(University of Buea, Cameroon)(2) Raoul Thepi Siewe
(University of Yaounde I, Cameroon)*corresponding author
AbstractUsing simulation from analog electronic circuits and from a microcontroller, this paper considers the control or synchronization of pulse-like self-sustained oscillators described by the equations derived from the chemical system known as Brusselator. The attention is focused on the effect of proportional control when the Brusselator is subjected to disturbances such as pulse-like oscillations and square signals. The analog electronic circuits simulation is based on Multisim, while the microcontroller simulation uses mikroC software and PIC 18F4550. In order to determine the intervals for which the synchronization is effective, the equations of the Brusselator are solved numerically using the fourth-order Runge-Kutta method. As software used for conducting numerical simulations, FORTRAN 95 version PLATO is used for numerical simulation and MATLAB for plotting curves using the data generated from FORTRAN simulations. It has been shown that the control is effective for some values of the proportional control parameter. A good qualitative and quantitative agreement is found from the results of the numerical simulation and those obtained from the analog electronic circuits as well as those delivered by the microcontroller. Since the oscillations delivered by the heart are pulsed oscillations, this study gives an idea of how to control the heart frequency of an individual whose heart is subject to certain disturbances related to stress or illness, to name just a few examples. KeywordsPulse-like oscillators; Brusselator oscillators; Microcontrollers; analog circuits; Control; Synchronization
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DOIhttps://doi.org/10.31763/ijrcs.v3i1.802 |
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References
[1] E. de Pinto Sandro, R. Lopez Sergio and L. Viana Ricardo, “Collective behavior in a chain of Van der Pol oscillators with power-law coupling,” Physica A: Statistical Mechanics and its Applications, vol. 303, no. 3-4, pp. 339-356, 2002, https://doi.org/10.1016/S0378-4371(01)00549-0.
[2] B. Ramakrishnan, A. Durdu, K. Rajagopal, and A. Akgul, “Infinite attractors in a chaotic circuit with exponential memristor and Josephson junction resonator,” AEU–International Journal of Electronics and Communications, vol. 123, p. 153319, 2020, https://doi.org/10.1016/j.aeue.2020.153319.
[3] R. Rand and P. Holmes, “Bifurcation of periodic motions in two coupled Van der Pol oscillators,” International Journal of Non-Linear Mechanics, vol. 15, no. 4-5, pp. 387-399, 1980, https://doi.org/10.1016/0020-7462(80)90024-4.
[4] J. Murray, Mathematical biology. New York: Springer, 2002, https://doi.org/10.1007/b98868.
[5] J. Kozlowski, U. Parlitz and W. Lauterborn, “Bifurcation analysis of two coupled periodically driven Duffing oscillators,” Physical Review E, vol. 51, no. 3, p. 1861, 1995. https://doi.org/10.1103/PhysRevE.51.1861.
[6] H. Simo, “Etude théorique et expérimentale de la dynamique des oscillateurs pulsés et applications aux systèmes électromécaniques,” Doctorat/PhD thesis, University of Yaounde 1: Yaoundé (Cameroon), 2014, http://www.lamsebp.org/PDF/ABSTRACT_SIMO.pdf.
[7] A. Destexhe and P. Gaspard, “Bursting oscillations from a homoclinic tangency in a time delay system,” Physics Letters A, vol. 173, no. 4-5, pp. 386-391, 1993, https://doi.org/10.1016/0375-9601(93)90256-Y.
[8] E. M. Izhikevich, “Neural excitability, spiking and bursting,” International Journal of Bifurcation and Chaos, vol. 10, no. 6, pp. 1171-12660, 2000, https://doi.org/10.1142/S0218127400000840.
[9] Q. S. Bi, “The mechanism of bursting phenomena in Belousov-Zhabotinsky (BZ) chemical reaction with multiple time scales,” Science China Technological Sciences, vol. 53, pp. 748-760, 2010, https://doi.org/10.1007/s11431-010-0082-8.
[10] U. Simo Domguia, “Theoretical and experimental study of electromechanical systems powered by bio/chemo-inspired oscillators,” Doctorat/Ph.D. thesis, University of Yaounde 1: Yaoundé (Cameroon), 2019.
[11] M. Tlidi, Y. Gandica, G. Sonnino, E. Averlant and K. Panajotov, “Self-replicating spots in the Brusselator model and extreme events in the one-dimensional case with delay,” Entropy, vol. 18, no. 3, p. 64, 2016, https://doi.org/10.3390/e18030064.
[12] L. W. Luyben, Chemical Reactor Design and Control. Wiley & Sons, New York, USA: 2007, https://books.google.co.id/books?id=P-zvB8z3djYC.
[13] O. Levenspiel, Chemical Reaction Engineering. Wiley & Sons, New York, USA: 1999, https://books.google.co.id/books?id=vw48EAAAQBAJ.
[14] R. Thepi Siewe, “Microcontroller and analog study of the synchronization of coupled Van der Pol oscillators,” Doctorat/Ph.D. thesis, University of Yaounde 1: Yaoundé (Cameroon), 2020.
[15] F. Wang, L. Zhang, X. Feng and H. Guo, “An Adaptive Control Strategy for Virtual Synchronous Generator,” Transactions on Industry Applications, vol. 54, no. 5, pp. 5124-5133, 2018, https://doi.org/10.1109/TIA.2018.2859384.
[16] W. Bai, T. Li and S. Tong, “NN Reinforcement Learning Adaptive Control for a Class of Nonstrict-Feedback Discrete-Time Systems,” IEEE Transactions on Cybernetics, vol. 50, no. 11, pp. 4573-4584, 2020, https://doi.org/10.1109/TCYB.2020.2963849.
[17] L. Liu, T. Gao, Y. J. Liu, S. Tong, C. L. Philip Chen and L. Ma, “Time-varying IBLFs-based adaptive control of uncertain nonlinear systems with full state constraints,” Automatica, vol. 129, p. 109595, 2021, https://doi.org/10.1016/j.automatica.2021.109595.
[18] R. Chiu R, Mora-Gonzalez and Lopez-Mancilla, “Implementation of a Chaotic Oscillator into a Simple Microcontroller,” IERI Procedia, vol. 4, pp. 247-252, 2013, https://doi.org/10.1016/j.ieri.2013.11.035.
[19] H. Hamiche, S. Guermah, R. Saddaoui, K. Hannoun, M. Laghrouche, and S. Djennoune, “Analysis and implementation of a novel robust transmission scheme for private digital communications using Arduino Uno board,” Nonlinear Dyn., vol. 81, no. 4, pp. 1921-1932, 2015, https://doi.org/10.1007/s11071-015-2116-z.
[20] A. P. Fournaris and N. Sklavos, “Secure embedded system hardware design - A flexible security and trust enhanced approach,” Comput. Elect. Eng., vol. 40, no. 1, pp. 121–133, 2014. https://doi.org/10.1016/j.compeleceng.2013.11.011.
[21] A. A. Elbaset, H. Ali, M. Abd-El Sattar and M. Khaled, “Implementation of a modified perturb and observe maximum power point tracking algorithm for photovoltaic system using an embedded microcontroller,” IET Renew Power Gen, vol. 10, no. 4, pp. 551–560, 2016, https://doi.org/10.1049/iet-rpg.2015.0309.
[22] M. A. Murillo-Escobar, C. Cruz-Hernández, F. Abundiz-Pérez and R. M. López-Gutiérrez, “Implementation of an improved chaotic encryption algorithm for real-time embedded systems by using a 32-bit microcontroller,” Microprocess. Microsyst., vol. 45, pp. 297–309, 2016. https://doi.org/10.1016/j.micpro.2016.06.004
[23] S. Kaçar, “Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system,” Optik, vol. 127, no. 20, pp. 9551-9561, 2016, https://doi.org/10.1016/j.ijleo.2016.07.044.
[24] J. Chandramohan, R. Nagarajan, K. Satheeshkumar, N. Ajithkumar, P. A. Gopinath and S. Ranjithkumar, “Intelligent smart home automation and security system using Arduino and Wi-fi,” Int. J. Eng. And Comp. Sci., vol. 6, no. 3, pp. 20694–20698, 2017.
[25] Y. Raghavender Rao, “Automatic smart parking system using Internet of Things (IoT),” Int. J. Eng. Tech. Sci. Res., vol. 4, no. 5, pp. 225–228, 2017, http://www.ijetsr.com/images/short_pdf/1495021347_nitttr888_ijetsr.pdf.
[26] M. Z. De la Hoz, L. Acho and Y. Vidal, “An experimental realization of a chaos-based secure communication using Arduino microcontrollers,” The Scientif. World J., vol. 2015, 2015. https://doi.org/10.1155/2015/123080.
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International Journal of Robotics and Control Systems
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