Nonlinear Dynamics of Folded-MEMS Comb Drive Resonators with time&ndash;delayed control

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (18) : 40-45.

Nonlinear Dynamics of Folded-MEMS Comb Drive Resonators with time–delayed control

ZHANG Qi-chang ,REN Huan ,HAN Jian-xin

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Abstract

Time-delayed velocity feedback is taken into consideration in the DC and AC driving voltage of the folded-MEMS comb drive resonators and the single degree of freedom model of the folded-MEMS comb drive resonators under the influence of time-delayed control is presented. This paper feedback from the velocity with small vibration amplitude to the electricity driving force and approximate the expression with the Taylor expansion. The method of multiple-scales is used to obtain the amplitude-frequency response equation of the system under the influence of time-delay parameters. The change of time-delayed parameter in the system nonlinear resonance result in jumping phenomena when the driving frequency is in the vicinity of resonance frequency. The resonance frequency and nonlinear characteristics of softening or hardening vary under conditions with different physical parameters such as DC and AC voltage. Stability region and vibration amplitude of the system with different physical parameters can be controlled by changing the time-delay parameters. The conclusion that the positive time-delayed control gain make the system instable and the negative time-delayed control gain lead to the disappearance of jumping phenomena is verified by the computation with numerical method.

Key words

folded-MEMS comb / time-delayed velocity feedback / control / nonlinear vibration

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ZHANG Qi-chang,REN Huan,HAN Jian-xin. Nonlinear Dynamics of Folded-MEMS Comb Drive Resonators with time–delayed control[J]. Journal of Vibration and Shock, 2016, 35(18): 40-45

References

[1] Fan L S,Tai Y C,Muller R S. IC-processed electrostatic micromotors[J]. Sensors and Actuators A:Physical,1989 20: 41-47.
[2] 孟光,张文明. 微机电系统动力学[M], 北京:科学出版社, 2008: 137-172.
MENG Guang, ZHANG Wen-ming. Micro electronic mechanical system dynanmics[M], BeiJing: Science Press，2008: 137-172.
[3] 许立. 梳齿式振动微机械谐振器的相关特性研究[D]. 杭州：杭州电子科技大学，2010.
XU li. Research on comb micro resonator[D]. Hangzhou: Hangzhou Electronic Science and Technology University, 2010.
[4] 黄庆安. 微机电系统基础[M]. 北京：机械工业出版社，2007: 8-10.
HUANG Qing-an. Foundations of MEMS[M]. Beiji -ng:China Machine Press，2007: 8-10.
[5] Elshurafa AM, Khirallah K, Tawfik HH, Emira A Aziz AKSA, Sedky SM. Nonlinear dynamics of spring soften and hardening in folded-MEMS comb drive resonators[J]. Journal of micro-electro–mechanical systems，2011, 20(4):943-958.
[6] Zuo-Yang Zhong,Wen-Ming Zhang,Guang Meng et at. Inclination effects on the frequency tuning of comb-driven resonators[J]. Journal of microelectromechanical systems，2013, 22(4)：865-875.
[7] 张文明，孟光，周建斌，等. 参数激励下静电驱动MEMS共振传感器的非线性动力特性研究[J]. 力学季刊，2009, 30(1)：44-48.
ZHANG Wen-ming，MENG Guang，Zhou Jian-bin，et al． Nonlinear dynamic characteristics of electrostatically actuated MEMS resonant sensors under parametric excitation[J]． Chinese quarterly of mechanics，2009， 30(1):44－48．
[8] Pyragas, K.: Continuous control of chaos by selfcontrolli -ng feedback.[J]. Phys Lett A，1992, 170:421-428.
[9] Nayfeh, A.H., Nayfeh, N.A.:Time-delay feedback contro -lof lathe cutting tools[J]. Vib. Control, 2012,18:1106 –1115.
[10] Hu H.Y., Dowell E.H., Virgin L.N. Resonances of aharmo -nically forced duffing oscillator with time delaystatefeed -back[J]. Nonlinear Dyn, 1998, 15:311–327.
[11] Clar T. C., Roger T. H. A integrated CMOS micromech -anical resonator high-Q oscillator[J]. IEEE journal of solid state circuits,1999, 34(4):440-455
[12] S. Shao, K M Masri, M.I. Younis: The effect of time delayed feedback controller on an electrically actuated resonator[J]. Nonlinear Dyn,2013, 74:257-70.
[13] 张峰，苑伟政等. 静电梳齿结构的稳定性分析[J]. 传感技术学报,2011， 24（8）：1122-1125.
Zhang Feng, Yuan Wei-zheng, Chang Hong-long et at. Analsis of lateral stability of electrostatic comb-drive structure[J]. Chinese journal of sensors and actuators, 2011, 24(8):1122-1125.
[14] 尚慧琳，文永蓬. 一类静电微结构谐振传感器的吸合不稳定性研究[J]. 振动与冲击, 2013，32（8）：8-13.
Shang Hui-lin, WEN Yong-peng. Pull-in stability of electr -ostatically actuated MEMS resonant sensor and its contr -ol[J]. Journal of vibration and shock，2013， 32(8): 8 13．