Abstract
Pull-in instability of the electrostatic microstructures is a common undesirable phenomenon which implies the loss of reliability of micro-electromechanical systems. Therefore, it is necessary to understand its mechanism and then reduce the phenomenon. In this work, pull-in instability of a typical electrostatic MEMS resonator is discussed in detail. Delayed position feedback and delayed velocity feedback are introduced to suppress pull-in instability, respectively. The thresholds of AC voltage for pull-in instability in the initial system and the controlled systems are obtained analytically by the Melnikov method. The theoretical predictions are in good agreement with the numerical results. It follows that pull-in instability of the MEMS resonator can be ascribed to the homoclinic bifurcation inducing by the AC and DC load. Furthermore, it is found that the controllers are both good strategies to reduce pull-in instability when their gains are positive. The delayed position feedback controller can work well only when the delay is very short and AC voltage is low, while the delayed velocity feedback will be effective under a much higher AC voltage and a wider delay range.
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References
Younis, M.I.: MEMS Linear and Nonlinear Statics and Dynamics. Springer, New York (2011)
Zhang, W.M., Yan, H., Peng, Z.K., Meng, G.: Electrostatic pull-in instability in MEMS/NEMS: a review. Sens. Actuators A Phys. 214(4), 187–218 (2014)
Arkan, E.F., Sacchetto, D., Yildiz, I., Leblebici, Y., Alaca, B.E.: Monolithic integration of Si nanowires with metallic electrodes: NEMS resonator and switch applications. J. Micromech. Microeng. 21(12), 125018 (2011)
Loh, O.Y., Espinosa, H.D.: Nanoelectromechanical contact switches. Nat. Nanotechnol. 7(5), 283–295 (2012)
Nayfeh, A.H., Younis, M.I., Abdel-Rahman, E.M.: Dynamic pull-in phenomenon in MEMS resonators. Nonlinear Dyn. 48(1–2), 153–163 (2007)
Ruzziconi, L., Ramini, A.H., Younis, M.I., Lenci, S.: Theoretical prediction of experimental jump and pull-in dynamics in a MEMS sensor. Sensors 14(9), 17089–17111 (2014)
Rega, G., Settimi, V.: Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy. Nonlinear Dyn. 73(1), 101–123 (2013)
Rokni, H., Lu, W.: A continuum model for the static pull-in behavior of graphene nanoribbon electrostatic actuators with interlayer shear and surface energy effects. J. Appl. Phys. 113(15), 153512 (2013)
Das, K., Batra, R.C.: Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems. J. Micromech. Microeng. 19(3), 035008 (2009)
Elata, D., Bamberger, H.: On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources. J. Microelectromech. Syst. 15(1), 131–140 (2013)
Sedighi, H.M., Changizian, M., Noghrehabadi, A.: Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory. Lat. Am. J. Solids Struct. 11(5), 810–825 (2014)
Rega, G., Lenci, S.: Dynamical integrity and control of nonlinear mechanical oscillators. J. Vib. Control 14(1–2), 159–179 (2008)
Liu, Y., Hu, A., Han, F., Lu, Y.: Stability analysis of nonlinear ship-roll dynamics under wind and wave. Chaos Solitons Fractals 76, 32–39 (2015)
Lenci, S., Rega, G.: Control of pull-in dynamics in a nonlinear thermoelastic electrically actuated microbeam. J. Micromech. Microeng. 16(2), 390–401 (2006)
Ruzziconi, L., Younis, M.I., Lenci, S.: An efficient reduced-order model to investigate the behavior of an inperfect microbeam under axial load and electric excitation. J. Comput. Nonlinear Dyn. 8(1), 011014 (2013)
Zhu, Z.W., Li, X.M., Xu, J.: Bifurcation characteristics and safe basin of MSMA microgripper subjected to stochastic excitation. AIP Adv. 5(2), 027124 (2015)
Alsaleem, F.M., Younis, M.I., Ouakad, H.M.: On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators. J. Micromech. Microeng. 19(4), 045013 (2009)
Alsaleem, F.M., Younis, M.I., Ruzziconi, L.: An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically. J. Microelectromech. Syst. 19(4), 794–806 (2010)
Rocha, L.A., Cretu, E., Wolffenbuttel, R.F.: Using dynamic voltage drive in a parallel-plate electrostatic actuators for full-gap travel range and positioning. J. Microelectromech. Syst. 15(1), 69–83 (2006)
Shirazi, F.A., Velni, J.M., Grigoriadis, K.M.: An LPV design approach for voltage control of an electrostatic MEMS actuator. J. Microelectromech. Syst. 20(1), 302–311 (2011)
Nbendjo, B.R.N., Woafo, P.: Active control with delay of horseshoes chaos using piezoelectric absorber on a buckled beam under parametric excitation. Chaos Solitons Fractals 32(1), 73–79 (2007)
Kirrou, I., Belhaq, M.: Control of bistability in non-contact mode atomic force microscopy using modulated time delay. Nonlinear Dyn. 81(1–2), 607–619 (2015)
Shang, H., Xu, J.: Delayed feedbacks to control the fractal erosion of safe basins in a parametrically excited system. Chaos Solitons Fractals 41(4), 1880–1896 (2009)
Shang, H., Wen, Y.: Fractal erosion of the safe basin in a Helmholtz oscillator and its control by linear delayed velocity feedback. Chin. Phys. Lett. 28(11), 110503 (2011)
Alsaleem, F.M., Younis, M.I.: Stabilization of electrostatic MEMS resonators using a delayed feedback controller. Smart Mater. Struct. 19(3), 035016 (2010)
Shao, S., Masri, K.M., Younis, M.I.: The effect of time-delay feedback controller on an electrically actuated resonator. Nonlinear Dyn. 74(1–2), 257–270 (2013)
Masri, K.M., Shao, S., Younis, M.I.: Delayed feedback controller for microelectromechanical systems resonators undergoing large motion. J. Vib. Control 21(13), 2604–2615 (2015)
Cao, Y.Y., Chung, K.W., Xu, J.: A novel construction of homoclinic and heteroclinic orbits in nonlinear oscillators by a perturbation-incremental method. Nonlinear Dyn. 64(3), 221–236 (2011)
Haghighi, H.S., Markazi, A.H.D.: Chaos prediction and control in MEMS resonators. Commun. Nonlinear Sci. Numer. Simul. 15(10), 3091–3099 (2010)
Siewe, M.S., Hegazy, U.H.: Homoclinic bifurcation and chaos control in MEMS resonators. Appl. Math. Model. 35(12), 5533–5552 (2011)
Acknowledgements
This work has been totally developed during the author’s stay at University of Michigan in Ann Arbor. The author gratefully acknowledges the help and fruitful discussions of Professor Gabor Orosz. This work was supported by the National Natural Science Foundation of China under Grant No. 11472176.
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Shang, H. Pull-in instability of a typical electrostatic MEMS resonator and its control by delayed feedback. Nonlinear Dyn 90, 171–183 (2017). https://doi.org/10.1007/s11071-017-3653-4
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DOI: https://doi.org/10.1007/s11071-017-3653-4