Various Methods of Realization for Fractional-Order Elements
Main Article Content
Abstract
Fractional-order circuits are finding applications in control systems, signal processing, and other allied fields. As a result, realizing fractional-order elements or fractance devices is an essential research topic. A unique fractance device is realized in this study using continued fraction expansion (CFE) and partial fraction expansion (PFE) formulas. Continued fraction expansion is used to calculate the rational approximation. For simulation, the fourth order rational approximation for fractional order, =-1/2, -1/3, -1/4 is used. All simulations are carried out with the help of the MATLAB and TINA software packages. The theoretical and simulation results are in agreement.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
- Creative Commons Copyright License
The journal allows readers to download and share all published articles as long as they properly cite such articles; however, they cannot change them or use them commercially. This is classified as CC BY-NC-ND for the creative commons license.
- Retention of Copyright and Publishing Rights
The journal allows the authors of the published articles to hold copyrights and publishing rights without restrictions.
References
K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. New York, USA: Academic Press, 1974.
A. Yüce and N. Tan, “Electronic realisation technique for fractional order integrators,” The Journal of Engineering, vol. 2020, no. 5, pp. 157–167, May 2020.
B. T. Krishna, “Realization of fractance device using fifth order approximation,” Communications on Applied Electronics, vol. 7, no. 34, Sep. 2020.
M. Nakagawa and K. Sorimachi, “Basic characteristics of a fractance device,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E75-A, no. 12, pp. 1814–1819, Dec. 1992.
I. Podlubny, I. Petráš, B. M. Vinagre, P. O’Leary, and L’. Dorčák, “Analogue realizations of fractionalorder controllers,” Nonlinear Dynamics, vol. 29, pp. 281–296, 2002.
P. Yifei, Y. Xiao, L. Ke, Z. Jiliu, Z. Ni, Z. Yi, and P. Xiaoxian, “Structuring analog fractance circuit for 1/2 order fractional calculus,” in Proceedings of the 6th International Conference on ASIC, Shanghai, China, 2005, pp. 1136–1139.
A. Iqbal and R. R. Shekh, “A comprehensive study on different approximation methods of fractional order system,” International Research Journal of Engineering and Technology, vol. 3, no. 8, pp. 1848–1853, Aug. 2016.
G. Carlson and C. Halijak, “Approximation of fractional capacitors (1/s)^(1/n) by a regular newton process,” IEEE Transactions on Circuit Theory, vol. 11, no. 2, pp. 210–213, Jun. 1964.
K. Matsuda and H. Fujii, “H(infinity) optimized wave-absorbing control - analytical and experimental results,” Journal of Guidance, Control, and Dynamics, vol. 16, no. 6, pp. 1146–1153, Nov. 1993.
B. T. Krishna and K. V. V. S. Reddy, “Active and passive realization of fractance device of order 1/2,” Active and Passive Electronic Components, vol. 2008, 2008, Art. no. 369421.
B. T. Krishna, “Studies on fractional order differentiators and integrators: A survey,” Signal Processing, vol. 91, no. 3, pp. 386–426, Mar. 2011.
T. C. Haba, G. L. Loum, J. T. Zoueu, and G. Ablart, “Use of a component with fractional impedance in the realization of an analogical regulator of order ½,” Journal of Applied Sciences, vol. 8, no. 1, pp. 59–67, 2007.
A. Kartci, A. Agambayev, M. Farhat, N. Herencsar, L. Brancik, H. Bagci, and K. N. Salama, “Synthesis and optimization of fractional-order elements using a genetic algorithm,” IEEE Access, vol. 7, pp. 80 233–80 246, 2019.
Y. Wei, Y. Chen, Y. Wei, and X. Zhang, “Consistent approximation of fractional order operators,” Journal of Dynamic Systems, Measurement, and Control, vol. 143, no. 8, Aug. 2021, Art. no. 084501.
S. Kapoulea, C. Psychalinos, and A. S. Elwakil, “FPAA-based realization of filters with fractional Laplace operators of different orders,” Fractal and Fractional, vol. 5, no. 4, Dec. 2021, Art. no. 218.
M. S. Semary, M. E. Fouda, H. N. Hassan, and A. G. Radwan, “Realization of fractional-order capacitor based on passive symmetric network,” Journal of Advanced Research, vol. 18, pp. 147–159, Jul. 2019.
N. Mijat, D. Jurisic, and G. S. Moschytz, “Analog modeling of fractional-order elements: A classical circuit theory approach,” IEEE Access, vol. 9, pp. 110 309–110 331, 2021.
P. Prommee, N. Wongprommoon, and R. Sotner, “Frequency tunability of fractance device based on OTA-c,” in 2019 42nd International Conference on Telecommunications and Signal Processing (TSP), 2019, pp. 76–79.
P. Prommee, P. Pienpichayapong, N. Manositthichai, and N. Wongprommoon, “OTA-based tunable fractional-order devices for biomedical engineering,” AEÜ - International Journal of Electronics and Communications, vol. 128, Jan. 2021, Art. no. 153520.
A. N. Khovanskiĭ, The Application of Continued Fractions and Their Generalizations to Problems in Approximation Theory. Groningen, The Netherlands: P. Noordhoff, 1963.