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Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs as previously studied. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient maneuvers. A family of, climb-range paths appears for thrust exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems. Minimizing paths of long duration follow a certain corridor in the V-h chart. The features of the family sharpen for the special case of thrust and drag independent of altitude, and considerable analytical attention is accorded to this for the insight it provides to the more general model. The problem of "steepest climb" is found to be ill-posed with the vehicle model under consideration, straight-vertically-upward maneuver sequences being furnished by a family of paths alternating between upward and downward vertical flight and including a limiting "chattering" member. / Ph. D.

For the future of sustainable energy, renewable energy will need to significantly penetrate existing utility grids. While various renewable energy sources are networked with high-voltage DC grids, integration between these high-voltage DC grids and the existing AC grids is a significant technical challenge. Among the limited choices available, the modular multi-level converter (MMC) is the most prominent interface converter used between the DC and AC grids. This subject has been widely pursued in recent years. One of the important design challenges when using an MMC is to reduce the capacitor size associated with each module. Currently, a rather large capacitor bank is required to store a certain amount of line-frequency related circulating energy. Several control strategies have been introduced to reduce the capacitor voltage ripples by injecting certain harmonic current. Most of these strategies were developed using trial and error and there is a lack of a systematic means to address this issue. Most recently, Yadong Lyu has proposed to control the modulation index in order to reduce capacitor ripples. The total elimination of the unwanted circulating power associated with both the fundamental line frequency and the second-order harmonic was demonstrated, and this resulted in a dramatic reduction in capacitor size. To gain a better understanding of the intricate operation of the MMC, this thesis proposes a state-space analysis technique in the present paper. Combining the power flow analysis with the state trajectory portrayed on a set of two-dimensional state plans, it clearly delineates the desired power transfer from the unwanted circulating energy, thus leading to an ultimate reduction in the circulation energy and therefore the required capacitor volume. / Master of Science

The LLC resonant converter has been widely used as a DC-DC converter due to its high efficiency, high power density and hold-up capability in power supplies for communication systems, computers and consumer electronics. Use of the high-frequency LLC converter has also been increasing in recent years due to its high power density and integrated magnetics, which reduce the total cost. With the fast development of wideband gap devices and novel magnetic materials, the trend of pushing switching frequency higher continues. However, the control characteristics of the LLC resonant converter are much more complex than that of the PWM converter due to the dynamics of the resonant tank. This paper employs state-trajectory analysis to describe and analyze the behavior of the resonant tank. Control methods based on state-trajectory analysis were used to solve the challenges in the control of the LLC resonant converter, including unpredictable dynamics, burst mode for light-load efficiency, soft start-up and short circuit protection. Additionally, digital controllers are gradually taking the place of analog controllers in the control of the LLC resonant converter due to the advantages of the digital controllers over the analog controllers, such as their ability to be flexible and re-configurable, capable of non-linear control, and able to communicate with other controllers. Among the digital controllers, cost-effective microcontrollers (MCU) are preferred for industrial applications. Because of the advantages of the state-trajectory control and the industrial preference in the cost-effective digital controllers, it would be of great benefit to apply state-trajectory control to high-frequency LLC converters with cost-effective digital controllers. This thesis investigates the impact of digital delay on state-trajectory control. Simplified Optimal Trajectory Control (SOTC) for LLC converters is further simplified so that SOTC can be achieved with cost-effective digital controllers. Furthermore, the limitations caused by digital controller are explained in detail, and methods are proposed to apply the SOTC to high frequency LLC converter is proposed. A detailed analysis of fast load transient response, soft start-up, burst mode for light-load efficiency and synchronous rectification (SR) driving is provided. Multi-step SOTC for fast load transient response is proposed to apply cost-effective digital controllers to high-frequency LLC converters; SOTC for soft start-up with only sensing Vo is proposed to minimized the impact of digital delay on state-trajectory control; SOTC for burst mode with multi-step is proposed to eliminate the limitation of minimum off-time caused by digital controllers in constant burst-on time control; a generalized adaptive SR driving method using the ripple counter concept is proposed to significantly reduce controller resource utilization for the SR control of high-frequency LLC converters. The whole control system is demonstrated on a 500kHz 1kW 400V/12V LLC converter with a 60MHz MCU, which integrates all the proposed control methods. / Master of Science

At international border areas that suffer from poor quality, assessment of pollutant sources and transport across the border is important for designing effective air quality management strategies. As part of the Cal-Mex 2010 field campaign at the US-Mexico border in San Diego and Tijuana, we measured black carbon (BC) concentrations at three locations in Mexico and one in the United States. The measurements were intended to support the following objectives: to characterize the spatial and temporal variability in BC concentrations and emissions in the border region, to identify potential source areas of BC emissions, and to characterize the cross-border transport of BC and assess its impact on local and regional air quality. BC concentrations at Parque Morelos, the campaign's supersite, averaged 2.1 ?g m?? and reached a maximum value of 55.9 ?g m??. This average value is comparable to levels in large American cities like Los Angeles and similarly sized Mexican cities like Mexicali. The maximum value occurred near midnight, and similar incidents were observed on nearly half of the overnight monitoring periods. BC and carbon monoxide (CO) were strongly correlated at the Mexican sites. The BC/CO ratio was ~3 times higher in Tijuana than in Mexico City, suggesting that gasoline-powered vehicles in Tijuana emit more BC than is typical or that diesel vehicles comprise a relatively high proportion of the vehicle fleet. Tijuana's emissions of BC are estimated to be 380-1470 metric tons yr??. BC measurements were used in conjunction with modeled wind fields to simulate forward and backward particle trajectories. Generally, BC in Tijuana appears to originate locally, as backward simulations showed transport from the US into Mexico at only one site. The majority of the trajectory analyses indicate that there is often transport from Tijuana into the US, crossing the border in a northeasterly direction to the east of San Diego-Tijuana and sometimes as far east as Imperial County at the eastern edge of California. These results suggest that any air quality management strategies considering BC should account for contributions from the border region, as BC is chemically inert in the atmosphere and can travel up to thousands of kilometers. / Master of Science

The method of singular-perturbation analysis is applied to the determination of range-fuel-time optimal aircraft trajectories. The problem is shown to break down into three sub-problems which are studied separately. In particular, the inner layer containing the altitude path-angle dynamics is analyzed in detail. The outer solutions are discussed in an earlier work. As a step forward in solving the ensuing nonlinear two-point boundary-value problem, linearization of the equations is suggested. Conditions for the stability of the linearized boundary-layer equations are discussed. Also, the question of parameter selection to fit the solution to the split boundary conditions is resolved. Generation of feedback laws for the angle-of-attack from the linear analysis is discussed. Finally, the techniques discussed are applied to a numerical example of a missile. The linearized feedback solution is compared to the exact solution obtained using a multiple shooting method. / Master of Science

Singular subarcs arise in quite a few problems of flight dynamics. The present study is devoted to the specific problem of ascent and acceleration of a vehicle in atmospheric flight in which a variable-thrust arc forms a part of the optimal trajectory. A two-parameter family of singular arcs was generated for time-range-fuel problems of an ascending rocket, using the modelling of Zlatskiy and Kiforenko. The short-term optimality of the singular subarcs has been checked in terms of certain necessary conditions: the classical Clebsch condition, the Kelley condition or the Generalized Legendre-Clebsch condition and the Goh condition. All these are found to be satisfied computationally for all the candidates. The calculations were repeated for simplified thrust-along-the-path modelling and similar results on optimality obtained. / Master of Science

In aircraft research, there is keen interest in the procedure of determining the set of controls required to perform a maneuver from a definition of the trajectory. This is called the inverse problem. It has been proposed that if a complete set of states and state time derivatives can be derived from a trajectory then a model-following solution can allocate the controls necessary for the maneuver. This paper explores the problem of finding the complete state definition and provides a solution that requires numerical differentiation, fixed point iteration and a Newton's method solution to nonlinear equations. It considers trajectories that are smooth, piecewise smooth, and noise ridden. The resulting formulation was coded into a FORTRAN program. When tested against simple smooth maneuvers, the program output was very successful but demonstrated the limitations imposed by the assumptions and approximations in the development. / Master of Science

This thesis presents two studies related to head injury. The study presented in Chapter 1 reviewed findings of cranial movement in animal and human specimens and evaluate the validity of cranial movement due to manual manipulation in humans through engineering analysis. The study had two parts. In Part I, the literature was reviewed to determine the cranial motion in animals and humans. Engineering analysis was done in Part II to determine the amount of force necessary to cause cranial motion in the studies from Part I using skull stiffness values from published studies. Chapter 2 explored data collection methodologies used in frontal sled tests. Several data collection methodologies exist for collecting kinematic data, such as Vicon motion analysis, video analysis, and sensors. Head trajectories from motion data and accelerometer data were plotted up to maximum forward excursion of the head for eight frontal sled tests, four conducted at Virginia Tech and four at the University of Virginia. In addition, the percent difference between maximum forward excursion values from sensor and motion data were calculated. Finally, Chapter 3 discusses the literary contributions of each study and to which journals they will be submitted. / Master of Science

The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / The capability to perform rendezvous and proximity operations about space objects is central to the next generation of space situational awareness. The ability to diagnose and respond to spacecraft anomalies is often hampered by the lack of capability to perform inspection or testing on the target vehicle in flight. While some limited ability to perform inspection can be provided by an extensible boom, such as the robotic arms deployed on the space shuttle and space station, a free-flying companion vehicle provides maximum flexibility of movement about the target. Safe and efficient utilization of a companion vehicle requires trajectories capable of minimizing spacecraft resources, e.g., time or fuel, while adhering to complex path and state constraints. This paper develops an efficient solution method capable of handling complex constraints based on a grid search A* algorithm and compares solution results against a state-of-the-art nonlinear optimization method. Trajectories are investigated that include complex nonlinear constraints, such as complex keep-out-regions and thruster plume impingement, that may be required for inspection of a specific target area in a complex environment. This work is widely applicable and can be expanded to apply to a variety of satellite relative motion trajectory planning problems. / Master of Science / The ability of one satellite to perform actions near a second space satellite or other space object is important for understanding the space environment and accomplishing space mission goals. The development of a method to plan the path that one satellite takes near a second satellite such that fuel usage is minimized and other constraints satisfied is important for accomplishing mission goals. This thesis focuses on developing a fast solution method capable of handling complex constraints that can be applied to plan paths satellite relative motion operations. The solution method developed in this thesis is then compared to an existing solution method to determine the efficiency and accuracy of the method.