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.

Issue Section:
Technical Papers
Keywords:
electrostatic actuators, observers, capacitive sensors, time-varying systems, electric current measurement, differential equations
Topics:
Cantilevers, Resonance, Signals, Excitation, Dynamics (Mechanics), Design, Differential equations
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