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Bifurcation-Based Stability Analysis of Electrostatically Actuated Micromirror as a Two Degrees of Freedom System

Kuntao Ye1,*, Yan Luo1, Yingtao Jiang2,*

Jiangxi University of Science and Technology, School of Science, Ganzhou, Jiangxi, China 341000
University of Nevada Las Vegas, Department of Electrical and Computer Engineering, Las Vegas, NV, USA 89154

* Corresponding author: Kuntao Ye. Email: ; Yingtao Jiang. Email:

Computer Modeling in Engineering & Sciences 2018, 114(3), 261-276.


Torsional micromirror devices have been widely used in micro displays, RF switches, optical communications, and optical coherence tomography systems. In order to study the stability of electrostatically driven torsional micromirror system with double bottom plates and two voltage sources, a dimensionless, two degrees of freedom (2-DoF) dynamic model was constructed. Governed by the dimensionless phase space model equation, the pull-in and bifurcation phenomena were analyzed using the Hamiltonian method and numerical simulation. In particular, the influence of the damping coefficient and the torsion-bending coupling effect on the phase trajectory was investigated. Furthermore, the conditions that can lead to pull-in were numerically determined for saddle-node, pitchfork and Hopf bifurcations in the framework of 2-DoF system. Result showed that the dynamic pull-in voltage as predicted by the proposed 2-DoF system model is considerably lower than that by the one degree of freedom (1-DoF) system model. It was also confirmed that the pull-in voltage varies with the damping coefficient and/or the ratio of the two voltages applied to the bottom plates of the micromirror. The modelling method and stability analysis presented in this paper shall provide valuable insight to the design and control of electrostatically actuated micromirror systems.


Cite This Article

Ye, K., Luo, Y., Jiang, Y. (2018). Bifurcation-Based Stability Analysis of Electrostatically Actuated Micromirror as a Two Degrees of Freedom System. CMES-Computer Modeling in Engineering & Sciences, 114(3), 261–276.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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