UCLA

This dissertation describes the design, modeling, and testing of a system to electrostatically suspend and manipulate a silicon disk between two sets of stator electrodes. Dual variants of the system are investigated for two disk sizes to yield four total electrode-disk configurations that differ in transduction schemes and the number of disk degrees of freedom that must be actively regulated. Transformers couple the electrodes into pairs 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. Both disks are six-degree-of-freedom systems, however, yaw motion is not measurable using either electrode arrangement and in-plane translations of the smaller disk are passively stabilized by the fringe electrical field. Contributions of the dissertation include the development of a modeling paradigm that is easily adapted to additional electrode-disk geometry, the design and fabrication of a new levitation platform that eliminates actuator-sensor feedthrough, the development of a novel parametric fitting technique for open-loop unstable systems from closed-loop data, and the synthesis of a family of robust multivariable controllers.

The first electrode arrangement uses common electrodes for both control and sensing, however, redundant use of the electrodes produces significant feedthrough from the control inputs to the electronic pick-offs. Feedback controllers are designed for the smaller disk to maximize robustness to perturbations of the plant's normalized coprime factors and multivariable loop-shaping techniques are used to improve closed-loop performance. The disk is suspended and comparisons between the analytical model and empirical data are made. Estimates of the RMS uncertainties of the disk position reveal nanometer- and sub-microradian-level precision for the vertical and rotational degrees of freedom, respectively. A new levitation platform aimed to eradicate actuator-sensor feedthrough is designed and fabricated. The updated system utilizes similar transduction methodology, however, the electrodes used for sensing and actuation are segregated. Analytical models are generated and multivariable controllers robust to various forms of uncertainty are synthesized. This system is under development for non-contact testing of micro-scale devices.