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.
Similar content being viewed by others
References
P. Pany, R. Singh, R. Tripathi, Energy Convers. Manag. 122, 195 (2016)
F. Beltran-Carbajal, R. Tapia-Olvera, O. Aguilar-Mejia, A. Favela-Contreras, I. Lopez-Garcia, Int. Trans. Electron. Energy Syst. 28, 1 (2018)
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--657
F. Beltran-Carbajala, R. Tapia-Olverab, I. Lopez-Garciaa, D. Guillen, Electr. Power Syst. Res. 164, 70 (2018)
A. Tepljakov, E.A. Gonzalez, E. Petlenkov, J. Belikov, C.A. Monje, I. Petráš, ISA Trans. 60, 262 (2016)
S.H. HosseinNia, I. Tejado, B.M. Vinagre, Mechatronics 23, 781 (2013)
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)
A.A. Kashif, A.M. Anwar, A.U. Muhammad, Eur. Phys. J. Plus 133, 113 (2018)
A. Atangana, S.T.A. Badr, Adv. Mech. Eng. 7, 1 (2015)
I. Koca, A. Atangana, Therm. Sci. 20, 2137 (2016)
K.A. Abro, M. Hussain, M.M. Baig, Eur. Phys. J. Plus 132, 439 (2017)
M. Saqib, A. Farhad, K. Ilyas, A.S. Nadeem, S. Sharidan, J. Therm. Anal. Calorim. 135, 523 (2019)
Kashif Ali Abro, Mukarrum Hussain, Mirza Mahmood Baig, Prog. Fract. Differ. Appl. 3, 69 (2017)
A.A. Zafar, C. Fetecau, Alex. Eng. J. 55, 2789 (2016)
A.M. Qasem, A.A. Kashif, K. Ilyas, Complexity 2018, 8918541 (2018)
H.L. Muzaffar, A.A. Kashif, A.S. Asif, Int. J. Adv. Appl. Sci. 4, 97 (2017)
A.S. Nadeem, F. Ali, I. Khan, M. Saqib, Neural Comput. Appl. 30, 1865 (2018)
A.A. Kashif, A.S. Muhammad, Punjab Univ. J. Math. 49, 113 (2017)
I. Khan, A. Gul, S. Shafie, J. Porous Media 20, 435 (2017)
K.A. Abro, H. Mukarrum, M.B. Mirza, Int. J. Nonlinear Anal. Appl. 9, 99 (2018)
A. Carpinteri, P. Cornetti, A. Sapora, Eur. Phys. J. ST 193, 193 (2011)
A. Atangana, B.S.T. Alkahtani, Entropy 17, 4439 (2015)
Kashif Ali Abro, Anwer Ahmed Memon, Shahid Hussain Abro, Ilyas Khan, I. Tlili, Energy Rep. 5, 41 (2019)
O.J. Algahtani, Chaos, Solitons Fractals 89, 552 (2016)
F. Tchier, M. Inc, Z.S. Korpinar, D. Baleanu, Adv. Mech. Eng. 8, 1 (2016)
Kashif Ali Abro, Ali Asghar Memon, Anwer Ahmed Memon, Analog-Integr. Circ. Signal Process. 99, 11 (2019)
J. Hristov, Therm. Sci. 21, 827 (2017)
S. Ambreen, A.A. Kashif, A.S. Muhammad, J. Therm. Anal. Calorim. 136, 2295 (2019)
H.W. Zhou, S. Yang, J. Hydrol. 566, 910 (2018)
M. Abdulhameed, M.M. Muhammad, A.Y. Gital, D.G. Yakubu, I. Khan, Physica A 519, 42 (2019)
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
J.-F. Gómez-Aguilar, Torres, H. Yepez-Martínez, D. Baleanu, J.M. Reyes, I.O. Sosa, Adv. Differ. Equ. 2016, 173 (2016)
A. Yusuf, S. Qureshi, M. Inc, A.I. Aliyu, D. Baleanu, A. Shaikh, Chaos 28, 123121 (2018)
Fahd Jarad, Thabet Abdel jawad, Zakia Hammouch, Chaos, Solitons Fractals 117, 16 (2018)
Muhammad Saqib, Ilyas Khan, Sharidan Shafie, Chaos, Solitons Fractals 116, 79 (2018)
Z. Shah, E. Bonyah, S. Islam, T. Gul, AIP Adv. 9, 015115 (2019)
Ndolane Sene, Chaos, Solitons Fractals 117, 68 (2018)
Kashif Ali Abro, Anwar Ahmed Memon, Muhammad Aslam Uqaili, Eur. Phys. J. Plus 133, 113 (2018)
M. Sheikholeslami, Z. Shah, A. shafi, I. khan, Tilli, Sci. Rep. 9, 1196 (2019)
K.M. Owolabi, A. Atangana, Adv. Differ. Equ. 2017, 223 (2017)
J. Singh, D. Kumar, Z. Hammouch, A. Atangana, Appl. Math. Comput. 316, 504 (2018)
Z. Shah, T. Gul, S. Islam, A. Khan, J. Eng. Technol. 6, 280 (2017)
Kashif Ali Abro, Shaikh Hina Saeed, Norzieha Mustapha, Ilyas Khan, Asifa Tassadiq, Malays. J. Fundam. Appl. Sci. 14, 20 (2018)
A. Atangana, R.T. Alqahtani, Entropy 18, 40 (2016)
C. Fetecau, D. Vieru, W.A. Azhar, Appl. Sci. 7, 247 (2017)
A. Atangana, J.F. Gómez-Aguilar, Chaos, Solitons Fractals 102, 285 (2017)
Arshad Khan, Kashif Ali Abro, Asifa Tassaddiq, Ilyas Khan, Entropy 19, 1 (2017)
A. Atangana, Chaos, Solitons Fractals 102, 396 (2017)
Kashif Ali Abro, Ilyas Khan, J.F. Gómez-Aguilar, Eur. Phys. J. Plus 133, 397 (2018)
A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)
A.K. Abro, M.R. Mohammad, K. Ilyas, A.A. Irfan, T. Asifa, J. Nanofluids 7, 738 (2018)
A.A. Kashif, K. Ilyas, T. Asifa, Math. Model. Nat. Phenom. 13, 1 (2018)
M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 1, 73 (2015)
Kashif Ali Abro, Ilyas Khan, Chin. J. Phys. 55, 1583 (2017)
Dur Muhammad Mugheri, Kashif Ali Abro, Muhammad Anwar Solangi, Int. J. Adv. Appl. Sci. 5, 97 (2018)
K.A. Abro, J.F. Gomez-Aguilar, Eur. Phys. J. Plus 134, 101 (2019)
A.K. Ali, K. Ilyas, F.G.A. Jose, J. Braz. Soc. Mech. Sci. Eng. 41, 174 (2019)
A.A. Kashif, Y. Ahmet, Iran. J. Sci. Technol. Trans. A 43, 1 (2019)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abro, K.A., Gómez-Aguilar, J.F., Khan, I. et al. Role of modern fractional derivatives in an armature-controlled DC servomotor. Eur. Phys. J. Plus 134, 553 (2019). https://doi.org/10.1140/epjp/i2019-12957-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2019-12957-6