functional observers for linear systems. Automatica 47, 164–169 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hou, M., Muller, P.C.: Design of decentralized linear state function observers. Automatica 11, 1801–1805 (1994)

    Article  MathSciNet  Google Scholar 

  17. Trinh, H., Ha, Q.: Design of linear functional observers for linear systems with unknown inputs. Int. J. Syst. Sci. 31, 741–749 (2000)

    Article  MATH  Google Scholar 

  18. Trinh, H., Fernando, T., Nahavandi, S.: Design of reduced-order functional observers for linear systems with unknown inputs. Asian J. Control 6, 514–520 (2004)

    Article  Google Scholar 

  19. Trinh, H., Tran, T.D., Fernando, T.: Disturbance decoupled observers for systems with unknown inputs. IEEE. Trans. Autom. Control 53, 2397–2402 (2008)

    Article  MathSciNet  Google Scholar 

  20. Er, M.J., Anderson, B.D.O.: Design of reduced-order multirate output linear functional observer-based compensator. Automatica 31, 237–242 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Utkin, V.I.: Variable structure systems with sliding modes. IEEE Tran. Autom. Control 22(2), 212–222 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  22. Astrom, K.J., Wittenmark, B.: Computer Control System–Theory and Design. Prentie-Hall Inc., Englewood Cliffs (1984)

    Google Scholar 

  23. Chen, T.W., Francis, B.: Optimal Sampled-Data Control Systems. Springer, London (1995)

    Book  MATH  Google Scholar 

  24. Hagiwara, T., Araki, M.: Design of a stable state feedback controller based on the multirate sampling of the plant output. IEEE Trans. Automat. Contr. AC-33, 812–819 (1988)

    Article  MathSciNet  Google Scholar 

  25. Werner, H.: Robust control of a laboratory flight simulator by nondynamic multirate output feedback. In: Proceeding of 35th International Conference on Control, pp. 1575–1580 (December 1996)

    Google Scholar 

  26. Saaj, C.M., Bandyopadhyay, B., Unbehauen, H.: A new algorithm for discrete-time sliding mode control using fast output sampling feedback. IEEE Trans. Ind. Electr 49(3), 518–523 (2002)

    Article  Google Scholar 

  27. Sarpturk, S.Z., Istefanopulos, Y., Kaynak, O.: On the stability of discrete-time sliding mode systems. IEEE Tran. Autom. Control AC-32, 930–932 (1987)

    Article  Google Scholar 

  28. Furta, K.: Sliding mode control of a discrete system. Syst. Control. Lett. 14(2), 144–152 (1990)

    Google Scholar 

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

    Article  Google Scholar 

  30. Tang, C.Y., Misawa, E.A.: Discrete variable structure control for linear multivariable systems: the state feedeback case. In: Proceeding of Amer. Control Conf., pp. 14–118 (June 1998)

    Google Scholar 

  31. Bandyopadhyay, B., Janardhanan, S.: Discrete-time sliding mode control: A multirate-output feedback approach. LNCIS, vol. 323, 147 p. Springer, Heidelberg (2005)

    Google Scholar 

  32. Bandyopadhyay, B., Janardhanan, S.: Discrete-time Sliding Mode Control using Multirate Output Feedback. LNCIS, vol. 334, pp. 351–371. Springer, Berlin (2006)

    Google Scholar 

  33. Janardhanan, S., Bandyopadhyay, B.: Discrete sliding mode control of systems with unmatched uncertainty using multirate output feedback. IEEE Trans. Autom. Control AC-51(6), 1030–1035 (2006)

    Article  MathSciNet  Google Scholar 

  34. Janardhanan, S., Bandyopadhyay, B.: Output feedback sliding-mode control for uncertain systems using fast output sampling technique. IEEE Trans. Ind. Electron. AC-53(5), 1677–1682 (2006)

    Article  Google Scholar 

  35. Bartoszewicz, A.: Discrete-time quasi-sliding-mode control strategies. IEEE Trans. Ind. Electron. AC-45(4), 633–637 (1998)

    Article  Google Scholar 

  36. Reddy, G.D., et al.: Discrete-time output feedback sliding mode control for spatial control of a large PHWR. Automatica 45, 2159–2163 (2009)

    Article  MATH  Google Scholar 

  37. Janardhanan, S., Satyanarayana, N.: Design of Multirate Output Feedback Sampling based Functional Observer and State Feedback. In: Proceeding of 11th International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, pp. 1297–1301 (December 2010)

    Google Scholar 

  38. Janardhanan, S., Inamdar, S.: Multirate Output Feedback Sliding Mode Control Design Using Reduced Order Functional Observer. In: Proceeding of 11th International Workshop on Variable Structure Systems (VSS 2010), Mexico City, Mexico, pp. 395–398 (June 2010)

    Google Scholar 

  39. Chen, C.T.: Linear System Theory and Design. Oxford University Press, New York (1999)

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology, Delhi, India

    S. Janardhanan & Neeli Satyanarayana

Authors
  1. S. Janardhanan
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  2. Neeli Satyanarayana
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Corresponding author

Correspondence to S. Janardhanan .

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Editors and Affiliations

  1. , Interdisciplinary Programme in Systems, Indian Institute of Technology Bombay, ACRE Building 114 B, Mumbai, 400 076, Maharashtra, India

    B Bandyopadhyay

  2. , Dept. of Electrical Engineering, Indian Institute of Technology Delhi, Room No : II/335, New Delhi, 110 016, India

    S Janardhanan

  3. , Department of Electronics, University of Kent, Jennison Building - Room 1.54, Kent, CT2 7NT, United Kingdom

    Sarah K. Spurgeon

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Janardhanan, S., Satyanarayana, N. (2013). Multirate Functional Observer Based Discrete-Time Sliding Mode Control. In: Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. (eds) Advances in Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36986-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-36986-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36985-8

  • Online ISBN: 978-3-642-36986-5

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