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Discrete Sliding Mode Control of Fractional Order Systems

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Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 317))

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Abstract

All the developments reported in the earlier chapters are for the continuous fractional order systems. However, a large class of continuous time systems are controlled by computers and micro-controllers. In these cases information about the system is available only at specific time instants and control inputs can only be applied at these instants.

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References

  1. Baleanu, D., Güvenç, Z.B., Machado, J.T. (eds.): New trends in nanotechnology and fractional calculus applications. Springer, Netherlands (2010)

    MATH  Google Scholar 

  2. Kaczorek, T.: Selected problems of fractional systems theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  3. Raynaud, H.F., Zergaınoh, A.: State-space representation for fractional order controllers. Automatica 36(7), 1017–1021 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dzielinski, A., Sierociuk, D.: Adaptive feedback control of fractional order discrete state-space systems. In: International Conference on Computational Intelligence for Modelling, Control and Automation, 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, vol. 1, pp. 804–809. (2005).

    Google Scholar 

  5. Guermah, S., Djennoune, S., Bettayeb, M.: Controllability and observability of linear discrete-time fractional-order systems. Int. J. Appl. Math. Comput. Sci. 18(2), 213–222 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Podlubny, I.: Fractional-order systems and pi/sup/spl lambda//d/sup/spl mu//-controllers. IEEE Trans. Autom. Control 44(1), 208–214 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Sierociuk, D., Dzieliński, A.: Fractional kalman filter algorithm for the states, parameters and order of fractional system estimation. Int. J. Appl. Math. Comput. Sci. 16, 129–140 (2006)

    MathSciNet  Google Scholar 

  8. Dzieliński, A., Sierociuk, D.: Stability of discrete fractional order state-space systems. J. Vib. Control 14(9–10), 1543–1556 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Utkin, V., Guldner, J.: Sliding mode control in electro-mechanical systems. CRC Press, US (2009)

    Book  Google Scholar 

  10. Edwards, C., Spurgeon, S.K.: Sliding mode control: theory and applications. CRC Press, US (1998)

    Google Scholar 

  11. Utkin, V.I.: Sliding modes in control and optimization. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  12. Fridman, L., Levant, A.: Higher order sliding modes. Sliding Mode Control Eng. 11, 53–102 (2002)

    Google Scholar 

  13. Drakunov, S.V., Utkin, V.: Sliding mode control in dynamic systems. Int. J. Control 55(4), 1029–1037 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  14. Milosavljevic, C.: General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems. Autom. Remote Control 46(3), 307–314 (1985)

    MATH  Google Scholar 

  15. Sarpturk, S., Istefanopulos, Y., et al.: On the stability of discrete-time sliding mode control systems. IEEE Trans. Autom. Control 32(10), 930–932 (1987)

    Article  MATH  Google Scholar 

  16. Aly, G.M., Ali, W.G.: Digital design of variable structure control systems. Int. J. Syst. Sci. 21(8), 1709–1720 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  17. Furuta, K.: Sliding mode control of a discrete system. Syst. Control Lett. 14(2), 145–152 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  18. Sira-Ramirez, H.: Non-linear discrete variable structure systems in quasi-sliding mode. Int. J. Control 54(5), 1171–1187 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  19. Spurgeon, S.: Hyperplane design techniques for discrete-time variable structure control systems. Int. J. Control 55(2), 445–456 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Trans. Industr. Electron. 40(1), 2–22 (1993)

    Article  Google Scholar 

  21. Bartolini, G., Ferrara, A., Utkin, V.I.: Adaptive sliding mode control in discrete-time systems. Automatica 31(5), 769–773 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  23. Jung, S.L., Tzou, Y.Y.: Discrete sliding-mode control of a pwm inverter for sinusoidal output waveform synthesis with optimal sliding curve. IEEE Trans. Power Electron. 11(4), 567–577 (1996)

    Article  Google Scholar 

  24. Iordanou, H.N., Surgenor, B.W.: Experimental evaluation of the robustness of discrete sliding mode control versus linear quadratic control. IEEE Trans. Control Syst. Technol. 5(2), 254–260 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Hui, S., Żak, S.H.: On discrete-time variable structure sliding mode control. Syst. Control Lett. 38(4), 283–288 (1999)

    Article  MATH  Google Scholar 

  27. Golo, G., Milosavljević, Č.: Robust discrete-time chattering free sliding mode control. Syst. Control Lett. 41(1), 19–28 (2000)

    Article  MATH  Google Scholar 

  28. Koshkouei, A.J., Zinober, A.: Sliding mode control of discrete-time systems. J. Dyn. Syst. Meas. Contr. 122, 793 (2000)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  30. Ramírez, H.S., Battle, V.F.: A generalized pi sliding mode and pwm control of switched fractional systems. Modern sliding mode control theory, pp. 201–221. Springer, Berlin (2008)

    Google Scholar 

  31. Si-Ammour, A., Djennoune, S., Bettayeb, M.: A sliding mode control for linear fractional systems with input and state delays. Commun. Nonlinear Sci. Numer. Simul. 14(5), 2310–2318 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  32. Pisano, A., Rapaić, M., Usai, E.: Second-order sliding mode approaches to control and estimation for fractional order dynamics. Sliding modes after the first decade of the 21st century, pp. 169–197. Springer, Berlin (2012)

    Google Scholar 

  33. Kamal, S., Raman, A., Bandyopadhyay, B.: Discrete sliding mode control of fractional linear systems. In: IEEE international symposium on industrial electronics (ISIE), pp. 820–825. (2012)

    Google Scholar 

  34. Hilfer, R.: Appl. Fractional Calc. Phys. Word Scientific, Singapore (2000)

    Book  Google Scholar 

  35. Ostalczyk, P.: The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J. Syst. Sci. 31(12), 1551–1561 (2000)

    Article  MATH  Google Scholar 

  36. Dzielinski, A., Sierociuk, D.: Ultracapacitor modelling and control using discrete fractional order state-space model. Acta Montanist. Slovaca 13(1), 136–145 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Interdisciplinary Programme in Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai, India

    Bijnan Bandyopadhyay & Shyam Kamal

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  1. Bijnan Bandyopadhyay
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  2. Shyam Kamal
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Correspondence to Bijnan Bandyopadhyay .

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Bandyopadhyay, B., Kamal, S. (2015). Discrete Sliding Mode Control of Fractional Order Systems. In: Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach. Lecture Notes in Electrical Engineering, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-319-08621-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-08621-7_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08620-0

  • Online ISBN: 978-3-319-08621-7

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