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

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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.

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References

  1. J.P. Eckmann, S.O. Kamphurst, D. Ruelle, S. Ciliberto, Phys. Rev. A 34, 4971 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  2. R.G. Harrison, D.J. Biswas, Nature 321, 394 (1986)

    Article  ADS  Google Scholar 

  3. L.F. Olsen, H. Degn, Quart. Rev. Biophys. 18, 165 (1985)

    Article  Google Scholar 

  4. L. Glass, M.C. Mackey, in From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988), pp. 454–532

  5. J.C. Roux, R.H. Simoyi, H.L. Swinney, Physica D 8, 257 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  6. S.K. Scott, Chemical Chaos (Clarendon Press, Oxford, 1991)

  7. M.T.M. Koper, P. Gaspard, J.H. Sluyters, J. Chem. Phys. 97, 8250 (1992)

    Article  ADS  Google Scholar 

  8. P. Gaspard, Physica A 263, 315 (1999)

    Article  ADS  Google Scholar 

  9. H. Wang, Q. Li, J. Phys. Chem. A 104, 472 (2000)

    Article  Google Scholar 

  10. H. Wang, Q. Li, Sci. China Ser. B 43, 357 (2000)

    Article  Google Scholar 

  11. F. Sagues, I.R. Epstein, Dalton Trans. 0, 1201 (2003)

    Article  Google Scholar 

  12. Y. Huang, X.S. Yang, J. Math. Chem. 38, 107 (2005)

    Article  MathSciNet  Google Scholar 

  13. S. Rasoulian, M. Shahrokhi, Iran. J. Chem. Chem. Eng. 29, 149 (2010)

    Google Scholar 

  14. A. Sanayei, in Proceedings of the World Congress on Engineering (WEC), London (2010), Vol. 3, pp. 107–117

  15. N. Vasegh, F. Khellat, Int. J. Appl. Sci. Technol. 1, 233 (2011)

    Google Scholar 

  16. S. Kuntanapreedaa, P.M. Marusakb, Comput. Chem. Eng. 41, 10 (2012)

    Article  Google Scholar 

  17. R.R. Karri, V. Chimmiri, Adv. Chem. Eng. Res. (ACER) 2, 1 (2013)

    Google Scholar 

  18. M. Lawnik, M. Berezowski, Chem. Process Eng. 35, 387 (2014)

    Article  Google Scholar 

  19. P.P. Singh, B.K. Roy, Ann. Rev. Control 45, 152 (2018)

    Article  Google Scholar 

  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

  21. S. Mukherjee, S.K. Palit, S. Banerjee, M.R.K. Ariffin, L. Rondoni, D.K. Bhattacharya, Physica A 439, 93 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  22. S. Banerjee, J. Kurths, Eur. Phys. J. Special Topics 223, 1441 (2014)

    Article  ADS  Google Scholar 

  23. P.P. Singh, J.P. Singh, B.K. Roy, IETE J. Res. 63, 853 (2017)

    Article  Google Scholar 

  24. J.P. Singh, B.K. Roy, Trans. Inst. Meas. Control (2017), https://doi.org/10.1177/0142331217727580

  25. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 171 (2016)

    Google Scholar 

  26. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 9, 159 (2016)

    Google Scholar 

  27. P.P. Singh, J.P. Singh, B.K. Roy, Int. J. Control Theory Appl. 8, 995 (2015)

    Google Scholar 

  28. P.P. Singh, J.P. Singh, B.K. Roy, Res. Rev. J. Phys. 3, 1 (2014)

    Google Scholar 

  29. P.P. Singh, J.P. Singh, B.K. Roy, Chaos Solitons Fractals 69, 31 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  30. J.P. Singh, B.K. Roy, S. Jafari, Chaos Solitons Fractals 106, 243 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  31. J.P. Singh, B.K. Roy, Optik 145, 209 (2017)

    Article  ADS  Google Scholar 

  32. J.P. Singh, B.K. Roy, Int. J. Dyn. Control 45, 1 (2017)

    Google Scholar 

  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

  34. S. Jafari, V.T. Pham, T. Kapitaniak, Int. J. Bifurc. Chaos 26, 1650031 (2016)

    Article  Google Scholar 

  35. S. Jafari, J.C. Sprott, F. Nazarimehr, Eur. Phys. J. Special Topics 224, 1469 (2015)

    Article  ADS  Google Scholar 

  36. S. Jafari, J.C. Sprott, Chaos Solitons Fractals 57, 79 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  37. S. Jafari, J.C. Sprott, S. Golpayegani, Phys. Lett. A 337, 699 (2013)

    Article  ADS  Google Scholar 

  38. G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Phys. Lett. A 375, 2230 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  39. G.A. Leonov, N.V. Kuznetsov, V.I. Vagaitsev, Physica D 241, 1482 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  40. Z. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  41. Z. Wei, I. Moroz, J.C. Sprott, Z. Wang, W. Zhang, Int. J. Bifurc. Chaos 27, 1730008 (2017)

    Article  Google Scholar 

  42. Z. Wei, P. Yu, W. Zhang, M. Yao, Nonlinear Dyn. 82, 131 (2015)

    Article  Google Scholar 

  43. Z. Wei, W. Zhang, Int. J. Bifurc. Chaos 24, 1450127 (2014)

    Article  Google Scholar 

  44. Z. Wei, W. Zhang, Z. Wang, M. Yao, Int. J. Bifurc. Chaos 25, 1550028 (2015)

    Article  Google Scholar 

  45. S. Vaidyanathan, Int. J. ChemTech Res. 8, 146 (2015)

    Google Scholar 

  46. S. Vaidyanathan, Int. J. PharmTech Res. 8, 377 (2015)

    Google Scholar 

  47. H. Kheiri, B. Naderi, Iran. J. Math. Chem. 6, 81 (2015)

    Google Scholar 

  48. M. Berezowski, Chem. Eng. Sci. 101, 451 (2013)

    Article  Google Scholar 

  49. M. Berezowski, Chaos Solitons Fractals 78, 22 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  50. M. Berezowski, CMSIM 1, 43 (2016)

    Google Scholar 

  51. S. Vaidyanathan, in Applications of Sliding Mode Control in Science and Engineering: Studies in Computational Intelligence (Springer, Cham, 2017), pp. 371–392

  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. N. Samardzija, L.D. Greller, E. Wasserman, J. Chem. Phys. 90, 2296 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  54. J.E. Slotine, W. Li, in Applied Nonlinear Control (Prentice Hall Inc., Englewood Cliffs, New Jersey, 1991), pp. 100–154, 276–311

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Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Technology Meghalaya, Shillong, Meghalaya, 793003, India

    Piyush Pratap Singh

  2. Department of Electrical Engineering, National Institute of Technology, Silchar, Assam, 788010, India

    Binoy Krishna Roy

Authors
  1. Piyush Pratap Singh
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  2. Binoy Krishna Roy
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Correspondence to Piyush Pratap Singh.

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Singh, P.P., Roy, B.K. Microscopic chaos control of chemical reactor system using nonlinear active plus proportional integral sliding mode control technique. Eur. Phys. J. Spec. Top. 228, 169–184 (2019). https://doi.org/10.1140/epjst/e2019-800115-4

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  • DOI: https://doi.org/10.1140/epjst/e2019-800115-4

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