Position Estimator Design for a MEMS Top-Drive Electrostatic Rotary Actuator

The capacitance and rotor angle of a MEMS top-drive electrostatic rotary actuator do not have a linear relationship due to the non-ignorable fringe effect and low aspect ratio of the electrodes. Therefore, the position estimation is not as straightforward as that for a comb-drive linear actuator or a side-drive rotary actuator. The reason is that the capacitance is a nonlinear and periodic function of the rotor angle and is affected by the three-phase input voltages. Therefore, it cannot be approximated as a simple two-plate capacitor. Sensing the capacitance between a rotor and a stator is another challenge. The capacitance can be measured in the electrodes (stators), but the electrodes also have to perform actuation, so a method is needed to combine actuation and sensing. In this study, a nonlinear capacitance model was derived as a data-driven model that effectively represents the nonlinear capacitance with sufficient accuracy. To measure the capacitance accurately, the stator parts for actuation and those for sensing are separated. Using the nonlinear model and the capacitance measurement, an unscented Kalman filter was designed to mitigate the large estimation error due to the periodic nonlinearity. The proposed method shows stable and accurate estimation that cannot be achieved with a simple two-plate capacitor model. The proposed approach can be applied to a similar system with highly nonlinear capacitance.