Vibration Control in MEMS Resonator Using Positive Position Feedback (PPF) Controller
DOI:
https://doi.org/10.24297/jam.v12i11.1114Keywords:
MEMS Resonators, multiple scales perturbation, the simultaneous primary resonance case, PPF controller, stabilityAbstract
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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References
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11. EL-Sayed A. T., Kamel M. and Eissa M.: Vibration reduction of a pitch-roll ship model with longitudinal and transverse absorbers under multi excitations, Mathematical and Computer Modelling, 52, 1877-1898, 2010.
12. Eissa M., Kamel M. and EL-Sayed A. T.: Vibration reduction of a nonlinear spring pendulum under multi external and parametric excitations via a longitudinal absorber, Meccanica, 46, 325-340, 2011.
13. Eissa M., Kamel M. and EL-Sayed A. T.: Vibration suppression of a 4-DOF nonlinear spring pendulum via longitudinal and transverse absorbers, Journal of Applied Mechanics. ASME, 79(1), 011007 (11 pages), 2012.
14. EL-Sayed A. T and Bauomy H.S.: Vibration control of helicopter blade flapping via time-delay absorber, Meccanica, 49(3), 587-600, 2014.
2. Shaw S., Turner K., Rhoads J. and Baskaranm R.: Parametrically excited MEMS- based filters. Proc. IUTAM Symp. Caotic Dyn, Control Syst, Process 122, 37–146, 2003.
3. El-Ganaini W.A., Saeed N.A. and Eissa M.: Positive position feedback (PPF) controller for suppression of nonlinear system vibration, Nonlinear Dyn, 72, 517–537, 2013.
4. Warminski, J., Bochenski, M., Jarzyna, W., Filipek, P. and Augustyinak, M.: Active suppression of nonlinear composite beam vibrations by selected control algorithms. Commun. Nonlinear Sci. Numer. Simul. 16, 2237–2248, 2011.
5. Hegazy U.H.: Dynamics and control of a self-sustained electromechanical seismographs with time-varying stiffness, Meccanica, 44, 355–368, 2009.
6. Ahamed B. and Pota H.R.: Dynamic compensation for control of a rotary wing UAV using positive position feedback., J. Intell. Robot. Syst., 61, 43–56, 2011.
7. Shan J., Liu H. and Sun D.: Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF), Mechatronics, 15,487–503, 2005.
8. Amer Y. A. and EL-Sayed A. T.: Vibration suppression of nonlinear system via nonlinear absorber, Communication in Nonlinear Science and Numerical Simulation, 13, 1948–63, 2008.
9. Kamel M., Eissa M. and EL-Sayed A. T.: Vibration reduction of a non-linear spring pendulum under multi-parametric excitations via a longitudinal absorber, Physica Scripta, 80, (12pp) 025005, 2009.
10. Eissa M., Kamel M. and EL-Sayed A. T.: Vibration reduction of multi parametric excited spring pendulum via a transversally tuned absorber, Nonlinear Dynamics, 61, 109-121, 2010.
11. EL-Sayed A. T., Kamel M. and Eissa M.: Vibration reduction of a pitch-roll ship model with longitudinal and transverse absorbers under multi excitations, Mathematical and Computer Modelling, 52, 1877-1898, 2010.
12. Eissa M., Kamel M. and EL-Sayed A. T.: Vibration reduction of a nonlinear spring pendulum under multi external and parametric excitations via a longitudinal absorber, Meccanica, 46, 325-340, 2011.
13. Eissa M., Kamel M. and EL-Sayed A. T.: Vibration suppression of a 4-DOF nonlinear spring pendulum via longitudinal and transverse absorbers, Journal of Applied Mechanics. ASME, 79(1), 011007 (11 pages), 2012.
14. EL-Sayed A. T and Bauomy H.S.: Vibration control of helicopter blade flapping via time-delay absorber, Meccanica, 49(3), 587-600, 2014.
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Published
2016-12-14
How to Cite
Amer, Y. A., Sayed, A. E., & Salem, A. (2016). Vibration Control in MEMS Resonator Using Positive Position Feedback (PPF) Controller. JOURNAL OF ADVANCES IN MATHEMATICS, 12(11), 6821–6834. https://doi.org/10.24297/jam.v12i11.1114
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