Mitigation of residual oscillations in electrostatically actuated microbeams using a command-shaping approach

Abstract

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.

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

“…The response of the DE balloon actuator for the applied value of dimensionless electric field e below critical value is periodic for any given value of non-dimensional pressure. The least value of the applied field that distinguishes the periodic and aperiodic motion of the balloon is known as the electric field at the onset of dynamic pull-in instability [42,50,51]. On further increment in the applied electric field, the DE balloon finally fails because of dielectric breakdown [44].…”

“…On inheriting the non-dimensional kinetic energy (T) expression from equation (3.12) and the non-dimensional total potential energy (Û) expression from equation (3.7) and inserting into equation (3.19), the resulting equation of motion of the balloon actuator in dimensionless form is written as The response of the DE balloon actuator for the applied value of dimensionless electric field e below critical value is periodic for any given value of non-dimensional pressure. The least value of the applied field that distinguishes the periodic and aperiodic motion of the balloon is known as the electric field at the onset of dynamic pull-in instability [42,50,51]. On further increment in the applied electric field, the DE balloon finally fails because of dielectric breakdown [44].…”

Effect of anisotropy on the dynamic electromechanical instability of a dielectric elastomer actuator

“…If the value of applied nominal electric field exceeds the critical electric field e c D , phase plane plots become nonperiodic and are represented by the dashed lines. The minimum value of the applied electric field that differentiates between the periodic and aperiodic motion of the system is referred to as the DC dynamic electric field at the instability [59][60][61]. , where e a and w ˜denote the amplitude and dimensionless excitation frequency of the AC electric field, respectively.…”

Suppression of contact bounce in beam-type microelectromechanical switches using a feedforward control scheme

“…Further, the resulting equation is integrated over the domain 0, 1. As result, we get a discretized system of N nonlinear coupled ordinary differential equations as (Godara and Joglekar, 2015) …”