Active and Time Delay Controls on Vibrations of the Micro-Electro-Mechanical System (MEMS) Resonator

In this paper, the active control and time delay control are applied on a nonlinear mechanical system subjected to external force to reduce the resulted vibration. The system is modeled by a unique nonlinear differential equation. The multiple scale perturbation technique (MSPT) was applied to obtain an approximate solution and showing the response equation. The stability of the system at primary resonance case is investigated using both of phase plane and frequency response equation. Numerical solution is obtained using Runge – Kutta forth order method.Also, MATLAB 14.0 and Maple 18.0 programs were used to study the numerical solution and the effect of the different parameters for the response of the nonlinear dynamic mechanical system.

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Vibration Control in MEMS Resonator Using Positive Position Feedback (PPF) Controller

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v12i11.1114 ◽

2016 ◽

Vol 12 (11) ◽

pp. 6821-6834

Author(s):

Y A Amer ◽

A.T EL Sayed ◽

A.M. Salem

Keyword(s):

Order Approximation ◽

Perturbation Technique ◽

Multiple Scale ◽

Steady State Solution ◽

Positive Position Feedback ◽

Mems Resonator ◽

Position Feedback ◽

Resonator System ◽

The Stability ◽

First Order Approximation

In this paper, the vibration of a micro-electromechanical resonator with positive position feedback controller is studied. The analytical results are obtained to the first order approximation by using the multiple scale perturbation technique. The stability of the steady-state solution is presented and studied applying frequency response equations near the simultaneous primary and internal resonance cases. The effects of the controller and some system parameters on the vibrating system are studied numerically. The main result of this paper indicates that it is possible to reduce the vibration for the resonator system.

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The Vibration reduction of a cantilever beam subjected to parametric excitation using time delay feedback

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v13i2.5971 ◽

2017 ◽

Vol 13 (2) ◽

pp. 7186-7193

Author(s):

Y A Amer

Keyword(s):

Time Delay ◽

Cantilever Beam ◽

Parametric Excitation ◽

Order Approximation ◽

Perturbation Technique ◽

Dynamical Behavior ◽

Multiple Scale ◽

Steady State Solution ◽

State Feedback Control ◽

Resonance Case

In this paper, dynamical behavior of a cantilever beam subject to parametric excitation under state feedback control with time delay is analyzed. The method of multiple scale perturbation technique is applied to obtain the solution up to the first order approximation. We obtain equations for the amplitude and phase. We studied all resonance cases numerically. Stability of the steady state solution for the selected resonance case is studied applying Rung-Kutta fourth method and frequency response equation via Matlab 7.0 and maple 16. From the results, it can be seen that the frequency and amplitude responses for the selected resonance case can be affected by the time delayed control. Effects of different parameters of the system are studied.

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Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback

Shock and Vibration ◽

10.1155/2006/842318 ◽

2006 ◽

Vol 13 (2) ◽

pp. 65-83 ◽

Cited By ~ 11

Author(s):

A.F. EL-Bassiouny

Keyword(s):

Time Delay ◽

State Feedback ◽

Order Approximation ◽

Perturbation Technique ◽

Multiple Scale ◽

State Feedback Control ◽

Response Curves ◽

Equivalent Damping ◽

Scale Perturbation ◽

First Order Approximation

Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.

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Positive Position Feedback Controllers for Reduction the Vibration of a Nonlinear Spring Pendulum

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v12i11.7 ◽

2016 ◽

Vol 12 (11) ◽

pp. 6758-6772

Author(s):

Y a Amer

Keyword(s):

Perturbation Technique ◽

Multiple Scale ◽

Resonance Case ◽

Feedback Controllers ◽

Pendulum System ◽

Nonlinear Spring ◽

Positive Position Feedback ◽

Position Feedback ◽

Scale Perturbation ◽

The Stability

In this paper, the two positive position feedback controllers (PPF) are proposed to reduce the longitudinal and angular vibrations of the nonlinear spring pendulum system which simulated the ship roll motion. This described by a four-degreeof- freedom system (4-DOF) which subjected to the external excitation force at simultaneous primary and internal resonance case. The method of multiple scale perturbation technique (MSPT) is applied to study the approximate solution of the given system. The stability of the system is investigated near the resonance case applying the frequency-response equations. Numerically, the effects of different controllers parameters on the basic system behavior are studied.

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Vibration Suppression of a Four-Degrees-of-Freedom Nonlinear Spring Pendulum via Longitudinal and Transverse Absorbers

Journal of Applied Mechanics ◽

10.1115/1.4004551 ◽

2011 ◽

Vol 79 (1) ◽

Cited By ~ 4

Author(s):

M. Eissa ◽

M. Kamel ◽

A. T. El-Sayed

Keyword(s):

Degrees Of Freedom ◽

Vibration Suppression ◽

Perturbation Technique ◽

Time History ◽

Multiple Scale ◽

Threshold Value ◽

Response Curves ◽

Pendulum System ◽

Nonlinear Spring ◽

The Stability

An investigation into the passive vibration reduction of the nonlinear spring pendulum system, simulating the ship roll motion is presented. This leads to a four-degree-of-freedom (4-DOF) system subjected to multiparametric excitation forces. The two absorbers in the longitudinal and transverse directions are usually designed to control the vibration near the simultaneous subharmonic and internal resonance where system damage is probable. The theoretical results are obtained by applying the multiple scale perturbation technique (MSPT). The stability of the obtained nonlinear solution is studied and solved numerically. The obtained results from the frequency response curves confirmed the numerical results which were obtained using time history. For validity, the numerical solution is compared with the analytical solution. Effectiveness of the absorbers (Ea) are about 13 000 for the first mode (x) and 10 000 for the second mode (ϕ). A threshold value of linear damping coefficient can be used directly for vibration suppression of both vibration modes. Comparison with the available published work is reported.

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Diagonal Riccati stability of a class of time-delay systems

Cybernetics and Physics ◽

10.35470/2226-4116-2018-7-4-167-173 ◽

2018 ◽

pp. 167-173

Author(s):

Alexander Aleksandrov ◽

Nadezhda Kovaleva

Keyword(s):

Complex System ◽

Population Dynamics ◽

Time Delay ◽

Mechanical System ◽

Formation Control ◽

Sufficient Conditions ◽

Delay Systems ◽

Time Delay Systems ◽

The Stability ◽

Necessary And Sufficient

A complex system describing interaction of subsystems of the second order with delay in connections between them is studied. Necessary and sufficient conditions of the existence of a diagonal Lyapunov–Krasovskii functional for the considered system are derived. The obtained results are applied for the stability a nalysis of a mechanical system and a model of population dynamics. In addition, it is shown that they can be used in a problem of formation control.

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