We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies.

Humans learn to interact with many complex physical systems. For example, humans learn to fly aircraft, operate drones, and drive automobiles. We present results from human-in-the-loop (HITL) experiments, where human subjects interact with dynamic systems while performing command-following tasks multiple times over a one-week period. We use a new subsystem identification (SSID) algorithm to estimate the control strategies (feedforward, feedforward delay, feedback, and feedback delay) that human subjects use during their trials. We use experimental and SSID results to examine the effects of system characteristics (e.g., system zeros, relative degree, system order, phase lag, time delay), reference command, and command-following objectives on humans command-following performance and on the control strategies that the humans learn. Results suggest that nonminimum-phase zeros, relative degree, phase lag, and time delay tend to make dynamic systems difficult for human to control. Subjects can generalize their control strategies from one task to another and use prediction of the reference command to improve their command-following performance. However, this dissertation also provides evidence that humans can learn to improve performance without prediction. This dissertation also presents a new SSID algorithm to model the control strategies that human subjects use in HITL experiments where they interact with dynamic systems. This SSID algorithm uses a two-candidate-pool multi-convex-optimization approach to identify feedback-and-feedforward subsystems with time delay that are interconnected in closed loop with a known subsystem. This SSID method is used to analyze the human control behavior in the HITL experiments discussed above.

Acoustic radiation efficiency is defined as the ratio of sound power radiated to the surface vibration power of a piston with equivalent surface area. It has been shown that the radiation efficiency is maximized and may exceed unity when the structural and acoustic wavelengths are approximately equal. The frequency at which this occurs is called the critical frequency and can be shifted with structural modifications. This has proven to be an effective way to reduce noise. The standard radiation efficiency measurement is comprised of an intensity scan for sound power measurement and accelerometer array for spatially averaged vibration determination. This method is difficult to apply to lightweight structures, complicated geometries, and when acoustic sources are in close proximity to one another. Recently, robust particle velocity sensors have been developed. Combined with a small microphone in the same instrument, particle velocity and sound pressure can be measured simultaneously and at the same location. This permits radiation efficiency to be measured using a non-contact approach with a single sensor. A suggested practice for measuring radiation efficiency has been developed and validated with several examples including two flat plates of different thickness, an oil pan, and components on a running small engine.

Active vibration control is a widely implemented method for the helicopter vibration control. Due to the significant progress in microelectronics, this technique outperforms the traditional passive control technique due to weight penalty and lack of adaptability for the changing flight conditions. In this thesis, an optimal controller is designed to attenuate the rotor blade vibration. The mathematical model of the triply coupled vibration of the rotating cantilever beam is used to develop the state-space model of an isolated rotor blade. The required natural frequencies are determined by the modified Galerkin method and only the principal aerodynamic forces acting on the structure are considered to obtain the elements of the input matrix. A linear quadratic regulator is designed to achieve the vibration reduction at the optimum level and the controller is tuned for the hovering and forward flight with different advance ratios.

Spacecraft pointing accuracy and structural longevity requirements often necessitate auxiliary vibration dissipation mechanisms. However, temperature sensitivity and material degradation limit the effectiveness of traditional damping techniques in space. Robust particle damping technology offers a potential solution, driving the need for microgravity characterization. A 1U cubesat satellite presents a low cost, low risk platform for the acquisition of data needed for this evaluation, but severely restricts available mass, volume, power and bandwidth resources. This paper details the development of an instrument subject to these constraints that is capable of capturing high resolution frequency response measurements of highly nonlinear particle damper dynamics.

A real time acoustic direction-finding module has been developed to estimate the ele- vation and azimuth of an impulsive event while function aboard a small unmanned air- craft vehicle. The generalized cross-correlation with phase transform method was used to estimate time differences of arrival in an 8 channel microphone array. A linear least squares approach was used to calculate an estimate for the direction of arrival. In order to accomplish this task, a vertical takeoff and landing small unmanned aircraft system was assembled to host the direction finding module. The module itself is made up of an eight-channel synchronous analog-to-digital converter connected to eight lightweight micro electro-mechanical microphones with pre-amplifiers. The data is processed on an embedded system with a field programmable gate array chip and a central processing unit. Noise canceling techniques were employed to address the noise propagating from the propellers under operation. The results from this research show that it is possible to perform direction-finding estimation while aboard an operating small unmanned aircraft vehicle with initial tests showing maximum errors of ± 7°.

Combustion instability is a problem that has plagued the development of rocket-propelled devices since their conception. It is characterized by the occurrence of high-frequency nonlinear gas oscillations inside the combustion chamber. This phenomenon degrades system performance and can result in damage to both structure and instrumentation. The goal of this dissertation is to clarify the role of unsteady combustion in the combustor instability problem by providing the first quantified estimates of its effect upon the stability of liquid rocket engines. The combination of this research with a new system energy balance method, accounting for all dynamic interactions within a system, allows for the isolation of combustion effects for this study. These effects are quantified through use of classical linear stability analysis to calculate the unsteady combustion heat release growth rate. Since combustion modeling can become very involved, including the mixing process and multiple reactions concerned, for this initial evaluation the model is limited to a one-dimensional flame analysis for a one-step premixed chemical reaction. Using classical analysis of oscillatory burning, the governing combustion equations are expanded into sets of steady and unsteady equations adapted for premixed liquid rockets. From this expansion process, the first real treatment of the effects of unsteady combustion in a rocket system is presented, and the first quantified values of the unsteady heat release in a rocket system are computed. Finally, the corresponding linear heat release growth rate for the system is then calculated for the first quantified effects of unsteady combustion on the overall system stability. The mechanism of unsteady combustion is shown to behave as a driving mechanism, serving as one of the more important stability mechanisms comparable to the magnitude of the nozzle damping mechanism. This analysis confirms that unsteady combustion is an important stability mechanism that warrants further investigation. This study also creates a firm foundation upon which to extend the analysis of this important mechanism to fully understand all of its effects within a rocket system.

State of the art research in hydrodynamic stability analysis has moved from classic one-dimensional methods such as the local nonparallel approach and the parabolized stability equations to two-dimensional, biglobal, methods. The paradigm shift toward two dimensional techniques with the ability to accommodate fully three-dimensional base flows is a necessary step toward modeling complex, multidimensional flowfields in modern propulsive applications. Here, we employ a two-dimensional spatial waveform with sinusoidal temporal dependence to reduce the three-dimensional linearized Navier-Stokes equations to their biglobal form. Addressing hydrodynamic stability in this way circumvents the restrictive parallel-flow assumption and admits boundary conditions in the streamwise direction. Furthermore, the following work employs a full momentum formulation, rather than the reduced streamfunction form, accounting for a nonzero tangential mean flow velocity. This approach adds significant complexity in both formulation and implementation but renders a more general methodology applicable to a broader spectrum of mean flows. Specifically, we consider the stability of three models for bidirectional vortex flow. While a complete parametric study ensues, the stabilizing effect of the swirl velocity is evident as the injection parameter, kappa, is closely examined.

Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed. Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s elastic moduli are related to their magnetic properties. Magnetization data, primarily M v. H, provides another measure the magnetic properties are used to help correlate the data to elasticity. Tb6FeSb2 and Tb6FeBi2 Curie temperatures are 253(3)K and 246(5)K respectively. The low temperature magnetic transition of Tb6FeSb2 is 65-90K and Tb6FeBi2 is 55-75K. RUS suggests that this low temperature transition is somehow related to a structural transition but this transition does not occur in these two compounds. Co-substitution of Tb6FeSb2 and Tb6FeBi2 seem to greatly affect this lower temperature transition in RUS. It does not greatly effect the curie temperature. Low temperature XRD shows that Co-substitution also creates a structural transition in this family of compounds.

The aerospace industry is utilizing low cost miniature inertial measurement units (IMUs) that employ Micro Electro-Mechanical Systems (MEMS) technology in an effort to reduce size, weight, and cost of systems. A drawback of these MEMS devices is they are sensitive to vibration, shock and acoustic environments, which limits the usefulness of such devices in the severe environments imposed by many aerospace applications. In an effort to reduce the vibration, shock and acoustic environments experienced by these MEMS devices, the desire to develop passive damping treatments to structural components used to mount these devices. The damping treatments can be applied at the printed circuit board (PCB) level, the component level, the component interface, or at the airframe level. The purpose is to reduce the overall environment and improve the usefulness and performance of the MEMS based sensors. The primary technique to introduce damping into metallic parts and PCBs is to provide a viscoelastic coating or layer. The ability to analyze structures with this configuration requires a thorough understanding of the dynamic properties. Hooke’s law of elasticity is one of the most fundamental relationships governing dynamic properties. Metals typically have a low damping coefficient, and Hooke’s law of elasticity represents a linear relationship between the ratio of stress and strain, known as the modulus of elasticity. But for viscous materials the modulus of elasticity becomes a complex value since the stress and strain are not in phase. The complex modulus of elasticity is a complex function of frequency. The complex modulus can be established via frequency response function measurements of compliance, mobility, and accelerance, and the dimensions of the block of material under test. At low frequencies (less than resonance of the block) the results are relatively straight forward, but at higher frequencies where resonances of the block occur the inertial forces begin to influence the FRF results. This thesis effort establishes techniques for measuring the complex moduli associated with viscoelastic materials, and presents methods and results from modulus tests conducted for this thesis.