Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances

Siewe, Raoul Thepi; Domguia, U. Simo; Woafo, P.

doi:10.1515/ijnsns-2017-0025

Cited by 13 publications

(4 citation statements)

References 17 publications

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“…In comparison to the results of the previous research, remind that Thepi et al in 2017 presented a study based on Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances [14]. They used three control methods, among which the proportional control method, for the synchronization of their oscillators.…”

Section: Effectiveness Of the Control Using A Microcontrollermentioning

confidence: 97%

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Controlling Pulse-Like Self-Sustained Oscillators Using Analog Circuits and Microcontrollers

Domguia

Siewe

2023

IJRCS

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Using 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.

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Section: Effectiveness Of the Control Using A Microcontrollermentioning

confidence: 97%

“…When self-sustained oscillators are subjected to the effect of perturbations, they suffer distortions and phase shifts [14]. These disturbances can have consequences in the context of applications when there is a need for precision, as the phase shift leads to the change of times at which prescribed actions are needed.…”

Section: Introductionmentioning

confidence: 99%

Controlling Pulse-Like Self-Sustained Oscillators Using Analog Circuits and Microcontrollers

Domguia

Siewe

2023

IJRCS

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“…They have the ability to have lower power consumption, higher computing power and speed, sufficient memory size, and larger address space. Recent work has shown the capacity of the latter to simulate nonlinear dynamic systems [30][31][32][33][34][35]. Thus, thanks to microcontroller simulation, we obtain electrical signals of very simple and complex shapes, which is explained by their stability to noise compared to analog circuits which suffer from noise, the sizing of parameters, and environmental disturbances.…”

Section: Microcontroller Simulationmentioning

confidence: 99%

Dynamical behavior of cardiac conduction system under external disturbances: simulation based on microcontroller technology

Fonkou¹,

Louodop²,

Talla³

2022

Phys. Scr.

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The heart rhythm is one of the most interesting aspects of the dynamic behavior of biological systems. Understanding heart rhythms is essential in the dynamic analysis of the heart. Each type of dynamic behaviour can describe normal or pathological physiology. The heart is made up of nodes ranging from SA node (natural pacemaker) to Purkinje fibers. The electric current originates in the sinus node and travels through the heart until it reaches the Purkinje fibers, causing after its passage through each of the nodes a heartbeat thus constituting the electrocardiogram (ECG). Since the origin of the electric current is the sinus node, in this article we study numerically and experimentally by microcontroller the influence of the sinus node on the propagation of electric current through the heart. A study of the sinus node in its autonomous state shows us that in their coupled state, the nodes of the heart qualitatively reproduce the time series of the action potential of this latter, which leads to the recording of the ECG. A study when the sinus node is subjected to periodic pulsed excitation E 1(t) = kP(t), assumed to come from blood pressure, with P(t) the blood pressure, shows that for some selected frequencies, it is found that the nodes of the heart and the ECG exhibit responses having the same shape and the same frequencies as those of the pulsatile blood pressure. This suggests the possibility of using such a conversion and excitation mechanism to replicate the functioning of cardiac conduction system. The chaotic analysis of the sinus node subjected to a sinusoidal type disturbance (E 0sin(ωt)) is also presented, it shows that in its chaotic state, the nodes of the heart, as well as the ECG, provide very high frequency signals. This requires the control of the sinus node (natural pacemaker) in such a situation

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“…In recent years, microcontrollers have been shown to be well suited to simulating non-linear dynamic systems [45,46] and to delivering real electrical signals of simple and complex shapes. Due to their compactness, microcontrollers are reliable and stable against noise unlike analog circuits which suffer from noise, environmental disturbances and poor matching between parameter values.…”

Section: Chaos Analysismentioning

confidence: 99%

Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

Fonkou¹,

Louodop²,

Talla³

et al. 2021

Phys. Scr.

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In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term ( ) x sin n is proposed. A generalization in the case of small oscillations on the ( ) x sin n function is studied. Due to ( ) x sin n function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge-Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results. RECEIVED

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Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances

Cited by 13 publications

References 17 publications

Controlling Pulse-Like Self-Sustained Oscillators Using Analog Circuits and Microcontrollers

Controlling Pulse-Like Self-Sustained Oscillators Using Analog Circuits and Microcontrollers

Dynamical behavior of cardiac conduction system under external disturbances: simulation based on microcontroller technology

Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

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