Analysis and design of a capacitive accelerometer based on a electrostatically levitated micro-disk

A system-level model of an electrostatically actuated accelerometer is presented. The accelerometer comprises a proof mass levitated between an arrangement of upper and lower pie-shaped electrodes. The proof mass is an electroplated nickel disk, 1 mm in diameter and 200 μm thick. The position and orientation of the disk is detected by measuring the differential capacitance between the disk and each of the four upper and corresponding lower electrodes. Control of the accelerometer is achieved by incorporating the mechanical sensing element in a ΣΔ modulator control system. The ΣΔ modulator actively controls three degrees of freedom of the disk: out-of-plane translation and in-plane rotations. Relative translation of the disk with respect to the electrodes causes a small restoring force to be generated. The result is passive feedback for the in-plane degrees of freedom. The paper details the Simulink/Matlab model used to evaluate the control system performance. The derivation of the analytical expressions for the differential capacitance and electrostatic feedback forces implemented in the model are presented. These are verified using the finite element method. The results of the simulations validate the feasibility of the levitation concept, show that the ΣΔ modulator can achieve excellent control of the disk and predict that the accelerometer can sense triaxial acceleration separately and synchronously.