Lateral stability of a periodically forced electrostatic comb drive

Constant-gap electrostatic comb drives are a commonly used MEMS actuator design. The operating range of these devices is limited by an instability called “side pull-in” that arises from the geometric nonlinearity of the electrostatic force. Side pull-in corresponds to a pitchfork bifurcation in the plane of the actuator, perpendicular to the intended travel direction. We refer to this as the lateral direction. This paper considers the effect of a periodic drive voltage on the side pull-in instability. Electrode flexibility, out-of-plane motion, and rotation are not considered. The planar translational behavior is modeled by two coupled second-order nonlinear systems. Considering small lateral perturbations and neglecting damping, the lateral dynamics may be approximated by a second-order, linear, periodic time-varying, model in the form of Hill's equation. Application of Floquet theory shows that a periodically time-varying drive voltage may be chosen to stabilize the linearized lateral dynamics about an equilibrium well beyond the side pull-in point. Simulation of the fully coupled nonlinear ODEs shows good agreement with the linear stability map. In terms of the MEMS comb drive model, this corresponds to travel extension of up to 200% beyond the side pull-in point.