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When electrostatically actuated microbeams are driven by an input-waveform comprising multiple voltage steps, the resulting response inherently contains residual oscillations, which may prove detrimental to the device performance and accuracy. In this article, we report the systematic development of a command shaping technique for mitigating such residual oscillations in electrostatically actuated microbeams and achieving fast switching between the successive equilibrium states. Invoking the force balance at a critical point in an oscillation cycle, the proposed technique relies on bringing the actuator to a stagnation state by applying an additional voltage signal of specific amplitude at a predetermined time. The underlying principle of the technique is enunciated for the lumped parallel-plates model of the microactuator, and further extended to the cases of microbeams. The electromechanical model of the microbeam incorporates the effects of full-order electrostatic nonlinearity, moderately large deflections, viscous energy dissipation, and fringing fields. The modal superposition method is employed to obtain the dynamic response of microbeams. Based on a single-mode assumption, the proposed technique lends itself to a simple multistep waveform, which is attractive from the implementation point of view. The applicability of the proposed technique is demonstrated by considering a wide range of parameters involving variations in the extent of geometric nonlinearity, damping, and equilibrium sequences. The impact of higher modes on the stabilized response is exposited, and a command shaping approach based on the multi-mode response of the actuator is suggested. In particular, such an approach is shown to be effective in controlling the motion of the beam in the vicinity of the static pull-in displacement, which is associated with strong electrostatic nonlinearity. The present investigation can find its potential use in the development of an open-loop controller for electrostatically actuated microbeams.

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