Three degree-of-freedom control of an electrostatically suspended disk

Abstract

A system for suspending and manipulating the vertical position, pitch and roll of a silicon disk is proposed. The disk is situated between sets of transformer-coupled electrodes that measure disk-electrode differential capacitances and exert electrostatic forces on the disk. There is no physical contact with the disk when it is suspended. Models of the system reveal three unstable modes. An initial controller is designed to maximize robustness to perturbations of the plant’s normalized coprime factors. With the disk suspended, an empirical frequency response of the plant is measured and used to subsequently identify a parametric model. An updated controller based on the identified model improves closed-loop performance. Estimates of noise spectral densities show the RMS uncertainties of the disk position and angles are less than 7 nm and 0.5 $\mu$rad, respectively, over the 2.5 kHz signal bandwidth.