Advertisement

Role of modern fractional derivatives in an armature-controlled DC servomotor

  • Kashif Ali Abro
  • J. F. Gómez-Aguilar
  • Ilyas KhanEmail author
  • K. S. Nisar
Regular Article
  • 4 Downloads

Abstract.

This paper deals with the comparative analysis of modern fractional techniques for an armature-controlled DC servomotor. The mathematical modeling of an armature-controlled DC servomotor is based on the angular displacement of the motor shaft and the armature current in ampere. The governing linear differential equations are fractionalized in terms of Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional differentiations in the ranges \( 0\leq\xi_{1} \leq 1\) and \( 0\leq\xi_{2}\leq 1\), respectively. The fractional ordinary differential equations have been solved by implementing Laplace transform techniques. The transfer function of an armature-controlled DC servomotor is obtained by the coupling of fractional ordinary differential equations. The calculations of transfer functions have been traced out through the Mathcad 15 software while graphical simulation is based on MATLAB. In order to control the systems’ behavior, the transfer function is depicted graphically for fractional and non-fractional solutions along with embedded parameters. Our results suggest that the speed of rotation relies on the voltage which precisely controls the angular position of servomechanism through both types of fractional differentiation.

References

  1. 1.
    P. Pany, R. Singh, R. Tripathi, Energy Convers. Manag. 122, 195 (2016)CrossRefGoogle Scholar
  2. 2.
    F. Beltran-Carbajal, R. Tapia-Olvera, O. Aguilar-Mejia, A. Favela-Contreras, I. Lopez-Garcia, Int. Trans. Electron. Energy Syst. 28, 1 (2018)Google Scholar
  3. 3.
    F. Rios-Gutierrez, Y.F. Makableh, Efficient position control of DC Servomotor using backpropagation Neural Network, in 2011 Seventh International Conference on Natural Computation (IEEE, 2011) pp. 653--657Google Scholar
  4. 4.
    F. Beltran-Carbajala, R. Tapia-Olverab, I. Lopez-Garciaa, D. Guillen, Electr. Power Syst. Res. 164, 70 (2018)CrossRefGoogle Scholar
  5. 5.
    A. Tepljakov, E.A. Gonzalez, E. Petlenkov, J. Belikov, C.A. Monje, I. Petráš, ISA Trans. 60, 262 (2016)CrossRefGoogle Scholar
  6. 6.
    S.H. HosseinNia, I. Tejado, B.M. Vinagre, Mechatronics 23, 781 (2013)CrossRefGoogle Scholar
  7. 7.
    J.F. Gomez-Aguilar, V.F. Morales-Delgado, M.A. Taneco-Hernandez, D. Baleanu, R.F. Escobar Jimenez, M.M. Al Quarashi, Entropy 18, 402 (2016)ADSCrossRefGoogle Scholar
  8. 8.
    A.A. Kashif, A.M. Anwar, A.U. Muhammad, Eur. Phys. J. Plus 133, 113 (2018)CrossRefGoogle Scholar
  9. 9.
    A. Atangana, S.T.A. Badr, Adv. Mech. Eng. 7, 1 (2015)Google Scholar
  10. 10.
    I. Koca, A. Atangana, Therm. Sci. 20, 2137 (2016)CrossRefGoogle Scholar
  11. 11.
    K.A. Abro, M. Hussain, M.M. Baig, Eur. Phys. J. Plus 132, 439 (2017)CrossRefGoogle Scholar
  12. 12.
    M. Saqib, A. Farhad, K. Ilyas, A.S. Nadeem, S. Sharidan, J. Therm. Anal. Calorim. 135, 523 (2019)CrossRefGoogle Scholar
  13. 13.
    Kashif Ali Abro, Mukarrum Hussain, Mirza Mahmood Baig, Prog. Fract. Differ. Appl. 3, 69 (2017)CrossRefGoogle Scholar
  14. 14.
    A.A. Zafar, C. Fetecau, Alex. Eng. J. 55, 2789 (2016)CrossRefGoogle Scholar
  15. 15.
    A.M. Qasem, A.A. Kashif, K. Ilyas, Complexity 2018, 8918541 (2018)Google Scholar
  16. 16.
    H.L. Muzaffar, A.A. Kashif, A.S. Asif, Int. J. Adv. Appl. Sci. 4, 97 (2017)CrossRefGoogle Scholar
  17. 17.
    A.S. Nadeem, F. Ali, I. Khan, M. Saqib, Neural Comput. Appl. 30, 1865 (2018)CrossRefGoogle Scholar
  18. 18.
    A.A. Kashif, A.S. Muhammad, Punjab Univ. J. Math. 49, 113 (2017)Google Scholar
  19. 19.
    I. Khan, A. Gul, S. Shafie, J. Porous Media 20, 435 (2017)CrossRefGoogle Scholar
  20. 20.
    K.A. Abro, H. Mukarrum, M.B. Mirza, Int. J. Nonlinear Anal. Appl. 9, 99 (2018)Google Scholar
  21. 21.
    A. Carpinteri, P. Cornetti, A. Sapora, Eur. Phys. J. ST 193, 193 (2011)CrossRefGoogle Scholar
  22. 22.
    A. Atangana, B.S.T. Alkahtani, Entropy 17, 4439 (2015)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Kashif Ali Abro, Anwer Ahmed Memon, Shahid Hussain Abro, Ilyas Khan, I. Tlili, Energy Rep. 5, 41 (2019)CrossRefGoogle Scholar
  24. 24.
    O.J. Algahtani, Chaos, Solitons Fractals 89, 552 (2016)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    F. Tchier, M. Inc, Z.S. Korpinar, D. Baleanu, Adv. Mech. Eng. 8, 1 (2016)CrossRefGoogle Scholar
  26. 26.
    Kashif Ali Abro, Ali Asghar Memon, Anwer Ahmed Memon, Analog-Integr. Circ. Signal Process. 99, 11 (2019)CrossRefGoogle Scholar
  27. 27.
    J. Hristov, Therm. Sci. 21, 827 (2017)CrossRefGoogle Scholar
  28. 28.
    S. Ambreen, A.A. Kashif, A.S. Muhammad, J. Therm. Anal. Calorim. 136, 2295 (2019)CrossRefGoogle Scholar
  29. 29.
    H.W. Zhou, S. Yang, J. Hydrol. 566, 910 (2018)ADSCrossRefGoogle Scholar
  30. 30.
    M. Abdulhameed, M.M. Muhammad, A.Y. Gital, D.G. Yakubu, I. Khan, Physica A 519, 42 (2019)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    K.A. Abro, A.A. Irfan, M.A. Sikandar, K. Ilyas, J. King Saud Univ. Sci. (2018)  https://doi.org/10.1016/j.jksus.2018.07.012
  32. 32.
    J.-F. Gómez-Aguilar, Torres, H. Yepez-Martínez, D. Baleanu, J.M. Reyes, I.O. Sosa, Adv. Differ. Equ. 2016, 173 (2016)CrossRefGoogle Scholar
  33. 33.
    A. Yusuf, S. Qureshi, M. Inc, A.I. Aliyu, D. Baleanu, A. Shaikh, Chaos 28, 123121 (2018)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Fahd Jarad, Thabet Abdel jawad, Zakia Hammouch, Chaos, Solitons Fractals 117, 16 (2018)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Muhammad Saqib, Ilyas Khan, Sharidan Shafie, Chaos, Solitons Fractals 116, 79 (2018)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Z. Shah, E. Bonyah, S. Islam, T. Gul, AIP Adv. 9, 015115 (2019)ADSCrossRefGoogle Scholar
  37. 37.
    Ndolane Sene, Chaos, Solitons Fractals 117, 68 (2018)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Kashif Ali Abro, Anwar Ahmed Memon, Muhammad Aslam Uqaili, Eur. Phys. J. Plus 133, 113 (2018)CrossRefGoogle Scholar
  39. 39.
    M. Sheikholeslami, Z. Shah, A. shafi, I. khan, Tilli, Sci. Rep. 9, 1196 (2019)ADSCrossRefGoogle Scholar
  40. 40.
    K.M. Owolabi, A. Atangana, Adv. Differ. Equ. 2017, 223 (2017)CrossRefGoogle Scholar
  41. 41.
    J. Singh, D. Kumar, Z. Hammouch, A. Atangana, Appl. Math. Comput. 316, 504 (2018)MathSciNetGoogle Scholar
  42. 42.
    Z. Shah, T. Gul, S. Islam, A. Khan, J. Eng. Technol. 6, 280 (2017)Google Scholar
  43. 43.
    Kashif Ali Abro, Shaikh Hina Saeed, Norzieha Mustapha, Ilyas Khan, Asifa Tassadiq, Malays. J. Fundam. Appl. Sci. 14, 20 (2018)Google Scholar
  44. 44.
    A. Atangana, R.T. Alqahtani, Entropy 18, 40 (2016)ADSCrossRefGoogle Scholar
  45. 45.
    C. Fetecau, D. Vieru, W.A. Azhar, Appl. Sci. 7, 247 (2017)CrossRefGoogle Scholar
  46. 46.
    A. Atangana, J.F. Gómez-Aguilar, Chaos, Solitons Fractals 102, 285 (2017)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Arshad Khan, Kashif Ali Abro, Asifa Tassaddiq, Ilyas Khan, Entropy 19, 1 (2017)Google Scholar
  48. 48.
    A. Atangana, Chaos, Solitons Fractals 102, 396 (2017)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Kashif Ali Abro, Ilyas Khan, J.F. Gómez-Aguilar, Eur. Phys. J. Plus 133, 397 (2018)CrossRefGoogle Scholar
  50. 50.
    A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)CrossRefGoogle Scholar
  51. 51.
    A.K. Abro, M.R. Mohammad, K. Ilyas, A.A. Irfan, T. Asifa, J. Nanofluids 7, 738 (2018)CrossRefGoogle Scholar
  52. 52.
    A.A. Kashif, K. Ilyas, T. Asifa, Math. Model. Nat. Phenom. 13, 1 (2018)MathSciNetCrossRefGoogle Scholar
  53. 53.
    M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 1, 73 (2015)Google Scholar
  54. 54.
    Kashif Ali Abro, Ilyas Khan, Chin. J. Phys. 55, 1583 (2017)CrossRefGoogle Scholar
  55. 55.
    Dur Muhammad Mugheri, Kashif Ali Abro, Muhammad Anwar Solangi, Int. J. Adv. Appl. Sci. 5, 97 (2018)CrossRefGoogle Scholar
  56. 56.
    K.A. Abro, J.F. Gomez-Aguilar, Eur. Phys. J. Plus 134, 101 (2019)CrossRefGoogle Scholar
  57. 57.
    A.K. Ali, K. Ilyas, F.G.A. Jose, J. Braz. Soc. Mech. Sci. Eng. 41, 174 (2019)CrossRefGoogle Scholar
  58. 58.
    A.A. Kashif, Y. Ahmet, Iran. J. Sci. Technol. Trans. A 43, 1 (2019)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Kashif Ali Abro
    • 1
  • J. F. Gómez-Aguilar
    • 2
  • Ilyas Khan
    • 3
    Email author
  • K. S. Nisar
    • 4
  1. 1.Department of Basic Sciences and Related StudiesMehran University of Engineering and TechnologyJamshoroPakistan
  2. 2.CONACyT-Tecnológico Nacional de México/CENIDETInterior Internado Palmira S/NCuernavacaMexico
  3. 3.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Department of Mathematics, College of Arts and SciencePrince Sattam bin Abdulaziz UniversityWadi Al-DawaserSaudi Arabia

Personalised recommendations