Skip to main content
Log in

Analysis of fractional order inductive transducers

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Inductive sensors have been widely used for precise measurement of position, displacement, temperature and pressure as they are extremely reliable in the harsh industrial atmosphere. In this paper, fractional order models of inductive transducers namely fractional order variable reluctance inductive transducer and fractional order resonant inductive transducer are developed and its characteristics are analysed. The impact of fractional order parameter on the characteristics like sensitivity and nonlinearity of the fractional order transducer are studied. The results are enriched when a fractional order inductor is connected in parallel to the fractional order resonant inductive transducer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K.B. Oldham, J. Spanier, The fractional calculus, theory and applications of differentiation and integration to arbitrary order (Dover, New York, 1974)

  2. K.S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations (John Wiley, New York, 1993)

  3. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivatives, theory and applications (Gordon and Breach Science Publishers, Amsterdam, 1993)

  4. I. Podlubny, Fractional differential equations (Academic, New York, 1999)

  5. K.L. Shen, T.T. Soong, J. Eng. Mech. 121, 694 (1995)

    Article  Google Scholar 

  6. C. Yang, Y. Shang, IEEE Trans. Electron. Devices 62, 9 (2015)

    Article  Google Scholar 

  7. R.L. Magin, Comput. Math. Appl. 59, 1586 (2010)

    Article  MathSciNet  Google Scholar 

  8. S. Westerlund, IEEE Trans. Dielectr. Electr. Insul. 1, 5 (1984)

    Google Scholar 

  9. I. Schafer, K. Kruger, J. Phys. D Appl. Phys. 41, 4 (2008)

    Google Scholar 

  10. J. Bisquert, G. Garcia-Belmonte, P. Bueno, E. Longo, L.O.S. Bulhoes, J. Electroanal. Chem. 452, 2 (1998)

    Article  Google Scholar 

  11. A. Mujumdar, B. Tamhane, S. Kurode, in Proceedings of the American Control Conference, 2014 Portland, Oregon, USA, 2004 (2011). DOI: https://doi.org/10.1109/ACC.2014.6858955

  12. JD. Gabano, T. Poinot, B. Huard, Commun. Nonlinear Sci. Numer. Simulat. 47, 164 (2017)

    Article  ADS  Google Scholar 

  13. Y. Ma, X. Zhou, B. Li, H. Chen, IEEE/CAA J. Autom. Sin. 3, 3 (2016)

    Article  Google Scholar 

  14. J.A.T. Machado, Mechatronics 23, 789 (2013)

    Article  Google Scholar 

  15. A.G. Radwan, A.S Elwakil, A.M. Soliman, IEEE Trans. Circuits. Syst. I Regul. Pap. 55,7 (2008)

    Article  Google Scholar 

  16. A.S. Ali, A.G. Radwan, A.M. Soliman, IEEE Trans. Emerg. Sel. Topics Circuits Syst. 3, 3 (2013)

    Article  Google Scholar 

  17. B. Maundy, A. Elwakil, S. Gift, Analog Integr. Circ. Sig. Process. 62, 99 (2010)

    Article  Google Scholar 

  18. H. Bartsch, T. Geiling, J. Müller, Sens. Actuators A, Phys. 175, 28 (2012)

    Article  Google Scholar 

  19. M.R. Nabavi, S. Nihtianov, IEEE Trans. Ind. Electron. 58, 9 (2011)

    Article  Google Scholar 

  20. S. Fericean, R. Droxler, IEEE Sensors J. 7, 11 (2007)

    Article  Google Scholar 

  21. A. Danisi, A. Masi, R. Losito, Y. Perriard, IEEE Trans. Instrum. Meas. 62, 5 (2013)

    Google Scholar 

  22. H. Wang, Z. Feng, Sens. Actuators A, Phys. 203, 362 (2013)

    Article  Google Scholar 

  23. C. Franco, J. Acero, R. Alonso, C. Sagues, D. Paesa, IEEE Sensors J. 12, 5 (2012)

    Article  Google Scholar 

  24. E.G. Bakhoum, M.H.M. Cheng, IEEE Trans. Instrum. Meas. 60, 8 (2011)

    Article  Google Scholar 

  25. M.V. Rojas-Moreno, G. Robles, B. Tellini, C. Zappacosta, J. M. Martìnez-Tarifa, J. Sanz-Feito, IEEE Trans. Instrum. Meas. 60, 5 (2011)

    Article  Google Scholar 

  26. M. Sakthivel, B. George, M. Sivaprakasam, IEEE Trans. Magn. 52, 4 (2016)

    Article  Google Scholar 

  27. M.E. Fouda, A.S. Elwakil, A.G. Radwan, B.J. Maundy, Math. Prob. Eng. (2016). DOI: https://doi.org/10.1155/2016/5976301

  28. A.G. Radwan, K.N. Salama, IEEE Trans. Circuits Syst. I Regul. Pap. 58, 10 (2011)

    Article  Google Scholar 

  29. A.G. Radwan, A. Shamim, K.N. Salama, IEEE Microwave Wireless Compon. Lett. 21, 3 (2011)

    Article  Google Scholar 

  30. A.T. Machado, A.M.S.F. Galhano, Nonlinear Dyn. 68, 107 (2012)

    Article  Google Scholar 

  31. A. Atangana, B.S.T. Alkahtani, Adv. Mech. Eng. 7, 6 (2015)

    Google Scholar 

  32. A.M. Tusset, J.M. Balthazar, D.G Bassinello, et al., Nonlinear Dyn. 69, 1837 (2012)

    Article  Google Scholar 

  33. M.C. Tripathy, D. Mondal, K. Biswas, S. Sen, Int. J. Circuit Theory Appl. 43, 9 (2015)

    Google Scholar 

  34. V. Parthasarathi, G. Uma, M. Umapathy, Int. J. Electron. Commun. 79, 141 (2017)

    Article  Google Scholar 

  35. G. Tsirimokou, C. Psychalinos, T.J. Freeborn, A.S. Elwakil, Microelectron. J. 55, 70 (2016)

    Article  Google Scholar 

  36. I. Schafer, ZAMM 80, 356 (2000)

    Article  ADS  Google Scholar 

  37. I. Schafer, K. Kruger, J. Magn. Magn. Mater. 307, 91 (2006)

    Article  ADS  Google Scholar 

  38. N. Misron, L.Q. Ying, R.N. Firdaus, N. Abdullah, N.F. Mailah, H. Wakiwaka, Sensors 11, 11 (2011)

    Google Scholar 

  39. C. Bartoletti, R. Buonanni, L.G. Fantasia, R. Frulla, W. Gaggioli, G. Sacerdoti, Meas. Sci. Technol. 9, 1180 (1998)

    Article  ADS  Google Scholar 

  40. C. Coillot, J. Moutoussamy, M. Boda, P. Leroy, J. Sens. Sens. Syst. 3, 1 (2014)

    Article  Google Scholar 

  41. Y.L. Bihan, Eur. Phys. J. Appl. Phys. 65, 30901 (2014)

    Article  Google Scholar 

  42. Z.D. Deng, S.H. Lisanby, A.V. Peterchev, Clin. Neurophysiol. 125, 1202 (2014)

    Article  Google Scholar 

  43. A. Christopoulos, E. Hristoforou, I. Koulalis, G. Tsamasphyros, Smart Mater. Struct. 23, 085035 (2014)

    Article  ADS  Google Scholar 

  44. F.T. Calkins, A.B. Flatau, M.J. Dapino, J. Intell. Mater. Syst. Struct. 18, 10 (2007)

    Article  Google Scholar 

  45. K.D. Anim-Appiah, S.M. Riad, IEEE Trans. Magn. 33, 3 (1997)

    Article  Google Scholar 

  46. J.P. Bentley, Principles of measurement systems, 4th edn. (Pearson, New York, 2005)

  47. A. Soltan, A.G. Radwan, A.M. Soliman, Int. J. Circuit Theory Appl. 44, 1 (2016)

    Article  Google Scholar 

  48. D. Crescini, A. Flammini, D. Marioli, A. Taroni, IEEE Trans. Instrum. Meas. 47, 5 (1998)

    Article  Google Scholar 

  49. R.M. Ford, R.S. Weissbach, D.R. Loker, IEEE Trans. Instrum. Meas. 50, 3 (2001)

    Article  Google Scholar 

  50. S.K. Mishra, G. Panda, D.P. Das, IEEE Trans. Instrum. Meas. 59, 4 (2010)

    Article  Google Scholar 

  51. A.C. Corney, IEEE Trans. Instrum. Meas. 28, 3 (1979)

    Article  Google Scholar 

  52. N.K. Das, T. Jayakumar, B. Raj, IEEE Trans. Instrum. Meas. 59, 11 (2010)

    Article  Google Scholar 

  53. J.K. Clapp, Proc. IRE 36, 3 (1948)

    Article  Google Scholar 

  54. X. Ding, X. Chen, X. Li, Z. Wu, Y. Yao, IEEE Sens. J. 14, 6 (2014)

    Article  Google Scholar 

  55. X. Ding, X. Chen, W. Ma, X. Chen, N. Li, IEEE Trans. Instrum. Meas. 65, 3 (2016)

    Article  Google Scholar 

  56. A. Oustaloup, F. Levron, B. Mathieu, F.M. Nanot, IEEE Trans. Circuits Syst. I, Fundam. Theory 47, 1 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Umapathy Mangalanathan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Veeraian, P., Gandhi, U. & Mangalanathan, U. Analysis of fractional order inductive transducers. Eur. Phys. J. Spec. Top. 226, 3851–3873 (2017). https://doi.org/10.1140/epjst/e2018-00047-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2018-00047-9

Navigation