This thesis discusses application of a robust constrained optimization approach to control design to develop an Auto Balancing Controller (ABC) for a centrifuge rotor to be implemented on the International Space Station. The design goal is to minimize a performance objective of the system, while guaranteeing stability and proper performance for a range of uncertain plants. The performance objective is to minimize the translational response of the centrifuge rotor due to a fixed worst-case rotor imbalance. The robustness constraints are posed with respect to parametric uncertainty in the plant. The proposed approach to control design allows for both of these objectives to be handled within the framework of constrained optimization. The resulting controller achieves acceptable performance and robustness characteristics.

Shielding of spacecraft is a concern in the design of modern space vehicles. Due to unplanned spacecraft failures and naturally occurring planetary matter, the space environment is littered with orbital debris. This orbital debris poses a real threat to the safety of humans in space and the structural integrity and mission success of spacecraft. Debris shields mitigate the damage caused by debris impacting objects at hypervelocity. An effective shield shocks the incoming projectile, causing the projectile to break and expand. The expansion causes the projectile's momentum to be spread over a larger volume, thereby decreasing its potential to damage. A model is developed to estimate the velocity, shape, and mass distribution of debris clouds that are produced by the impact of a projectile on a bumper at hypervelocity. Models are developed for both normal and oblique impact in terms of the material and geometrical properties of the projectile and target. The model utilizes the Hugoniot shock equations to predict the states of stress and velocity in the projectile and bumper.

Methods of dynamic analysis of large structural systems used in aerospace applications are examined. Full-system solutions are undesirable due to computational cost and logistics issues. Traditional substructuring methods effectively reduce system size through truncation of component modes, but still require an eigen-value analysis of the integrated system. A new method is discussed which utilizes residual flexibility to more accurately represent the motion of each component. Through the use of traditional displacement and force constraints on the substructures, interface equations of motion are developed which may be solved directly. Junction forces are used to drive the components at the interface, and the component equations of motion are solved at each time step, without need to form the full system equations of motion. The method allows easy examination of non-classically damped and nonlinear problems due to its formulation. Two sample problems illustrate the advantages of this method.

Fluid-Structure Interaction (FSI) problems are of great importance to many fields of engineering and pose tremendous challenges to numerical analyst. This thesis addresses some of the hurdles faced for both 2D and 3D real life time-dependent FSI problems with particular emphasis on parachute systems. The techniques developed here would help improve the design of parachutes and are of direct relevance to several other FSI problems. The fluid system is solved using the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation for the Navier-Stokes equations of incompressible and compressible flows. The structural dynamics solver is based on a total Lagrangian finite element formulation. Newton-Raphson method is employed to linearize the otherwise nonlinear system resulting from the fluid and structure formulations. The fluid and structural systems are solved in decoupled fashion at each nonlinear iteration. While rigorous coupling methods are desirable for FSI simulations, the decoupled solution techniques provide sufficient convergence in the time-dependent problems considered here. In this thesis, common problems in the FSI simulations of parachutes are discussed and possible remedies for a few of them are presented. Further, the effects of the porosity model on the aerodynamic forces of round parachutes are analyzed. Techniques for solving compressible FSI problems are also discussed. Subsequently, a better stabilization technique is proposed to efficiently capture and accurately predict the shocks in supersonic flows. The numerical examples simulated here require high performance computing. Therefore, numerical tools using distributed memory supercomputers with message passing interface (MPI) libraries were developed.

This thesis develops a state estimation algorithm for the Centrifuge Rotor (CR) system where only relative measurements are available with limited knowledge of both rotor imbalance disturbances and International Space Station (ISS) thruster disturbances. A Kalman filter is applied to a plant model augmented with sinusoidal disturbance states used to model both the effect of the rotor imbalance and the ISS thrusters on the CR relative motion measurement. The sinusoidal disturbance states compensate for the lack of the availability of plant inputs for use in the Kalman filter. Testing confirms that complete disturbance modeling is necessary to ensure reliable estimation. Further testing goes on to show that increased estimator operational bandwidth can be achieved through the expansion of the disturbance model within the filter dynamics. In addition, Monte Carlo analysis shows the varying levels of robustness against defined plant/filter uncertainty variations.

The wavelet bases approximation idea which is first proposed by Daubechies is successfully introduced in both nongray and linear anisotropic scattering radiation fields. In nongray medium, wavelet bases are used in frequency domain in radiative transfer equation. Wavelet method allows the radiative problems to be calculated with fewer assumptions. Wavelet method also can be combined with arbitrary absorption coefficient model. Results by wavelet method compare well with box model absorption coefficient cases. Deviations are observed in situations in which the medium is optically thin. In scattering medium, wavelet bases are used in angular domain. Promising results are shown in linear anisotropic scattering cases. It also can be used with arbitrary scattering model.

Although chemical rocket propulsion is widely used in space transportation, large amounts of propellant mass limit designs for spacecraft missions to Mars. Electrical propulsion, which requires a smaller propellant load, is an alternative propulsion system that can be used for interplanetary flight. After the recent successes of the NASA Deep Space 1 spacecraft and the ESA SMART 1 spacecraft, which incorporate an electrical propulsion system, there is a strong need for trajectory tools to support these systems. This thesis describes the optimization of interplanetary trajectories from Earth to Mars for spacecraft utilizing low-thrust electrical propulsion systems. It is assumed that the controls are the thrust direction and the thrust setting. Specifically, the minimum time and minimum propellant problems are studied and solutions are computed with the sequential gradient-restoration algorithm (SGRA). The results indicate that, when the thrust direction and thrust setting are simultaneously optimized, the minimum time and minimum propellant solutions are not identical. For minimum time, it is found that the thrust setting must be at the maximum value; also, the thrust direction has a normal component with a switch at midcourse from upward to downward. This changes the curvature of the trajectory, has a beneficial effect on time, but a detrimental effect on propellant mass; indeed, the propellant mass ratio of the minimum time solution is about twice that of the Hohmann transfer solution. Thus, the minimum time solution yields a rather inefficient trajectory. For minimum propellant consumption, it is found that the best thrust setting is bang-zero-bang (maximum thrust, followed by coasting, followed by maximum thrust) and that the best thrust direction is tangent to the trajectory. This is a rather efficient trajectory; to three significant digits, the associated mass ratio is the same as that of the Hohmann transfer solution, even for thrust-to-weight ratios of order 10-4. For a robotic spacecraft, it is clear that the minimum propellant mass solution is to be preferred. For a manned spacecraft, the transfer time and propellant mass functionals have comparable importance; they are in conflict with one another for the following reason: any attempt at reducing the former increases the latter and viceversa. This suggests the construction of a compromise functional, which is the linear combination of the previous two functionals, suitably scaled. The compromise functional depends on a parameter C (compromise factor) in the range 0 ≤ C ≤ 1 and is such that it reduces to the transfer time functional for C = 0 and to the propellant mass functional for C = 1. (Abstract shortened by UMI.)

General problems of interest in computational fluid dynamics are investigated by means of optimization. Specifically, in the first part of the dissertation, a method of optimal incremental function approximation is developed for the adaptive solution of differential equations. Various concepts and ideas utilized by numerical techniques employed in computational mechanics and artificial neural networks (e.g. function approximation and error minimization, variational principles and weighted residuals, and adaptive grid optimization) are combined to formulate the proposed method. The basis functions and associated coefficients of a series expansion, representing the solution, are optimally selected by a parallel direct search technique at each step of the algorithm according to appropriate criteria; the solution is built sequentially. In this manner, the proposed method is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a-posteriori error estimates. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems, ensuring that the problem is well-posed. Complicated data structures and expensive remeshing algorithms and systems solvers are avoided. Computational efficiency is increased by using low-order basis functions and concurrent computing. Numerical results and convergence rates are reported for a range of steady-state problems, including linear and nonlinear differential equations associated with general boundary conditions, and illustrate the potential of the proposed method. Fluid dynamics applications are emphasized. Conclusions are drawn by discussing the method's limitations, advantages, and possible extensions. The second part of the dissertation is concerned with the optimization of the viscous-inviscid-interaction (VII) mechanism in an airfoil flow analysis code. The VII mechanism is based on the concept of a transpiration velocity boundary condition, whose convergence to steady state is accelerated. The number of variables in the associated optimization problem is reduced by means of function approximation concepts to ensure high number of parallel processors to number of necessary function evaluations ratio. Numerical results are presented for the NACA-0012 and the supercritical RAE-2822 airfoils subject to transonic flow conditions using a parallel direct search technique. They exhibit a satisfactory level of accuracy. Speed-up depends on the number of available computational units and increases for more challenging flow conditions and airfoil geometries. The enhanced code constitutes a useful tool for airfoil flow analysis and design and an acceptable alternative to computationally expensive high fidelity codes.

On January 16, 2003, the Space Shuttle Columbia (OV-102) was launched for a nominal 16-day mission of microgravity research. Fifteen days and 20 hours after launch, and just 16 minutes before its scheduled landing, the OV-102 vehicle disintegrated during its descent. The entire crew was lost. Film and video cameras located around the launch complex captured images of the vehicle during its ascent. Of note were data that showed a piece of debris strike the port wing at approximately 82 sec after lift-off (T+82). As resulting analysis would show, the source of the debris was the left bipod ramp of the Shuttle external tank. This foam debris struck the Orbiter leading edge at sufficient velocity to breech the thermal protection system (TPS). During reentry at the end of the mission, the hot plasma impinged inside the Orbiter wing and aerodynamic forces ultimately failed the wing structure. This thesis documents the activities conducted to evaluate the effects of foam impact on Orbiter TPS. These efforts were focused on, to the greatest extent practical, replicating the impact event during the STS-107 mission ascent. This thesis fully documents the test program development, methodology, results, analysis, and conclusions to the degree that future investigators can reproduce the tests and understand the basis for decisions made during the development of the tests.

Our target is to develop computational techniques for studying aerodynamic interactions between multiple objects with emphasis on studying the fluid mechanics and dynamics of an object exiting and separating from an aircraft. The object could be a paratrooper jumping out of a transport aircraft or a package of emergency aid dropped from a cargo plane. These are applications with major practical significance, and what I learn and what I develop can make a major impact on this technology area. In all these cases, the computational challenge is to predict the dynamic behavior and path of the object, so that the separation process is safe and effective. This is a very complex problem because it has an unsteady, three-dimensional nature and requires the solution of complex equations that govern the fluid dynamics of the object and the aircraft together, with their relative positions changing in time. The gravitational and aerodynamic forces acting on the object determine its dynamics and path. Sometimes those aerodynamic forces are not properly computed due to excessively thick numerical boundary layers (numerical meaning unphysical and unreal). Methods for reducing this thickness are presented here. The aerodynamic forces heavily depend on the unsteady flow field around the aircraft. The computational tools I am developing are based on the simultaneous solution of the time-dependent Navier-Stokes equations governing the airflow around the aircraft and the separating object, as well as the equations governing the motion of that object. These computational methods include suitable mesh update techniques that are essential for simulations with my core computational technique---the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation. In the research I present here, I focus on developing mesh update methods that help me perform my computations with more numerical accuracy and better computational efficiency. These methods range from remeshing tactics with reduced distortion, to methods reducing the error introduced through projection and, finally, even to a mesh moving alternative---Fluid Object Interaction Subcomputation Technique (FOIST). In FOIST, moving object problems are computed with an approximation technique, without the costs of mesh moving, remeshing, or projection.