Active vibration control of a nonlinear magnetic levitation system via Nonlinear Saturation Controller (NSC)

Kamel, M.; Kandil, Ali; El-Ganaini, W. A.; Eissa, M.

doi:10.1007/s11071-014-1323-3

Cited by 20 publications

(14 citation statements)

References 12 publications

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“…In the work of Ref. [3] the horizontal oscillation of the magnetic moving body object has been reduced by the including a nonlinear saturation controller (NSC) to the nonlinear differential equation. Multivariate the technique of multiple scales was applied to get an analytical solution and to explain the behavior of this model.…”

Section: Introductionmentioning

confidence: 99%

Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Amer

EL-Sayed

Saleh

et al. 2019

Al-Azhar Bulletin of Science

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In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the behavior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum working conditions for the PPF controller. The stability analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented.

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Section: Introductionmentioning

confidence: 99%

Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Amer

EL-Sayed

Saleh

et al. 2019

Al-Azhar Bulletin of Science

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“…The NSC controller (Ashour and Nayfeh, 2002; Warminski et al., 2011; Kamel et al., 2014; Eissa et al., 2015) is applied to the blade so the controlled system model will be: …”

Section: Perturbation Technique and Stability Analysismentioning

confidence: 99%

“…They used an effective frequency tuning mechanism based on quadratic coupling between the controller and the system. The authors (Warminski et al., 2011; Kamel et al., 2014; Eissa et al., 2015) studied active vibration control by applying the NSC controller. That controller was terrific in suppressing the amplitudes of the studied dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Suppressing the nonlinear vibrations of a compressor blade via a nonlinear saturation controller

Kandil

El-Gohary

2016

Journal of Vibration and Control

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A nonlinear saturation controller (NSC) is applied in this work to reduce the oscillations of a rotating blade dynamical system running at unsteady rotating speed. The controller is coupled quadratically to the main system by designing its natural frequency to be one half of the main system natural frequency. This is done to setup an energy bridge between them to make use of saturation phenomenon. That phenomenon is advantageous when the excitation force increases; the whole energy in the main system is channeled to the controller. The two system modes of vibrations are found to be linearly coupled powerfully, so the controller is applied only to the first mode and, consequently, the second mode tracks it. The multiple scales perturbation technique (MSPT) is adopted to derive the steady state equations that describe the modulations of amplitudes and phases of the system before and after control. Then, a stability analysis is achieved via Lyapunov’s indirect method to determine the stable and unstable solutions depending on the real parts of the Jacobian matrix eigenvalues. Time history and different response curves of the controlled system are included for showing the controller effect. Eventually, validation curves and comparison with previously published work are included.

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“…A study for (NSC) is presented by Hamed and Amer [12] that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation.Kamel et al [13] studied the active vibration control of a nonlinear magnetic levitation system via (NSC). Warminski et al [14] presented an application of (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force.…”

Section: Introductionmentioning

confidence: 99%

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

Amer

EL-Sayed

Darwesh

2019

ARJOM

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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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Active vibration control of a nonlinear magnetic levitation system via Nonlinear Saturation Controller (NSC)

Cited by 20 publications

References 12 publications

Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Suppressing the nonlinear vibrations of a compressor blade via a nonlinear saturation controller

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

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