Advertisement

Microscopic chaos control of chemical reactor system using nonlinear active plus proportional integral sliding mode control technique

  • Piyush Pratap SinghEmail author
  • Binoy Krishna Roy
Regular Article
  • 7 Downloads
Part of the following topical collections:
  1. Microscopic Dynamics, Chaos and Transport in Nonequilibrium Processes

Abstract

This paper puts forward the microscopic chaos control in the deterministic dynamics of the chemical reactor system. First, the dynamic behavior of the chemical reactor system is explored for some of the parameters and chaotic behavior is investigated. Phase plane, bifurcation plots and Lyapunov exponents are presented to verify the chaotic behavior. Second, nonlinear active plus proportional integral sliding mode control (NA-PISMC) is proposed to control microscopic chaos in the chemical reactor system. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics and controller is designed by using the relevant variables of the chemical system. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is done in MATLAB environment. Numerical simulation results are presented in order to show the effective performances of the proposed controller design. Simulation results correspond that the objectives of chaos existence and chaos control are achieved successfully.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.P. Eckmann, S.O. Kamphurst, D. Ruelle, S. Ciliberto, Phys. Rev. A 34, 4971 (1986) ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    R.G. Harrison, D.J. Biswas, Nature 321, 394 (1986) ADSCrossRefGoogle Scholar
  3. 3.
    L.F. Olsen, H. Degn, Quart. Rev. Biophys. 18, 165 (1985) CrossRefGoogle Scholar
  4. 4.
    L. Glass, M.C. Mackey, in From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988), pp. 454–532 Google Scholar
  5. 5.
    J.C. Roux, R.H. Simoyi, H.L. Swinney, Physica D 8, 257 (1983) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    S.K. Scott, Chemical Chaos (Clarendon Press, Oxford, 1991) Google Scholar
  7. 7.
    M.T.M. Koper, P. Gaspard, J.H. Sluyters, J. Chem. Phys. 97, 8250 (1992) ADSCrossRefGoogle Scholar
  8. 8.
    P. Gaspard, Physica A 263, 315 (1999) ADSCrossRefGoogle Scholar
  9. 9.
    H. Wang, Q. Li, J. Phys. Chem. A 104, 472 (2000) CrossRefGoogle Scholar
  10. 10.
    H. Wang, Q. Li, Sci. China Ser. B 43, 357 (2000) CrossRefGoogle Scholar
  11. 11.
    F. Sagues, I.R. Epstein, Dalton Trans. 0, 1201 (2003) CrossRefGoogle Scholar
  12. 12.
    Y. Huang, X.S. Yang, J. Math. Chem. 38, 107 (2005) MathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Rasoulian, M. Shahrokhi, Iran. J. Chem. Chem. Eng. 29, 149 (2010) Google Scholar
  14. 14.
    A. Sanayei, in Proceedings of the World Congress on Engineering (WEC), London (2010), Vol. 3, pp. 107–117 Google Scholar
  15. 15.
    N. Vasegh, F. Khellat, Int. J. Appl. Sci. Technol. 1, 233 (2011) Google Scholar
  16. 16.
    S. Kuntanapreedaa, P.M. Marusakb, Comput. Chem. Eng. 41, 10 (2012) CrossRefGoogle Scholar
  17. 17.
    R.R. Karri, V. Chimmiri, Adv. Chem. Eng. Res. (ACER) 2, 1 (2013) Google Scholar
  18. 18.
    M. Lawnik, M. Berezowski, Chem. Process Eng. 35, 387 (2014) CrossRefGoogle Scholar
  19. 19.
    P.P. Singh, B.K. Roy, Ann. Rev. Control 45, 152 (2018) CrossRefGoogle Scholar
  20. 20.
    S. Banerjee, L. Rondoni, M. Mitra, in Applications of Chaos and Nonlinear Dynamics in Science and Engineering (Springer, Berlin, 2015), Vol. 3, pp. 371–392 Google Scholar
  21. 21.
    S. Mukherjee, S.K. Palit, S. Banerjee, M.R.K. Ariffin, L. Rondoni, D.K. Bhattacharya, Physica A 439, 93 (2015) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    S. Banerjee, J. Kurths, Eur. Phys. J. Special Topics 223, 1441 (2014) ADSCrossRefGoogle Scholar
  23. 23.
    P.P. Singh, J.P. Singh, B.K. Roy, IETE J. Res. 63, 853 (2017) CrossRefGoogle Scholar
  24. 24.
    J.P. Singh, B.K. Roy, Trans. Inst. Meas. Control (2017),  https://doi.org/10.1177/0142331217727580
  25. 25.
    P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 171 (2016) Google Scholar
  26. 26.
    P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 159 (2016) Google Scholar
  27. 27.
    P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 8, 995 (2015) Google Scholar
  28. 28.
    P.P. Singh, J.P. Singh, B.K. Roy, Res. Rev. J. Phys. 3, 1 (2014) Google Scholar
  29. 29.
    P.P. Singh, J.P. Singh, B.K. Roy, Chaos Solitons Fractals 69, 31 (2014) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    J.P. Singh, B.K. Roy, S. Jafari, Chaos Solitons Fractals 106, 243 (2018) ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    J.P. Singh, B.K. Roy, Optik 145, 209 (2017) ADSCrossRefGoogle Scholar
  32. 32.
    J.P. Singh, B.K. Roy, Int. J. Dyn. Control 45, 1 (2017) Google Scholar
  33. 33.
    P.P. Singh, J.P. Singh, M. Borah, B.K. Roy, in 4th International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS) (2016), Vol. 49, pp. 522–525 Google Scholar
  34. 34.
    S. Jafari, V.T. Pham, T. Kapitaniak, Int. J. Bifurc. Chaos 26, 1650031 (2016) CrossRefGoogle Scholar
  35. 35.
    S. Jafari, J.C. Sprott, F. Nazarimehr, Eur. Phys. J. Special Topics 224, 1469 (2015) ADSCrossRefGoogle Scholar
  36. 36.
    S. Jafari, J.C. Sprott, Chaos Solitons Fractals 57, 79 (2013) ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    S. Jafari, J.C. Sprott, S. Golpayegani, Phys. Lett. A 337, 699 (2013) ADSCrossRefGoogle Scholar
  38. 38.
    G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Phys. Lett. A 375, 2230 (2011) ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Physica D 241, 1482 (2012) ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Z. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017) ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Z. Wei, I. Moroz, J.C. Sprott, Z. Wang, W. Zhang, Int. J. Bifurc. Chaos 27, 1730008 (2017) CrossRefGoogle Scholar
  42. 42.
    Z. Wei, P. Yu, W. Zhang, M. Yao, Nonlinear Dyn. 82, 131 (2015) CrossRefGoogle Scholar
  43. 43.
    Z. Wei, W. Zhang, Int. J. Bifurc. Chaos 24, 1450127 (2014) CrossRefGoogle Scholar
  44. 44.
    Z. Wei, W. Zhang, Z. Wang, M. Yao, Int. J. Bifurc. Chaos 25, 1550028 (2015) CrossRefGoogle Scholar
  45. 45.
    S. Vaidyanathan, Int. J. ChemTech Res. 8, 146 (2015) Google Scholar
  46. 46.
    S. Vaidyanathan, Int. J. PharmTech Res. 8, 377 (2015) Google Scholar
  47. 47.
    H. Kheiri, B. Naderi, Iran. J. Math. Chem. 6, 81 (2015) Google Scholar
  48. 48.
    M. Berezowski, Chem. Eng. Sci. 101, 451 (2013) CrossRefGoogle Scholar
  49. 49.
    M. Berezowski, Chaos Solitons Fractals 78, 22 (2015) ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    M. Berezowski, CMSIM 1, 43 (2016) Google Scholar
  51. 51.
    S. Vaidyanathan, in Applications of Sliding Mode Control in Science and Engineering: Studies in Computational Intelligence (Springer, Cham, 2017), pp. 371–392 Google Scholar
  52. 52.
    D. Mandragona, Hopf bifurcation analysis of chaotic chemical reactor model, Honors in the major theses, 342, University of Central Florida, 2018. http://stars.library.ucf.edu/honorstheses/342
  53. 53.
    N. Samardzija, L.D. Greller, E. Wasserman, J. Chem. Phys. 90, 2296 (1989) ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    J.E. Slotine, W. Li, in Applied Nonlinear Control (Prentice Hall Inc., Englewood Cliffs, New Jersey, 1991), pp. 100–154, 276–311 Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringNational Institute of Technology MeghalayaShillongIndia
  2. 2.Department of Electrical EngineeringNational Institute of TechnologySilcharIndia

Personalised recommendations