Harmonic Oscillations, Stability and Chaos Control in a Non-Linear Electromechanical System

Yamapi, R.; Orou, J. B. Chabi; Woafo, P.

doi:10.1006/jsvi.2002.5289

Cited by 52 publications

(28 citation statements)

References 13 publications

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“…Although other works [14,[17][18][19][20][21] provide insight into the chaotic behavior of non-linear electromechanical systems, global bifurcations (homoclinic and heteroclinic bifurcation) of our model are important theoretical problems in science and engineering applications as they can reveal the instabilities of motion and complicated dynamical behaviors. These effects, which can damage the electromechanical seismographs, have not been examined by the researches mentioned above accordingly to our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

et al. 2010

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This paper deals with problems for which it is necessary to represent the oscillations of the electromechanical seismograph about their position of equilibrium as regards the synchronous condition. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of the stable orbit with an unstable one. Then, global bifurcations and chaotic dynamics of an electromechanical seismograph are the aims of this study. The electrical part of the model is described by an extended force Rayleigh M. Siewe Siewe ( ) oscillator with Φ 6 -potential, while the mechanical part is described by a damped and driven linear oscillator. By using the direct perturbation technique, we analytically obtain the general solution of the first-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos in the case where the Φ 6 -potential is three wells, which are complemented by numerical simulations by which we illustrate the bifurcation curves and the fractality of the basins of attraction. The results show that the threshold amplitude of harmonic excitation for the onset of instability will move upwards as the amplitude intensity of the ground motion increases. These results suggest that much attention should be paid to controlling the increase of the amplitude of the ground motion, especially when the harmonic excited electromechanical seismograph system as a main device is applied to some practical systems.

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Section: Introductionmentioning

confidence: 99%

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

et al. 2010

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“…This kind of devices with nonlinear resistor and capacitor were studied by Yamapi et al [15], Yamapi and Woafo [16], [17] and Mbouna Ngueuteu, Yamapi and Woafo [18].…”

Section: Introductionmentioning

confidence: 99%

On the Response of the Small Buildings to Vibrations

Munteanu¹,

Chiroiu²,

Sireteanu³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…These investigations have progressed due to the integrated formulation of mechanical, electric and magnetic circuits [2][3][4][5][6][7], as well as the combined use of chaos, bifurcation and control theory [8][9][10][11][12][13]. On the other hand, the appearance of micro electromechanical systems and the developing of new recording systems offer the possibility to examine new interesting dynamical behaviors [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Steady-state self-oscillations and chaotic behavior of a controlled electromechanical device by using the first Lyapunov value and the Melnikov theory

Pérez-Polo

Pérez-Molina

2014

Journal of Sound and Vibration

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In this paper regular and chaotic oscillations in a controlled electromechanical transducer are investigated. The nonlinear control laws are defined by an electric tension excitation and an external force applied to the mobile piece of the transducer.The paper shows that an Andronov-Poincaré-Hopf bifurcation appears as long as adequate parameters are chosen for the nonlinear control laws. The stability of the weak focuses associated to such bifurcation is examined according to the sign of the first Lyapunov value, showing that chaotic behavior can arise when the first Lyapunov value is varied harmonically. The appearance of a homoclinic orbit is investigated assuming an approximated model for the device. On the basis of the parametric equations of the homoclinic orbit and the presence of harmonic disturbances on the platform, it is demonstrated that chaotic oscillations can also appear, and they have been examined by means of the Melnikov theory. Chaotic behavior is corroborated by means of the sensitive dependence, Lyapunov exponents and power spectral density, and it is applied to drive the transducer mobile piece to a predefined set point assuming that noise due to the measurement process can appear in the control signals. The steady state error associated to such random noise is eliminated by adding a PI linear controller to the control force. Numerical simulations are used to corroborate the analytical results.

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Harmonic Oscillations, Stability and Chaos Control in a Non-Linear Electromechanical System

Cited by 52 publications

References 13 publications

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

On the Response of the Small Buildings to Vibrations

Steady-state self-oscillations and chaotic behavior of a controlled electromechanical device by using the first Lyapunov value and the Melnikov theory

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