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Fringing field has to be taken into account in the formulation ofelectrostatic parallel-plate actuators when the gap separating the electrodesis comparable to the geometrical dimensions of the moving plate. Even in thiscase, the existing formulations often result in complicated mathematical modelsfrom which it is difficult to determine the deflection of the moving plate forgiven voltages and therefore to predict the necessary applied voltages foractuation control. This work presents a new method for the modeling of fringingfield, in which the effect of fringing field is modeled as a serial capacitor.Numerical simulation demonstrates the suitability of this formulation. Based onthis model, a robust control scheme is constructed using the theory ofinput-to-state stabilization (ISS) and back-stepping state feedback design. Thestability and the performance of the system using this control scheme aredemonstrated through both stability analysis and numerical simulation.

A New Model of Fringing Capacitance and its Application to the Control of Parallel-Plate Electrostatic Micro Actuators