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Micromachines 2016, 7(10), 177; doi:10.3390/mi7100177

Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback

1
Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin University, Tianjin 300072, China
2
Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China
3
Tianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin 300222, China
*
Author to whom correspondence should be addressed.
Academic Editor: Stefano Mariani
Received: 11 August 2016 / Revised: 8 September 2016 / Accepted: 19 September 2016 / Published: 1 October 2016
View Full-Text   |   Download PDF [5038 KB, uploaded 1 October 2016]   |  

Abstract

The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS), which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction. View Full-Text
Keywords: MEMS actuators; bifurcations; multiple scales; parametric resonance; time-delay control; monostable vibration MEMS actuators; bifurcations; multiple scales; parametric resonance; time-delay control; monostable vibration
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Li, L.; Zhang, Q.; Wang, W.; Han, J. Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback. Micromachines 2016, 7, 177.

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