Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. Multibody formulations with joint friction were developed in the recent years and these systems have to be modeled by highly non-linear differential algebraic equations (DAEs) that are difficult to solve using numerical methods. The sensitivity analysis of such systems and the subsequent design optimization is a novel area of research that has been explored in this work. The contribution of this work is in the development of the analytical methods for computation of sensitivities for the most commonly used multibody formulations incorporated with joint friction. Two different friction models have been studied, capable of emulating behaviors of stiction (static friction), sliding friction and viscous drag. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. The Brown and McPhee friction model has been implemented using an index-1 formulation for computation of the dynamics and sensitivities in this case study. The effect of friction on the dynamics and model sensitivities has been analyzed by comparing the sensitivities of slider velocity with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, it can be concluded that the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa. / Master of Science / Mechanisms have been in existence since the earliest days of technology and are more relevant than ever in this age of robotics, artificial intelligence and space exploration. Innovations like myoelectric and neural prosthetics, legged robotics, robotic surgeries, advanced manufacturing, extra-terrestrial vehicles and so on are the modern day manifestations of the traditional mechanisms that formed the backbone of the industrial revolution. All of these innovations implement precision controlled multibody dynamic systems as part of their function. This thesis explores the modelling of such dynamic systems using different mathematical formulations. The contribution of this work is the incorporation of friction in the formulation of such systems. The performance of any dynamical system depends on certain parameters, which can be optimized to meet a certain objective criteria. This is achieved by performing a sensitivity analysis with respect to those parameters on the mathematical formulation of the mechanism. The derivation of this approach has been explored in this thesis. For the benefit of the reader, the application of this method has been discussed using a case study of a simple 3-dimensional slider crank mechanism.

We present optimal solutions for a point-mass electrodynamic tether (EDT) performing phasing and orbit-raising maneuvers. An EDT is a conductive tether on the order of 20 km in length and uses a Lorentz force to provide propellantless thrust. We develop the optimal equations of motion using Pontryagin's Minimum Principle. We find numerical solutions using a global, stochastic optimization method called Adaptive Simulated Annealing. The method uses Markov chains and the system's cost function to narrow down the search space. Newton's Method brings the error in the residual to below a specific tolerance. We compare the EDT solutions to similar constant-thrust solutions and investigate the patterns in the solution space. The EDT phasing maneuver has invariance properties similar to constant-thrust phasing maneuvers. Analyzing the solution space reveals that the EDT is faster at performing phasing maneuvers but slower at performing orbit-raising maneuvers than constant-thrust spacecraft. Also several bifurcation lines occur in the solution spaces for all maneuvers studied. / Master of Science

The exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exact controls for linear parabolic equations by reducing the problem to a hypoelliptic equation problem. A numerical scheme for the exact zero control of the Burger's equation is then constructed, based on the simple iteration of the corresponding linearized problem. The efficiency of the computational methods are illustrated by a variety of numerical experiments. / Ph. D.

We consider the analysis of the scattering problem. Assume that an incoming time harmonic wave is scattered by a surface of an impenetrable obstacle. The reflected wave is determined by the surface impedance of the obstacle. In this paper we will investigate the problem of choosing the surface impedance so that a desired scattering amplitude is achieved. We formulate this control problem within the framework of the minimization of a Tikhonov functional. In particular, questions of the existence of an optimal solution and the derivation of the optimality conditions will be addressed. / Master of Science

Abstract Based upon the Nordhaus' model, we can analyze the political business cycle (PBC) of parliamentarian system. This is our point in this paper. Adding an uncertain factor in the Nordhaus' assumptions, we can get unemployment rate of optimal control path by using the dynamic optimal control theory. Comparing these two results, the model of political business cycle of parliamentarian system has higher elective frequency and lower amplitude in the unemployment rate of optimal control path. From the social welfare point of view, which one is better is hard to say? The social welfare is decided by voters' preferences when voters face these two type of PBC. Keywords: Political business cycle (PBC). Parliamentarian system. The optimal

This dissertation investigates advanced concepts in terminal missile guidance. The terminal phase of missile guidance usually lasts less than ten seconds and calls for very accurate maneuvering to ensure intercept. Technological advancements have produced increasingly sophisticated threats that greatly reduce the effectiveness of traditional approaches to missile guidance. Because of this, terminal missile guidance is, and will remain, an important and active area of research. The complexity of the problem and the desire for an optimal solution has resulted in researchers focusing on simplistic, usually linear, models. The fruit of these endeavors has resulted in some of the world's most advanced weapons systems. Even so, the resulting guidance schemes cannot possibly counter the evolving threats that will push the system outside the linear envelope for which they were designed. The research done in this dissertation greatly extends previous research in the area of optimal missile guidance. Herein it is shown that optimal missile guidance is fundamentally a pairing of an optimal guidance strategy and an optimal control strategy. The optimal guidance strategy is determined from a missile's information constraints, which are themselves largely determined from the missile's sensors. The optimal control strategy is determined by the missile's control constraints, and works to achieve a specified guidance strategy. This dichotomy of missile guidance is demonstrated by showing that missiles having different control constraints utilize the same guidance strategy so long as the information constraints are the same. This concept has hitherto been unrecognized because of the difficulty in developing an optimal control for the nonlinear set of equations that result from control constraints. Having overcome this difficulty by indirect means, evidence of the guidance strategy paradigm emerged. The guidance strategy paradigm is used to develop two advanced guidance laws. The new guidance laws are compared qualitatively and quantitatively with existing guidance laws.

Uruguay is a pioneer in the use of renewable sources of energy and can usually satisfy its total demand from renewable sources. Control and optimization of the system is complicated by half of the installed power - wind and solar sources - be- ing non-controllable with high uncertainty and variability. In this work we present a novel optimization technique for efficient use of the production facilities. The dy- namical system is stochastic, and we deal with its non-Markovian dynamics through a Lagrangian relaxation. Continuous-time optimal control and value function are found from the solution to a sequence of Hamilton-Jacobi-Bellman partial differential equations associated with the system. We introduce a monotone scheme to avoid spurious oscillations in the numerical solution and apply the technique to a number of examples taken from the Uruguayan grid. We use parallelization and change of variables to reduce the computational times. Finally, we study the usefulness of extra system storage capacity offered by batteries.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23887号 / 工博第4974号 / 新制||工||1777(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 泉田 啓, 教授 大塚 敏之 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The content of this dissertation consists of three parts. In the first part, optimal control strategies are developed for Unified Power Flow Controller (UPFC) following the clearance of fault conditions. UPFC is one of the most versatile Flexible AC Transmission devices (FACTs) that have been implemented thus far. The optimal control scheme is composed of two parts. The first is an optimal stabilization control, which is an open-loop ‘Bang’ type of control. The second is an suboptimal damping control, which consists of segments of ‘Bang’ type control with switching functions the same as those of a corresponding approximate linear system. Simulation results show that the proposed control strategy is very effective in maintaining stability and damping out transient oscillations following the clearance of the fault. In the second part, a new power market structure is proposed. The new structure is based on a two-level optimization formulation of the market. It is shown that the proposed market structure can easily find the optimal solutions for the market while takeing factors such as demand elasticity into account. In the last part, a mathematical programming problem is formulated to obtain the maximum value of the loadibility factor, while the power system is constrained by steady-state dynamic security constraints. An iterative solution procedure is proposed for the problem, and the solution gives a slightly conservative estimate of the loadibility limit for the generation and transmission system.

Approved for public release; distribution in unlimited. / Spray cooling is a promising means of dissipating large steady state heat fluxes in high density power and electronic systems, such as thermophotovoltaic systems. The present study reports on the effectiveness of spray cooling in removing heat fluxes as high as 220 W/cm2. An experiment was designed to determine how the parameters of spray volumetric flow rate and droplet size influence the heat removal capacity of such a system. A series of commercially available nozzles were used to generate full cone water spray patterns encompassing a range of volumetric flow rates (3.79 to 42.32 L/h) and droplet Sauter mean diameters (17.4 to 35.5 micrometers). The non-flooded regime of spray cooling was studied, in which liquid spreading on the heater surface following droplet impact is the key phenomenon that determines the heat transfer rate. The experimental data established a direct proportionality of the heat flux with spray flow rate, and an inverse dependence on the droplet diameter. A correlation of the data was developed to predict heat flux as a function of the studied parameters over the range of values tested in this. / Lieutenant, United States Navy