Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität zu Bonn, 1984. / Includes bibliographical references (p. 189-194).

The research is concerned with the proposal and the development of a general method for computing rapidly oscillatory integrals with sine and cosine weight integrands of the form f(x) exp(iωq(x)). In this method the interval (finite or infinite) of integration is transformed to an equivalent contour in the complex plane and consequently the problem of evaluating the original oscillatory integral reduces to the evaluation of one or more contour integrals. Special contours, called the optimal contours, are devised and used so that the resulting real integrals are non-oscillatory and have rapidly decreasing integrands towards one end of the integration range. The resulting real integrals are then easily computed using any general-purpose quadrature rule.

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Dans cette étude, une méthodologie analytique est présentée pour dimensionner les machines fonctionnant sur cycle pour les applications de véhicules électriques. Les objectifs sont de minimiser simultanément les énergies perdues sur cycle et le volume de machines synchrones à aimants permanents (PMSM) non saillants à grande vitesse en considérant tous les points de fonctionnement du cycle de conduite. La méthode permet d'optimiser à la fois la géométrie de la machine et la stratégie de commande (via l'angle d’autopilotage et la force magnétomotrice). Les valeurs de l'angle d’autopilotage sont optimisées pour réduire les pertes totales (pertes cuivre et pertes fer) pendant le cycle de conduite. On montre comment le mode de défluxage réduit à la fois les pertes moyennes sur cycle dans la machine et les contraintes sur le convertisseur de puissance. La performance de la machine optimisée est validée pour tous les points du cycle de conduite à l’aide d'un réseau de réluctances. Ce modèle permet de prendre en compte le mouvement du rotor, les flux de fuites et la réaction de l'induit. De plus, il permet également de modéliser le couplage entre le moteur et son système d'alimentation, composé du convertisseur de puissance et de la commande. Cela permet d'étudier l'influence des différentes stratégies de commandes telles que la commande en pleine onde ou par modulation de largeur d'impulsion (MLI) sur les performances du moteur. Un dimensionnement optimal est réalisé pour un véhicule urbain sur le cycle Urban Dynamometer Driving Schedule (UDDS). / In this study, an analytical method is presented to size the machines working over a driving cycle for electrical vehicle applications. The objectives are to simultaneously minimize the energy losses over the cycle and the volume of high-speed non-salient Permanent Magnet Synchronous Machines (PMSM) considering all working points of a driving cycle. The method allows optimizing both the geometry of the machine and the control strategy (via the torque angle and the magnetic force). The values of the torque angle are optimized to reduce the energy losses during the driving cycle. It is shown how flux-weakening reduces both the constraints on the energy losses in the machine and the power converter. The performance of the optimal designed machine is validated at all working points of the driving cycle by means of a reluctance network model. This model allows taking into account the movement of the rotor, the flux leakage, the armature reaction. In addition, it permits to model the coupling between the motor and its power supply system composed of a power converter and its command. The model allows studying the influence of different control strategies such as the full wave operation or the Pulse Width Modulation (PWM) on the performance of the motor. A study is carried out for the Urban Dynamometer Driving Schedule (UDDS) and an urban vehicle.

To operate a production plant, one requires considerable amounts of power. With a wide range of energy sources, the price of electricity changes rapidly throughout the year, and so does the cost of satisfying the electricity demand. Battery technology allows storing energy while the electric power is lower, saving us from purchasing at higher prices. Thus, adding batteries to run plants can significantly reduce production costs. This thesis proposes a method to determine the optimal battery regime and its maximum capacity, minimizing the production plant's energy expenditures. We use stochastic differential equations to model the dynamics of the system. In this way, our spot price mimics the Uruguayan energy system's historical data: a diffusion process represents the electricity demand and a jump-diffusion process - the spot price. We formulate a corresponding stochastic optimal control problem to determine the battery's optimal operation policy and its optimal storage capacity. To solve our stochastic optimal control problem, we obtain the value function by solving the Hamilton-Jacobi-Bellman partial differential equation associated with the system. We discretize the Hamilton-Jacobi-Bellman partial differential equation using finite differences and a time splitting operator technique, providing a stability analysis. Finally, we solve a one-dimensional minimization problem to determine the battery's optimal capacity.

The aim of this thesis is to present a structural model for a wind turbine and its supporting pylon, to analyze and simulate attendant vibration phenomena and to suggest and simulate an appropriate control procedure. A wind turbine can be described as an elastic system consisting of distributed parameter, beam and rod type, elements coupled to a rotating lumped mass generator/turbine component at one end. We allow for both lateral and torsional movements of the beam. Solution methods for related vibration and control problems are suggested and analyzed. Results of computations for sample problems are presented. Applications of control of structural vibrations in wind energy units using proof mass type actuators as part of the tip mass are also analyzed. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / There are two computational bottlenecks for Big Data analysis: (1) the data is too large for a desktop to store, and (2) the computing task takes too long waiting time to finish. While the Divide-and-Conquer approach easily breaks the first bottleneck, the Subsampling approach simultaneously beat both of them. The uniform sampling and the nonuniform sampling--the Leverage Scores sampling-- are frequently used in the recent development of fast randomized algorithms. However, both approaches, as Peng and Tan (2018) have demonstrated, are not effective in extracting important information from data. In this thesis, we conduct regression analysis for big count data via A-optimal subsampling. We derive A-optimal sampling distributions by minimizing the trace of certain dispersion matrices in general estimating equations (GEE). We point out that the A-optimal distributions have the same running times as the full data M-estimator. To fast compute the distributions, we propose the A-optimal Scoring Algorithm, which is implementable by parallel computing and sequentially updatable for stream data, and has faster running time than that of the full data M-estimator. We present asymptotic normality for the estimates in GEE's and in generalized count regression. A data truncation method is introduced. We conduct extensive simulations to evaluate the numerical performance of the proposed sampling distributions. We apply the proposed A-optimal subsampling method to analyze two real count data sets, the Bike Sharing data and the Blog Feedback data. Our results in both simulations and real data sets indicated that the A-optimal distributions substantially outperformed the uniform distribution, and have faster running times than the full data M-estimators.

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The following is an exploration into the optimal guidance and control of gun-launched guided projectiles. Unlike their early counterparts, modern-day gun-launched projectiles are capable of considerable accuracy. This ability is enabled through the use of control surfaces, such as fins or wings, which allow the projectile to maneuver towards a target. These aerodynamic features are part of a control system which lets the projectile achieve some effect at the target. With the advent of very high velocity guns, such as the Navy's electromagnetic railgun, these systems are a necessary part of the projectile design. This research focuses on a control scheme that uses the projectile's angle of attack as the single control in the development of an optimal control methodology that maximizes impact velocity, which is directly related to the amount of damage in icted on the target. This novel approach, which utilizes a reference trajectory as a seed for an iterative optimization scheme, results in an optimal control history for a projectile. The investigation is geared towards examining how poor an approximation of the true optimal solution that reference trajectory can be and still lead to the determination of an optimal control history. Several different types of trajectories are examined for their applicability as a reference trajectory. Although the use of aerodynamic control surfaces enables control of the projectile, there is a potential down side. With steady development of guns with longer ranges and higher launch velocities, it becomes increasingly likely that a projectile will y into a region of the atmosphere (and beyond) in which there is not sufficient air ow over the control surfaces to maintain projectile control. This research is extended to include a minimum dynamic pressure constraint in the problem; the imposition of such a constraint is not examined in the literature. Several methods of adding the constraint are discussed and a number of cases with varying dynamic pressure limits are evaluated. As a result of this research, a robust methodology exists to quickly obtain an optimal control history, with or without constraints, based on a rough reference trajectory as input. This methodology finds its applicability not only for gun-launched weapons, but also for missiles and hypersonic vehicles. / Doctor of Philosophy / As the name implies, optimal control problems involve determining a control history for a system that optimizes some aspect of the system's behavior. In aerospace applications, optimal control problems often involve finding a control history that minimizes time of ight, uses the least amount of fuel, maximizes final velocity, or meets some constraint imposed by the designer or user. For very simple problems, this optimal control history can be analytically derived; for more practical problems, such as the ones considered here, numerical methods are required to determine a solution. This research focuses on the optimal control problem of a gun-launched guided projectile. Guided projectiles have the potential to be significantly more accurate than their unguided counterparts; this improvement is achieved through the use of a control mechanism. For this research, the projectile is modeled using a single control approach, namely using the angle of attack as the only control for the projectile. The angle of attack is the angle formed between the direction the projectile is pointing and the direction it is moving (i.e., between the main body axis and the velocity vector of the projectile). An approach is then developed to determine an optimal angle of attack history that maximizes the projectile's final impact velocity. While this problem has been extensively examined by other researchers, the current approach results in the analytical determination of the costate estimates that eliminates the need to iterate on their solutions. Subsequently, a minimum dynamic pressure constraint is added to the problem. While extensive investigation has been conducted in the examination of a maximum dynamic pressure constraint for aerospace applications, the imposition of a minimum represents a novel body of work. For an aerodynamically controlled projectile, (i.e., one controlled with movable surfaces that interact with the air stream), dropping below a minimum dynamic pressure may result in loss of sufficient control. As such, developing a control history that accommodates this constraint and prevents the loss of aerodynamic control is critical to the ongoing development of very long range, gun-launched guided projectiles. This new methodology is applied with the minimum dynamic pressure constraint imposed and the resulting optimal control histories are then examined. In addition, the possibility of implementing other constraints is also discussed.