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.

The research in this dissertation explores active control of a jet injected into quiescent surrounding or into a crossflow, a flowfield also known as the transverse jet. Periodic acoustic actuation is used to perturb the temporal jet injection profile about a mean in order to enhance important characteristics of the flow, such as mixing and penetration of the jet into the crossflow. In practice, nonlinear actuation system dynamics make it difficult to shape the injection profile to match a periodic reference. Discrete sinusoidal inputs necessary for periodic reference tracking produce harmonics that fall directly on the neighboring harmonic frequencies of the reference.

At low forcing amplitudes, approximately less than 0.5m/s RMS, a feedback controller designed from a linear model of the actuation system compensates the coupling between harmonics. A modulated-demodulated controller with feedback from a hotwire placed at the jet exit tracks the first N Fourier coefficients of the reference that fall within the actuation bandwidth. A fundamental improvement to modulated-demodulated control, dynamic phase compensation in place of static phase compensation, is presented to reduce sensitivity function peaking in the neighborhood of the frequencies targeted for rejection or tracking. Above 0.5m/s RMS, however, the harmonic coupling destabilizes modulated-demodulated control designed from a linear model of the actuator dynamics.

An alternative approach creates a stabilizing feedback control based on a multi-input, multi-output (MIMO) empirical model of the harmonic coupling. Transforming the system into baseband coordinates by demodulating the velocity measurement at the harmonic frequencies of the reference waveform simplifies the model to the point the harmonic coupling can be reasonably modeled as a linear MIMO gain. The static model accurately captures the relationship between each harmonic frequency in the neighborhood of an operating point close to a desired reference. The stable feedback loop asymptotically drives the jet velocity to its reference.

This control method is applied to the equidensity jet in crossflow to track pulse-like references at jet to crossflow velocity ratios of R=6.4 and R=2.2. The closed-loop waveforms are symmetric with little ringing and have sharp transitions between the low and high velocity regions of the pulse. Initial experiments with planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) flow diagnostics are also presented. These results show the pulsed jet in crossflow with optimized temporal pulse widths increases the jet spread compared to the unforced and sinusoidally forced jet in crossflow. Additionally, the pulsed jets increase the centerline scalar concentration decay in the near field but become approximately equal with the unforced jet in the far field.