Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion. A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated. Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods. One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems. In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.

This research deals with determining the acoustic attenuation of heating, ventilation, and air conditioning (HVAC) ductwork. A finite element approach was developed for calculating insertion loss and breakout transmission loss. Procedures for simulating the source and receiving rooms were developed and the effect of structureborne flanking was included. Simulation results have been compared with measurements from the literature and the agreement is very good. With a good model in place, the work was extended in three ways. 1) Since measurements on full-scale equipment are difficult, scale modeling rules were developed and validated. 2) Two different numerical approaches were developed for evaluating the transmission loss of silencers taking into account the effect of higher order modes. 3) A power transfer matrix approach was developed to assess the acoustic performance of several duct components connected in series.

This dissertation addresses rigid body attitude control with piecewise sinusoidal signals. We consider rigid-body attitude kinematics on SO(3) with a class of sinusoidal inputs. We present a new closed-form solution of the rotation matrix kinematics. The solution is analyzed and used to prove controllability. We then present kinematic-level orientation-feedback controllers for setpoint tracking and command following. Next, we extend the sinusoidal kinematic-level control to the dynamic level. As a representative dynamic system, we consider a CubeSat with vibrating momentum actuators that are driven by small $\epsilon$-amplitude piecewise sinusoidal internal torques. The CubeSat kinetics are derived using Newton-Euler's equations of motion. We assume there is no external forcing and the system conserves zero angular momentum. A second-order approximation of the CubeSat rotational motion on SO(3) is derived and used to derive a setpoint tracking controller that yields order O(ε2) closed-loop error. Numerical simulations are presented to demonstrate the performance of the controls. We also examine the effect of the external damping on the CubeSat kinetics. In addition, we investigate the feasibility of the piecewise sinusoidal control techniques using an experimental CubeSat system. We present the design of the CubeSat mechanical system, the control system hardware, and the attitude control software. Then, we present and discuss the experiment results of yaw motion control. Furthermore, we experimentally validate the analysis of the external damping effect on the CubeSat kinetics.

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.