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Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
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 c...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6190236/ https://www.ncbi.nlm.nih.gov/pubmed/30404350 http://dx.doi.org/10.3390/mi7100177 |
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author | Li, Lei Zhang, Qichang Wang, Wei Han, Jianxin |
author_facet | Li, Lei Zhang, Qichang Wang, Wei Han, Jianxin |
author_sort | Li, Lei |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-6190236 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-61902362018-11-01 Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback Li, Lei Zhang, Qichang Wang, Wei Han, Jianxin Micromachines (Basel) Article 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. MDPI 2016-10-01 /pmc/articles/PMC6190236/ /pubmed/30404350 http://dx.doi.org/10.3390/mi7100177 Text en © 2016 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Li, Lei Zhang, Qichang Wang, Wei Han, Jianxin Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title | Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title_full | Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title_fullStr | Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title_full_unstemmed | Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title_short | Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback |
title_sort | bifurcation control of an electrostatically-actuated mems actuator with time-delay feedback |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6190236/ https://www.ncbi.nlm.nih.gov/pubmed/30404350 http://dx.doi.org/10.3390/mi7100177 |
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