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Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi

Year 2022, Volume: 11 Issue: 3, 584 - 591, 18.07.2022
https://doi.org/10.28948/ngumuh.1039231

Abstract

Biyolojik yapıların fizyolojik karakteristiklerini ve bilgi transfer mekanizmalarını taklit ederek, hesaplamalı donanımlar geliştirilmesi konusunu ele alan araştırma alanı nöromorfik mühendisliktir. Merkezi desen üreteçlerinin hesaplamalı donanımlarla taklit edilmesi de bu araştırma alanının konuları dâhilindedir. Bu çalışmada merkezi desen üreteci dinamiklerinin taklidi için kullanılan osilatör modellerinden biri olan Rayleigh osilatörünün fraksiyonel tanımlaması üzerinde durulmuştur. Öncelikle sistemin kararlılık analizi yapılmış, ardından bu sistemin osilasyon sergileyebileceği en düşük fraksiyonel derece belirlenmiştir. En düşük fraksiyonel dereceden daha yüksek bir derece ile tanımlanan fraksiyonel sistemde ritmik osilasyon desenini gözlemlemek için sistemin nümerik simülasyonu yapılmıştır. Fraksiyonel Rayleigh osilatörünün nümerik simülasyonu için Grünwald-Letnikov (G-L) fraksiyonel türev yöntemi kullanılmıştır. Ardından fraksiyonel Rayleigh osilatörünün ayrık donanım elemanları kullanılarak deneysel gerçekleştirimi yapılmıştır. Gerçekleştirim sürecinde Matsuda yaklaşıklık metodu ve FOSTER-I R-C ağ dönüşümünden yararlanılmıştır. Tasarlanan bu devre yapısının doğrulaması için SPICE devre simülasyon programı kullanılmıştır. Böylece fraksiyonel derece ile tanımlanan ve merkezi desen üreteçlerinin ritmik desenlerinin elde edilmesinde sıklıkla kullanılan bir osilatör yapısının donanım gerçekleştirim sonuçları başarılı bir şekilde elde edilmiştir.

References

  • C.H. He, D. Tian, G.M. Moatimid, H.F. Salman, ve M.H. Zekry, Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller, J. Low Freq. Noıse. V. A., 14613484211026407, 2021. https://doi.org/10.1177/14613484211026407
  • P. Veskos, ve Y. Demiris, Experimental comparison of the van der Pol and Rayleigh nonlinear oscillators for a robotic swinging task. In proceedings of the AISB 2006 Conference, Adaptation in Artificial and Biological Systems, pp. 197-202, Bristol, 2006.
  • A.C. Filho, M.S. Dutra ve L.S. Raptopoulos, Modeling of a bipedal robot using mutually coupled Rayleigh oscillators, Biol. Cybern., 92(1), 1–7, 2005. https://doi.org/10.1007/s00422-004-0531-1
  • P.G. Drazin, Nonlinear Systems, (Cambridge Texts in AppliedMathematics), Cambridge, U.K.: Cambridge Univ. Press, 1992.
  • K. Matsuoka, Mechanisms of frequency and pattern control in the neural rhythm generators, Biol. Cybern., 56: 345–353, 1987. https://doi.org/10.1007 / BF00319514
  • T. Zielinska, Coupled oscillators utilized as gait rhythm generators of a two-legged walking machine. Biol. Cybern., 74(3): 263–273, 1996. https://doi.org/ 10.1007/BF00652227
  • K. Maleknejad ve L. Torkzadeh, Application of hybrid functions for solving oscillator equations. Rom. Journ. Phys., 60(1-2), 87-98, 2015.
  • I. Podlubny, Fractional-order systems and PIλDα-controllers, IEEE Trans. Automat. Contr., 44(1), 208-214, 1999. https://doi.org/10.1109/9.739144
  • T.J. Freeborn, A Survey of Fractional-Order Circuit Models for Biology and Biomedicine, IEEE J. Emerg. Sel. Topics Power Electron., 3(3), 416–424, 2013. https://doi.org/10.1109/JETCAS.2013.2265797
  • I.E. Sacu ve M. Alci, Low-power OTA-C based tunable fractional order filters, Electronic Components and Materials, 48(3), 135-144, 2018.
  • M.J. Brennan, B. Tang, B. ve J.C. Carranza, Insight into the dynamic behavior of the Van der Pol/Raleigh oscillator using the internal stiffness and damping forces. In Journal of Physics: Conference Series (Vol. 744, No. 1, p. 012122). IOP Publishing, (2016, September).
  • A. Silva-Jua´rez, E. Tlelo-Cuautle, L.G. de la Fraga ve R. Li, FPAA-based implementation of fractional-order chaotic oscillators using first-order active filter blocks. J. Adv. Res. 25, 77–85 2020. https://doi.org/10.1016/ j.jare.2020.05.014.
  • İ.E. Saçu ve N. Korkmaz, An effective method for the reduction of the device utilization amount in experimental realization of a fractional-order system. Nonlinear Dyn., 108(3), 2369-2384, 2022. https://doi.org/10.1007/s11071-022-07340-7.
  • N. Korkmaz ve İ.E. Saçu, Fraksiyonel dereceli FitzHugh-Nagumo nöron modelinin devre sentezi için alternatif bir yaklaşım, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 28(2), 248-254, 2022. https://doi.org/10.5505/pajes.2021.09382.
  • J. Yao, K. Wang, P. Huang, L. Chen ve T.J. Machado, Analysis and implementation of fractional-order chaotic system with standard components. J. Adv. Res. 25, 97–109 2020. https://doi.org/10.1016/j.jare. 2020.05.008.
  • B. Van Der Pol ve J. Van Der Mark, LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 6(38), 763-775, 1928. https://doi.org/ 10.1080/14786441108564652.
  • M.S. Tavazoei ve M. Haeri, A note on the stability of fractional order systems, Math. Comput. Simul., 79(5), 1566-1576, 2009. https://doi.org/10.1016/j.matcom. 2008.07.003
  • I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998.
  • K. Matsuda ve H. Fujii, H (infinity) optimized wave-absorbing control-Analytical and experimental results, J. Guid. Control. Dyn., 16(6), 1146-1153, 1993. https://doi.org/10.2514/3.21139
  • O. Elwy, S.H. Rashad, L.A. Said ve A.G. Radwan, Comparison between three approximation methods on oscillator circuits, Microelectronics J., 81, 162-178, 2018. https://doi.org/10.1016/j.mejo.2018.07.006

The fractional version and the circuit synthesis of the Rayleigh oscillator for the rhythmic pattern generators

Year 2022, Volume: 11 Issue: 3, 584 - 591, 18.07.2022
https://doi.org/10.28948/ngumuh.1039231

Abstract

The research area that deals with the development of computational hardware is neuromorphic engineering by mimicking the physiological characteristics and the information transfer mechanisms of biological structures. The emulation of the central pattern generators with computational hardware is also within the scope of this research area. In this study, the fractional definition of the Rayleigh oscillator, which is one of the oscillator models used for emulation of the central pattern generator dynamics, is handled. First of all, the stability analysis of the system has been made and then, the lowest fractional order at which this system could oscillate is determined. The numerical simulation of this system is made in order to observe the rhythmic oscillation pattern in the fractional system that is defined by a higher fractional order than the lowest one. The Grünwald-Letnikov (G-L) fractional derivative method is used for the numerical simulation of the fractional Rayleigh oscillator. After that, the experimental implementation of the fractional Rayleigh oscillator is made by using the discrete hardware elements. It is utilized from the Matsuda approximation method and the FOSTER-I R-C network transformation in this implementation process. SPICE circuit simulation program is used to verify the functionality of this designed circuit structure. Therefore, the hardware realization results of a fractional-order oscillator structure, which is frequently used in obtaining the rhythmic patterns of the central pattern generators, have been obtained successfully.

References

  • C.H. He, D. Tian, G.M. Moatimid, H.F. Salman, ve M.H. Zekry, Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller, J. Low Freq. Noıse. V. A., 14613484211026407, 2021. https://doi.org/10.1177/14613484211026407
  • P. Veskos, ve Y. Demiris, Experimental comparison of the van der Pol and Rayleigh nonlinear oscillators for a robotic swinging task. In proceedings of the AISB 2006 Conference, Adaptation in Artificial and Biological Systems, pp. 197-202, Bristol, 2006.
  • A.C. Filho, M.S. Dutra ve L.S. Raptopoulos, Modeling of a bipedal robot using mutually coupled Rayleigh oscillators, Biol. Cybern., 92(1), 1–7, 2005. https://doi.org/10.1007/s00422-004-0531-1
  • P.G. Drazin, Nonlinear Systems, (Cambridge Texts in AppliedMathematics), Cambridge, U.K.: Cambridge Univ. Press, 1992.
  • K. Matsuoka, Mechanisms of frequency and pattern control in the neural rhythm generators, Biol. Cybern., 56: 345–353, 1987. https://doi.org/10.1007 / BF00319514
  • T. Zielinska, Coupled oscillators utilized as gait rhythm generators of a two-legged walking machine. Biol. Cybern., 74(3): 263–273, 1996. https://doi.org/ 10.1007/BF00652227
  • K. Maleknejad ve L. Torkzadeh, Application of hybrid functions for solving oscillator equations. Rom. Journ. Phys., 60(1-2), 87-98, 2015.
  • I. Podlubny, Fractional-order systems and PIλDα-controllers, IEEE Trans. Automat. Contr., 44(1), 208-214, 1999. https://doi.org/10.1109/9.739144
  • T.J. Freeborn, A Survey of Fractional-Order Circuit Models for Biology and Biomedicine, IEEE J. Emerg. Sel. Topics Power Electron., 3(3), 416–424, 2013. https://doi.org/10.1109/JETCAS.2013.2265797
  • I.E. Sacu ve M. Alci, Low-power OTA-C based tunable fractional order filters, Electronic Components and Materials, 48(3), 135-144, 2018.
  • M.J. Brennan, B. Tang, B. ve J.C. Carranza, Insight into the dynamic behavior of the Van der Pol/Raleigh oscillator using the internal stiffness and damping forces. In Journal of Physics: Conference Series (Vol. 744, No. 1, p. 012122). IOP Publishing, (2016, September).
  • A. Silva-Jua´rez, E. Tlelo-Cuautle, L.G. de la Fraga ve R. Li, FPAA-based implementation of fractional-order chaotic oscillators using first-order active filter blocks. J. Adv. Res. 25, 77–85 2020. https://doi.org/10.1016/ j.jare.2020.05.014.
  • İ.E. Saçu ve N. Korkmaz, An effective method for the reduction of the device utilization amount in experimental realization of a fractional-order system. Nonlinear Dyn., 108(3), 2369-2384, 2022. https://doi.org/10.1007/s11071-022-07340-7.
  • N. Korkmaz ve İ.E. Saçu, Fraksiyonel dereceli FitzHugh-Nagumo nöron modelinin devre sentezi için alternatif bir yaklaşım, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 28(2), 248-254, 2022. https://doi.org/10.5505/pajes.2021.09382.
  • J. Yao, K. Wang, P. Huang, L. Chen ve T.J. Machado, Analysis and implementation of fractional-order chaotic system with standard components. J. Adv. Res. 25, 97–109 2020. https://doi.org/10.1016/j.jare. 2020.05.008.
  • B. Van Der Pol ve J. Van Der Mark, LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 6(38), 763-775, 1928. https://doi.org/ 10.1080/14786441108564652.
  • M.S. Tavazoei ve M. Haeri, A note on the stability of fractional order systems, Math. Comput. Simul., 79(5), 1566-1576, 2009. https://doi.org/10.1016/j.matcom. 2008.07.003
  • I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998.
  • K. Matsuda ve H. Fujii, H (infinity) optimized wave-absorbing control-Analytical and experimental results, J. Guid. Control. Dyn., 16(6), 1146-1153, 1993. https://doi.org/10.2514/3.21139
  • O. Elwy, S.H. Rashad, L.A. Said ve A.G. Radwan, Comparison between three approximation methods on oscillator circuits, Microelectronics J., 81, 162-178, 2018. https://doi.org/10.1016/j.mejo.2018.07.006
There are 20 citations in total.

Details

Primary Language Turkish
Subjects Electrical Engineering
Journal Section Electrical and Electronics Engineering
Authors

Nimet Korkmaz 0000-0002-7419-1538

İbrahim Ethem Saçu 0000-0002-8627-8278

Publication Date July 18, 2022
Submission Date December 21, 2021
Acceptance Date May 27, 2022
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

APA Korkmaz, N., & Saçu, İ. E. (2022). Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 11(3), 584-591. https://doi.org/10.28948/ngumuh.1039231
AMA Korkmaz N, Saçu İE. Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi. NOHU J. Eng. Sci. July 2022;11(3):584-591. doi:10.28948/ngumuh.1039231
Chicago Korkmaz, Nimet, and İbrahim Ethem Saçu. “Ritmik Desen üreteçleri için Rayleigh osilatörünün Fraksiyonel Versiyonu Ve Devre Sentezi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11, no. 3 (July 2022): 584-91. https://doi.org/10.28948/ngumuh.1039231.
EndNote Korkmaz N, Saçu İE (July 1, 2022) Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11 3 584–591.
IEEE N. Korkmaz and İ. E. Saçu, “Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi”, NOHU J. Eng. Sci., vol. 11, no. 3, pp. 584–591, 2022, doi: 10.28948/ngumuh.1039231.
ISNAD Korkmaz, Nimet - Saçu, İbrahim Ethem. “Ritmik Desen üreteçleri için Rayleigh osilatörünün Fraksiyonel Versiyonu Ve Devre Sentezi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11/3 (July 2022), 584-591. https://doi.org/10.28948/ngumuh.1039231.
JAMA Korkmaz N, Saçu İE. Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi. NOHU J. Eng. Sci. 2022;11:584–591.
MLA Korkmaz, Nimet and İbrahim Ethem Saçu. “Ritmik Desen üreteçleri için Rayleigh osilatörünün Fraksiyonel Versiyonu Ve Devre Sentezi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 11, no. 3, 2022, pp. 584-91, doi:10.28948/ngumuh.1039231.
Vancouver Korkmaz N, Saçu İE. Ritmik desen üreteçleri için Rayleigh osilatörünün fraksiyonel versiyonu ve devre sentezi. NOHU J. Eng. Sci. 2022;11(3):584-91.

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