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

[+] Author and Article Information
Mariateresa Napoli, Bassam Bamieh, Kimberly Turner

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

J. Dyn. Sys., Meas., Control 126(2), 319-326 (Aug 05, 2004) (8 pages) doi:10.1115/1.1767851 History: Received July 02, 2003; Revised November 03, 2003; Online August 05, 2004
Copyright © 2004 by ASME
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A schematic of an electrostatically driven cantilever
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SEM image of a polySi cantilever. The inset shows details of the mechanical connection to the base.
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Frequency response of the capacitive cantilever: the dashed line corresponds to measured data, the solid one is its least square fit
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Electrostatic resonance. The dots represent measured values of resonance frequency, the solid line is their linear fit.
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Mathieu equation: the shaded areas correspond to unstable behavior
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First instability region: experimental data points (circles) and curves with identified parameters. Inset: effect of damping visible on experimentally measured data, marked with circles.
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Cantilever response in parametric resonance (oscilloscope data)
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Exponential growth of oscillation following parametric excitation
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Frequency response above critical driving voltage amplitude (A=10 V). The solid and dashed lines have been added to the experimental data points (marked with o and +) to facilitate the reading.
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Phase portrait of Eq. (6). The labelling corresponds to the regions of Fig. 9.
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A schematic of the observer problem
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H-norm vs. frequency of excitation
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Performance of the observers in the presence of measurement noise and initial estimation error. The dashed line is the measured position signal, the solid line its estimate. a) Optimal observer b) Reduced order observer.
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Expected current signal from experimental velocity and position data
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Estimation error for different values of the observer gain: a) k>0 cos(ϕ)<0, b) k<0 cos(ϕ)>0



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