UCLA

The purpose of this research is to create a tool for electrostatically suspending planar, disk-shaped objects towards the effort to measure and analyze stem motion of planar disk-shaped resonators as a function of mass perturbations. Planar disk-shaped resonators, generally, operate as sensors which measure an object's rate of rotation. When measuring the vibratory response, resonant modes appear in degenerate pairs which are exploited in measurements to achieve exceptional signal-to-noise ratios relative to various noise sources. However, assorted errors and nonidealities in a resonator's fabrication ``detune'' the resonant frequencies. The resonator may be ``tuned'' by converging the split frequencies together through systematic mass modifications with post-fabrication techniques. No quantitative analysis has demonstrated changes in the dynamics at the resonator stem as a result of the mass perturbations. By electrostatically suspending a disk resonator, hard-mounts are removed, and repeatable and controllable boundary conditions are established for comparing analogous resonators. The electrostatic suspension of a disk is representative of an ``electrostatic bearing'' .

Two systems are modeled and analyzed to assess the dynamics of an electrostatically controlled object and assistin the design of stabilizing controllers. Inherently, each system is unstable and requires feedback control to adjust the forces acting on the electrostatically suspended body until a desired reference is achieved. Further, electrical measurements representative of the body's pose require compensation to achieve stability due to the colocation of the force actuation and sensing pick-off. A single degree of freedom system is initially fabricated and analyzed both experimentally and through the use of a modeling paradigm to aid in the development of the more complicated suspension platform, debug the electronics interface, and determine the methods of signal conditioning. The modeling paradigm, fabrication techniques, and electronics interface are then extended to a suspended disk platform. The model indicates the suspension system is not strongly stabilizable if only the electrode-disk gap measurements are available. Consequently, an unstable controller is proposed that stabilizes the disk. To control the lateral degrees of freedom, measurements of the disk's lateral position are used to regulate its in-plane motion. Comparisons of the model results and experimental results are given.