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.
A Capacitive Microcantilever: Modelling, Validation, and Estimation Using Current Measurements
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.
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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