[pt] Neste trabalho estudamos algoritmos de escala de tempo, que através da amostragem de um conjunto de relógios atômicos, geram tempo e freqüência com maior confiabilidade, estabilidade e exatidão de freqüência, do que qualquer um dos relógios do conjunto. Os algoritmos estudados foram o algoritmo de primeira ordem e o algoritmo usando filtro de Kalman. Propomos um algoritmo e mostramos que este gera escala de tempo atômico, com maior estabilidade do que os outros. Nós simulamos um conjunto de relógios atômicos e os usamos para testar os algoritmos. Com dados reais provenientes das medidas de diferença de tempo entre quatro relógios, do Observatório Nacional - Dept. Serviço da Hora, Laboratório Primário de Tempo e Freqüência, mostramos que o algoritmo proposto gera uma escala de tempo atômico com maior uniformidade do que os outros algoritmos. O sistema para materialização da Escala de Tempo Atômico Brasileira também é apresentado. / [en] The present work we study time scale algoritms that samples an ensemble of clocks to generate time and frequency with more reliability, stability, an frequency accuracy than any of the individual clocks in the ensemble. The algoriths studied were the first order algorithm and the Kalman filter algorithm. We propose an algorithm and we show that it generates atomic time scale, with better stability than any other one. We simulated an ensemble clocks and used them to test the algorithms. With the real data from the measurement of time differences between four clocks at National Observatory - Time Service Departament, Time and Frequency Primary Laboratory we show that the proposed algorithm generates atomic time scale with more uniformity than others. The systems for construction the Brazilian Atomic Time Scale is also discussed.

Improved basic understanding, predictability, and controllability of vortex-dominated and unsteady aerodynamic flows are important in enhancement of the performance of next generation helicopters. The primary objective of this research project was improved understanding of the fundamental vorticity and turbulent flow physics for a dynamically stalling airfoil at realistic helicopter flight conditions. An experimental program was performed on a large-scale (C = 0.45 m) dynamically pitching NACA 0012 wing operating in the Texas A&M University large-scale wind tunnel. High-resolution particle image velocimetry data were acquired on the first 10-15% of the wing. Six test cases were examined including the unsteady (k>0) and steady (k=0) conditions. The relevant mechanical, shear and turbulent time-scales were all of comparable magnitude, which indicated that the flow was in a state of mechanical non-equilibrium, and the expected flow separation and reattachment hystersis was observed. Analyses of the databases provided new insights into the leading-edge Reynolds stress structure and the turbulent transport processes. Both of which were previously uncharacterized. During the upstroke motion of the wing, a bubble structure formed in the leading-edge Reynolds shear stress. The size of the bubble increased with increasing angle-of-attack before being diffused into a shear layer at full separation. The turbulent transport analyses indicated that the axial stress production was positive, where the transverse production was negative. This implied that axial turbulent stresses were being produced from the axial component of the mean flow. A significant portion of the energy was transferred to the transverse stress through the pressure-strain redistribution, and then back to the transverse mean flow through the negative transverse production. An opposite trend was observed further downstream of this region.

This dissertation addresses the control problem for the general class of control non-affine, non-standard singularly perturbed continuous-time systems. The problem of control for nonlinear multiple time scale systems is addressed here for the first time in a systematic manner. Toward this end, this dissertation develops the theory of feedback passivation for non-affine systems. This is done by generalizing the Kalman-Yakubovich-Popov lemma for non-affine systems. This generalization is used to identify conditions under which non-affine systems can be rendered passive. Asymptotic stabilization for non-affine systems is guaranteed by using these conditions along with well-known passivity-based control methods. Unlike previous non-affine control approaches, the constructive static compensation technique derived here does not make any assumptions regarding the control influence on the nonlinear dynamical model. Along with these control laws, this dissertation presents novel hierarchical control design procedures to address the two major difficulties in control of multiple time scale systems: lack of an explicit small parameter that models the time scale separation and the complexity of constructing the slow manifold. These research issues are addressed by using insights from geometric singular perturbation theory and control laws are designed without making any assumptions regarding the construction of the slow manifold. The control schemes synthesized accomplish asymptotic slow state tracking for multiple time scale systems and simultaneous slow and fast state trajectory tracking for two time scale systems. The control laws are independent of the scalar perturbation parameter and an upper bound for it is determined such that closed-loop system stability is guaranteed. Performance of these methods is validated in simulation for several problems from science and engineering including the continuously stirred tank reactor, magnetic levitation, six degrees-of-freedom F-18/A Hornet model, non-minimum phase helicopter and conventional take-off and landing aircraft models. Results show that the proposed technique applies both to standard and non-standard forms of singularly perturbed systems and provides asymptotic tracking irrespective of the reference trajectory. This dissertation also shows that some benchmark non-minimum phase aerospace control problems can be posed as slow state tracking for multiple time scale systems and techniques developed here provide an alternate method for exact output tracking.

In this thesis, the asymptotic behavior and oscillation of solutions of dynamic equations on time scales are studied. In the first part of the thesis, asymptotic equivalence and asymptotic equilibrium of dynamic systems are investigated. Sufficient conditions are established for the asymptotic equivalence of linear systems and linear and quasilinear systems, respectively, and for the asymptotic equilibrium of quasilinear systems by unifying and extending some known results for differential systems and difference systems to dynamic systems on arbitrary time scales. In particular, for the asymptotic equivalence of differential systems, the well-known theorems of Levinson and Yakubovich are improved and the well-known theorem of Wintner for the asymptotic equilibrium of linear differential systems is generalized to arbitrary time scales. Some of our results for asymptotic equilibrium are new even for difference systems. In the second part, the oscillation of solutions of a particular class of second order nonlinear delay dynamic equations and, more generally, two-dimensional nonlinear dynamic systems, including delay-dynamic systems, are discussed. Necessary and sufficient conditions are derived for the oscillation of solutions of nonlinear delay dynamic equations by extending some continuous results. Specifically, the classical theorems of Atkinson and Belohorec are generalized. Sufficient conditions are established for the oscillation of solutions of nonlinear dynamic systems by unifying and extending the corresponding continuous and discrete results. Particularly, the oscillation criteria of Atkinson, Belohorec, Waltman, and Hooker and Patula are generalized.

Abstract In this dissertation, the eigenvalue analysis and decentralized robust controller design of uncertain multi-time-scale system with parametrical perturbations are considered. Because the eigenvalues of the multi-time-scale systems cluster in some difference regions of the complex plane, we can use the singular perturbation method to separate the systems into some subsystems. These subsystems are independent to each other. We can discuss the properties of eigenvalues and design controller for these subsystem respectively, then we composite these controllers to a decentralized controller. The eigenvalue positions dominate the stability and the performance of the dynamic system. However, we cannot obtain the precise position of the eigenvalues from the influence of parametrical perturbations. The sufficient conditions of the eigenvalues clustering for the multi-time-scale systems will be discussed. The uncertainties consider as unstructured and structured perturbations are taken into considerations. The design algorithm provides for designing a decentralized controller that can assign the poles to our respect regions. The specified regions are half-plane and circular disk. Furthermore, the concepts of decentralized control and optimal control are used to design the linear quadratic regulator (LQR) controller and linear quadratic Gaussian (LQG) controller for the perturbed multi-time-scale systems. That is, the system can get the optimal robust performance. The bound of the singular perturbation parameter would influence the robust stability of the multi-time-scale systems. Finally, the sufficient condition to obtain the upper bound of the singular perturbation parameter presented by the Lyapunov method and matrix norm. The condition also extends for the pole assignment in the specified regions of each subsystem respectively. The illustrative examples are presented behind each topic. They show the applicability of the proposed theorems, and the results are satisfactory.

Improved basic understanding, predictability, and controllability of vortex-dominated and unsteady aerodynamic flows are important in enhancement of the performance of next generation helicopters. The primary objective of this research project was improved understanding of the fundamental vorticity and turbulent flow physics for a dynamically stalling airfoil at realistic helicopter flight conditions. An experimental program was performed on a large-scale (C = 0.45 m) dynamically pitching NACA 0012 wing operating in the Texas A&M University large-scale wind tunnel. High-resolution particle image velocimetry data were acquired on the first 10-15% of the wing. Six test cases were examined including the unsteady (k>0) and steady (k=0) conditions. The relevant mechanical, shear and turbulent time-scales were all of comparable magnitude, which indicated that the flow was in a state of mechanical non-equilibrium, and the expected flow separation and reattachment hystersis was observed. Analyses of the databases provided new insights into the leading-edge Reynolds stress structure and the turbulent transport processes. Both of which were previously uncharacterized. During the upstroke motion of the wing, a bubble structure formed in the leading-edge Reynolds shear stress. The size of the bubble increased with increasing angle-of-attack before being diffused into a shear layer at full separation. The turbulent transport analyses indicated that the axial stress production was positive, where the transverse production was negative. This implied that axial turbulent stresses were being produced from the axial component of the mean flow. A significant portion of the energy was transferred to the transverse stress through the pressure-strain redistribution, and then back to the transverse mean flow through the negative transverse production. An opposite trend was observed further downstream of this region.

ABSTRACT SCOUR AND SCOUR PROTECTION AT BRIDGE ABUTMENTS Kayat&uuml / rk, Serife Yurdag&uuml / l Ph. D., Department of Civil Engineering Supervisor: Prof. Dr. Mustafa G&ouml / g&uuml / S Co-Supervisor: Dr. Mehmet Ali K&ouml / kpinar January 2005, 213 pages Bridge failures are mainly caused by scouring the bed material around bridge foundations during flood. In this study, scour phenomenon around bridge abutments is experimentally studied. Effect of abutment size, location and size of the collars placed around the abutments, time evaluation of scour hole around the abutment, scour characteristics of abutment and pier interaction were experimentally investigated. Scour measurements were conducted in a rectangular channel of 30 m long and 1.5 m wide filled with erodable uniform sediment. In the first part of the study, in order to investigate the size effect of the abutment on the maximum scour depth, abutments of nine different sizes were tested for three different water depths. It was found that the length of the abutment is more important parameter than the width of it. Secondly, efficiency of various sizes of collars, which are used to reduce the local scour depth, located at different elevations around the abutments was determined. It was noticed that when the collar width was increased and placed at or below the bed level, the reduction in scour depth increases considerably. Some tests for partial-collar arrangements around the abutments were conducted and it was shown that instead of full-collar one can use partial-collar arrangements around the abutments to achieve the same efficiency as the full-collar. Time development of scour holes around the abutments with and without collar cases were recorded. It was observed considerable reductions in scour depths around the abutments can be obtained with collars compared to the cases in which there are no collars over the same time period. Finally, a series of experiments were carried out to investigate the interaction between bridge abutments and piers related to the local scour around them. Based on the experiments conducted with two different abutment lengths and pier diameters varying the lateral distances between them it was observed that scour depth reduction capacities of collars vary significantly while comparing a single abutment or pier.

abstract: A previously developed small time scale fatigue crack growth model is improved, modified and extended with an emphasis on creating the simplest models that maintain the desired level of accuracy for a variety of materials. The model provides a means of estimating load sequence effects by continuously updating the crack opening stress every cycle, in a simplified manner. One of the significant phenomena of the crack opening stress under negative stress ratio is the residual tensile stress induced by the applied compressive stress. A modified coefficient is introduced to determine the extent to which residual stress impact the crack closure and is observed to vary for different materials. Several other literature models for crack closure under constant loading are also reviewed and compared with the proposed model. The modified model is then shown to predict several sets of published test results under constant loading for a variety of materials. The crack opening stress is formalized as a function of the plastic zone sizes at the crack tip and the current crack length, which provided a means of approximation, accounting for both acceleration and retardation effects in a simplified manner. A sensitivity parameter is introduced to modify the enlarged plastic zone due to overload, to better fit the delay cycles with the test data and is observed to vary for different materials. Furthermore, the interaction effect induced by the combination of overload and underload sequence is modeled by depleting the compressive plastic zone due to an overload with the tensile plastic zone due to an underload. A qualitative analysis showed the simulation capacity of the small time scale model under different load types. A good agreement between prediction and test data for several irregular load types proved the applicability of the small time scale model under variable amplitude loading. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

abstract: Fatigue is a degradation process of materials that would lead to failure when materials are subjected to cyclic loadings. During past centuries, various of approaches have been proposed and utilized to help researchers understand the underlying theories of fatigue behavior of materials, as well as design engineering structures so that catastrophic disasters that arise from fatigue failure could be avoided. The stress-life approach is the most classical way that academia applies to analyze fatigue data, which correlates the fatigue lifetime with stress amplitudes during cyclic loadings. Fracture mechanics approach is another well-established way, by which people regard the cyclic stress intensity factor as the driving force during fatigue crack nucleation and propagation, and numerous models (such as the well-known Paris’ law) are developed by researchers. The significant drawback of currently widely-used fatigue analysis approaches, nevertheless, is that they are all cycle-based, limiting researchers from digging into sub-cycle regime and acquiring real-time fatigue behavior data. The missing of such data further impedes academia from validating hypotheses that are related to real-time observations of fatigue crack nucleation and growth, thus the existence of various phenomena, such as crack closure, remains controversial. In this thesis, both classical stress-life approach and fracture-mechanics-based approach are utilized to study the fatigue behavior of alloys. Distinctive material characterization instruments are harnessed to help collect and interpret key data during fatigue crack growth. Specifically, an investigation on the sub-cycle fatigue crack growth behavior is enabled by in-situ SEM mechanical testing, and a non-uniform growth mechanism within one loading cycle is confirmed by direct observation as well as image interpretation. Predictions based on proposed experimental procedure and observations show good match with cycle-based data from references, which indicates the credibility of proposed methodology and model, as well as their capability of being applied to a wide range of materials. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2018

In this work, we propose three control strategies from different perspectives to solve the alignment problem for different optical wireless communication (OWC) systems. • Experimental modeling based strategy: we model and analyze the vibration effects on the stationary OWC system (e.g. urban free-space optical (FSO) communication system in our case). The proposed Bifurcated-Gaussian (B-G) distribution model of the receiver optical power is derived under different vibra- tion levels and link distances using the nonlinear iteration method. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model helps to easily evaluate the link performance of UFSO systems and paves the way for constructing completed auxiliary control subsys- tems for robust UFSO links. • Extremum seeking control based strategy: we propose an extremum seeking control (ESC) based strategy for the mobile OWC system. Our proposed ap- proach consists of coarse alignment and fine alignment. The coarse alignment using feedback proportional-derivative (PD) control is responsible for tracking and following the receiver. For fine alignment, the perturbation-based extremum seeking control (ESC) is adopted for a continuous search for the optimal posi- tion, where the received optical power is maximum in the presence of distur- bance. The proposed approach is simple, effective, and easy to implement. • Time scale theory based strategy: we design a time scale based Kalman filter for the intermittent OWC system. First, the algorithm of Kalman filter on time scales is presented, followed by several numerical examples for interpretation and analysis. The design of Kalman filter on time scales for our simulated vibrating OWC system is then discussed, whose results are analyzed thoroughly and further validated by a reference system. The proposed strategy has great potential for solving the problem of observer design in the case of intermittent received signals (non-uniform measurements) and paves the way for further controller design. The three proposed control strategies directly or indirectly solve the beam align- ment problem for optical communication systems, supporting the development of robust optical communication link.