We present a mathematical model for the dynamics of an electrostatically actuated micro-cantilever. For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular, illustrate that parametric resonance phenomena occur in capacitively actuated micro-cantilevers. We propose a system where the current measured is used as the sensing signal of the cantilever state and position through a dynamical observer. By investigating how the best achievable performance of an optimal observer depends on the excitation frequency, we show that the best such frequency is not necessarily the resonant frequency of the cantilever.
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e-mail: napoli@engineering.ucsb.edu
e-mail: bamieh@engineering.ucsb.edu
e-mail: turner@engineering.ucsb.edu
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June 2004
Technical Papers
A Capacitive Microcantilever: Modelling, Validation, and Estimation Using Current Measurements
Mariateresa Napoli,
e-mail: napoli@engineering.ucsb.edu
Mariateresa Napoli
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
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Bassam Bamieh,
e-mail: bamieh@engineering.ucsb.edu
Bassam Bamieh
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
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Kimberly Turner
e-mail: turner@engineering.ucsb.edu
Kimberly Turner
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
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Mariateresa Napoli
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
e-mail: napoli@engineering.ucsb.edu
Bassam Bamieh
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
e-mail: bamieh@engineering.ucsb.edu
Kimberly Turner
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106
e-mail: turner@engineering.ucsb.edu
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division July 2, 2003 final revision, November 3, 2003 Associate Editor: R. Gao.
J. Dyn. Sys., Meas., Control. Jun 2004, 126(2): 319-326 (8 pages)
Published Online: August 5, 2004
Article history
Received:
July 2, 2003
Revised:
November 3, 2003
Online:
August 5, 2004
Citation
Napoli, M., Bamieh, B., and Turner, K. (August 5, 2004). "A Capacitive Microcantilever: Modelling, Validation, and Estimation Using Current Measurements ." ASME. J. Dyn. Sys., Meas., Control. June 2004; 126(2): 319–326. https://doi.org/10.1115/1.1767851
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