Finite-Time Stabilization of a Comb-Drive Electrostatic Microactuator

The inherent nonlinear characteristic between the electrostatic force and the applied voltage causes electrostatic microactuators to show the pull-in bifurcation phenomenon. Exploiting a closed-loop control for stabilizing the electrostatic microactuators in its full travel range is the primary objective in the control of such devices. In this paper, the dynamics of a transverse comb-drive electrostatic microactuator is established with considering the presence of parasitic and parametric uncertainties, and it is shown that the dynamics can be transformed into the third-order Brunovsky´s canonical form. Then, a finite-time stabilizing controller is proposed for the third-order Brunovsky´s canonical form systems, and the finite-time stability of the presented controller is shown. The robust finite-time stability of the controller under the parasitic and parametric uncertainties is also verified using numerical simulations.