Charge control of parallel-plate, electrostatic actuators and the tip-in instability

Abstract

Controlling the charge, rather than the voltage, on a parallel-plate, electrostatic actuator theoretically permits stable operation for all deflections. Practically, we show that, using charge control, the maximum stable deflection is limited by 1) charge pull-in, in which the actuator snaps due to the presence of parasitic capacitance and 2) tip-in, in which the rotation mode becomes unstable. This work presents a circuit that controls the amount of charge on a parallel-plate, electrostatic actuator. This circuit reduces the sensitivity to parasitic capacitance, so that tip-in is the limiting instability. A small-signal model of the actuator is developed and used to determine the circuit bandwidth and gain requirements for stable deflections. Four different parallel-plate actuators have been designed and tested to verify the charge control technique as well as to verify charge pull-in, tip-in, and the bandwidth requirements. One design travels 83% of the gap before tip-in. Another design can only travel 20% of the gap before tip-in, regardless of whether voltage control or charge control is used.

A virtually floating dual-mass accelerometer

“…If we now calculate the net spring constant, it can be shown that k net = k, independent of the applied charge. This shows that applying a constant charge leads to a solution that is always stable [9][10][11]. Compared to voltage control, charge control does not result in a pull-in point, but there is also no negative spring effect.…”

New Approach to Pull-In Limit and Position Control of Electrostatic Cantilever Within the Pull-in Limit

“…So, there is no simple formula to calculate it. People have been using lumped model (Hyun-Ho Yang et al, 2010;Seeger & Boser, 1999;Nielson & Barbastathis, 2006;Faris et al, 2006;Mol et al, 2007;Chowdhury et al, 2006;Owusu & Lewis, 2007) for decades. Lump model estimates the pull-in limit as one-third of the initial gap (d/3).…”

Nonlinear Control Techniques for Micro Electrostatic Actuators in the Presence of Parasitics and Parametric Uncertainties

“…Seeger and Boser [10] presented a circuit that controls the amount of charge on a parallel-plate electrostatic actuator. They showed that charge control increased the stable ranges of motion but the maximum stable deflection is limited due to parasitic capacitance and tip-in.…”