Este trabalho de dissertação trata do problema de observabilidade e redundância de medidas para efeito de estimação de estado trifásica. É proposta a extensão de uma metodologia numérica eficiente para análise de observabilidade e identificação de medidas críticas e conjuntos críticos de medidas, desenvolvida para modelagem por fase, a fim de considerar redes trifásicas de energia, nas quais os desbalanços nas cargas e os desequilíbrios na rede são considerados. Ao longo do trabalho apresenta-se uma revisão dos principais conceitos de estimação de estado, observabilidade de redes e redundância de medidas, destacando a importância da estimação de estado trifásica para obtenção de uma operação segura de sistemas elétricos de potência desbalanceados e/ou desequilibrados. Os resultados obtidos em diversos testes realizados, com sistemas trifásicos já empregados em outros trabalhos da área contendo 4, 7 e 38 barras, atestam o adequado desempenho da extensão proposta e são apresentados detalhadamente nesta dissertação. Por fim, o conceito de observabilidade topológica, desenvolvido para modelagem monofásica da rede, é estendido para modelagem trifásica, permitindo um entendimento melhor do problema de observabilidade no contexto de estimação trifásica. / This thesis focuses on the problem of observability and measurement redundancy in the context of three-phase state estimation. It is proposed an extension of an efficient numerical methodology for observability and redundancy analysis, developed for the single-phase network model, in order to consider the three-phase network model, where the unbalanced loads and the asymmetric nature of the system are considered. During this work, a review of the main concepts related to state estimation, network observability and measurement redundancy are presented, highlighting the importance of the three-phase state estimation in order to obtain a reliable operation of unbalanced and/or asymmetric power systems. Simulations results obtained for several cases studies based on three three-phase systems already used in the literature, with 4, 7 and 38 buses, validate the proposed methodology extension and are presented in detail in this thesis. Finally, the concept of topological observability, developed for the single-phase network model, is extended for the three-phase model.

Modern control theory is today an interdisciplinary area of research. Just as much as this can be problematic, it also provides a rich research environment where practice and theory meet. This Thesis is conducted in the borderline between computing science (numerical analysis) and applied control theory. The design and analysis of a modern control system is a complex problem that requires high qualitative software to accomplish. Ideally, such software should be based on robust methods and numerical stable algorithms that provide quantitative as well as qualitative information. The introduction of the Thesis is dedicated to the underlying control theory and to introduce the reader to the main subjects. Throughout the Thesis, the theory is illustrated with several examples, and similarities and differences between the terminology from mathematics, systems and control theory, and numerical linear algebra are highlighted. The main contributions of the Thesis are structured in two parts, dealing with two mainly unrelated subjects. Part I is devoted to the qualitative information which is provided by the stratification of orbits and bundles of matrices, matrix pencils and system pencils. Before the theory of stratification is established the reader is introduced to different canonical forms which reveal the system characteristics of the model under investigation. A stratification reveals which canonical structures of matrix (system) pencils are near each other in the sense of small perturbations of the data. Fundamental concepts in systems and control, like controllability and observability of linear continuous-time systems, are considered and it is shown how these system characteristics can be investigated using the stratification theory. New results are presented in the form of the cover relations (nearest neighbours) for controllability and observability pairs. Moreover, the permutation matrices which take a matrix pencil in the Kronecker canonical form to the corresponding system pencil in (generalized) Brunovsky canonical form are derived. Two novel algorithms for determining the permutation matrices are provided. Part II deals with numerical methods for solving periodic Riccati differential equations (PRDE:s). The PRDE:s under investigation arise when solving the linear quadratic regulator (LQR) problem for periodic linear time-varying (LTV) systems. These types of (periodic) LQR problems turn up for example in motion planning of underactuated mechanical systems, like a humanoid robot, the Furuta pendulum, and pendulums on carts. The constructions of the nonlinear controllers are based on linear versions found by stabilizing transverse dynamics of the systems along cycles. Three different methods explicitly designed for solving the PRDE are evaluated on both artificial systems and stabilizing problems originating from experimental control systems. The methods are the one-shot generator method and two recently proposed methods: the multi-shot method (two variants) and the SDP method. As these methods use different approaches to solve the PRDE, their numerical behavior and performance are dependent on the nature of the underlying control problem. Such method characteristics are investigated and summarized with respect to different user requirements (the need for accuracy and possible restrictions on the solution time). / Modern reglerteknik är idag i högsta grad ett interdisciplinärt forskningsområde. Lika mycket som detta kan vara problematiskt, resulterar det i en stimulerande forskningsmiljö där både praktik och teori knyts samman. Denna avhandling är utförd i gränsområdet mellan datavetenskap (numerisk analys) och tillämpad reglerteknik. Att designa och analysera ett modernt styrsystem är ett komplext problem som erfordrar högkvalitativ mjukvara. Det ideala är att mjukvaran består av robusta metoder och numeriskt stabila algoritmer som kan leverera både kvantitativ och kvalitativ information.Introduktionen till avhandlingen beskriver grundläggande styr- och reglerteori samt ger en introduktion till de huvudsakliga problemställningarna. Genom hela avhandlingen illustreras teori med exempel. Vidare belyses likheter och skillnader i terminologin som används inom matematik, styr- och reglerteori samt numerisk linjär algebra. Avhandlingen är uppdelade i två delar som behandlar två i huvudsak orelaterade problemklasser. Del I ägnas åt den kvalitativa informationen som ges av stratifiering av mångfalder (orbits och bundles) av matriser, matrisknippen och systemknippen. Innan teorin för stratifiering introduceras beskrivs olika kanoniska former, vilka var och en avslöjar olika systemegenskaper hos den undersökta modellen. En stratifiering ger information om bl.a. vilka kanoniska strukturer av matrisknippen (systemknippen) som är nära varandra med avseende på små störningar i datat. Fundamentala koncept i styr- och reglerteori behandlas, så som styrbarhet och observerbarhet av linjära tidskontinuerliga system, och hur dessa systemegenskaper kan undersökas med hjälp av stratifiering. Nya resultat presenteras i form av relationerna för täckande (närmsta grannar) styrbarhets- och observerbarhets-par. Dessutom härleds permutationsmatriserna som tar ett matrisknippe i Kroneckers kanoniska form till motsvarande systemknippe i (generaliserade) Brunovskys kanoniska form. Två algoritmer för att bestämma dessa permutationsmatriser presenteras. Del II avhandlar numeriska metoder för att lösa periodiska Riccati differentialekvationer (PRDE:er). De undersökta PRDE:erna uppkommer när ett linjärt kvadratiskt regulatorproblem för periodiska linjära tidsvariabla (LTV) system löses. Dessa typer av (periodiska) regulatorproblem dyker upp till exempel när man planerar rörelser för understyrda (underactuated) mekaniska system, så som en humanoid (mänsklig) robot, Furuta-pendeln och en vagn med en inverterad (stående) pendel. Konstruktionen av det icke-linjära styrsystemet är baserat på en linjär variant som bestäms via stabilisering av systemets transversella dynamik längs med cirkulära banor. Tre metoder explicit konstruerade för att lösa PRDE:er evalueras på både artificiella system och stabiliseringsproblem av experimentella styrsystem. Metoderna är sk. en- och flerskotts metoder (one-shot, multi-shot) och SDP-metoden. Då dessa metoder använder olika tillvägagångssätt för att lösa en PRDE, beror dess numeriska egenskaper och effektivitet på det underliggande styrproblemet. Sådana metodegenskaper undersöks och sammanfattas med avseende på olika användares behov, t.ex. önskad noggrannhet och tänkbar begränsning i hur lång tid det får ta att hitta en lösning.

In this study, accurate target tracking for bearings-only tracking problem is investigated. A new tracking filter for this nonlinear problem is designed where both range parameterization and Rao-Blackwellized (marginalized) particle filtering techniques are used in a Gaussian mixture formulation to track both constant velocity and maneuvering targets. The idea of using target turn rate in the state equation in such a way that marginalization is possible is elaborated. Addition to nonlinear nature, unobservability is a major problem of bearings-only tracking. Observer trajectory generation to increase the observability of the bearings-only tracking problem is studied. Novel formulation of observability measures based on mutual information between the state and the measurement sequences are derived for the problem. These measures are used as objective functions to improve observability. Based on the results obtained better understanding of the required observer trajectory for accurate bearings-only target tracking is developed.

This dissertation addresses the development and use of novel software tools and environments for the computation and visualization of canonical information as well as stratification hierarchies for matrices and matrix pencils. The simplest standard shape to which a matrix pencil with a given set of eigenvalues can be reduced is called the Kronecker canonical form (KCF). The KCF of a matrix pencil is unique, and all pencils in the manifold of strictly equivalent pencils - collectively termed the orbit - can be reduced to the same canonical form and so have the same canonical structure. For a problem with fixed input size, all orbits are related under small perturbations. These relationships can be represented in a closure hierarchy with a corresponding graph depicting the stratification of these orbits. Since degenerate canonical structures are common in many applications, software tools to determine canonical information, especially under small perturbations, are central to understanding the behavior of these problems. The focus in this dissertation is the development of a software tool called StratiGraph. Its purpose is the computation and visualization of stratification graphs of orbits and bundles (i.e., union of orbits in which the eigenvalues may change) for matrices and matrix pencils. It also supports matrix pairs, which are common in control systems. StratiGraph is extensible by design, and a well documented plug-in feature enables it, for example, to communicate with Matlab(TM). The use and associated benefits of StratiGraph are illustrated via numerous examples. Implementation considerations such as flexible software design, suitable data representations, and good and efficient graph layout algorithms are also discussed. A way to estimate upper and lower bounds on the distance between an input S and other orbits is presented. The lower bounds are of Eckhart-Young type, based on the matrix representation of the associated tangent spaces. The upper bounds are computed as the Frobenius norm F of a perturbation such that S + F is in the manifold defining a specified orbit. Using associated plug-ins to StratiGraph this information can be computed in Matlab, while visualization alongside other canonical information remains within StratiGraph itself. Also, a proposal of functionality and structure of a framework for computation of matrix canonical structure is presented. Robust, well-known algorithms, as well algorithms improved and developed in this work, are used. The framework is implemented as a prototype Matlab toolbox. The intention is to collect software for computing canonical structures as well as for computing bounds and to integrate it with the theory of stratification into a powerful new environment called the MCS toolbox. Finally, a set of utilities for generating web computing environments related to mathematical and engineering library software is presented. The web interface can be accessed from a standard web browser with no need for additional software installation on the local machine. Integration with the control and systems library SLICOT further demonstrates the efficacy of this approach.

The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.

The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.

Modeling, fault assessment, and diagnostics of rolling element bearings and induction motors were studied. Dynamic model of rolling element bearings with faults were developed using vector bond graphs. The model incorporates gyroscopic and centrifugal effects, contact deflections and forces, contact slip and separations, and localized faults. Dents and pits on inner race, outer race and balls were modeled through surface profile changes. Experiments with healthy and faulty bearings validated the model. Bearing load zones under various radial loads and clearances were simulated. The model was used to study dynamics of faulty bearings. Effects of type, size and shape of faults on the vibration response and on dynamics of contacts in presence of localized faults were studied. A signal processing algorithm, called feature plot, based on variable window averaging and time feature extraction was proposed for diagnostics of rolling element bearings. Conducting experiments, faults such as dents, pits, and rough surfaces on inner race, balls, and outer race were detected and isolated using the feature plot technique. Time features such as shape factor, skewness, Kurtosis, peak value, crest factor, impulse factor and mean absolute deviation were used in feature plots. Performance of feature plots in bearing fault detection when finite numbers of samples are available was shown. Results suggest that the feature plot technique can detect and isolate localized faults and rough surface defects in rolling element bearings. The proposed diagnostic algorithm has the potential for other applications such as gearbox. A model-based diagnostic framework consisting of modeling, non-linear observability analysis, and parameter tuning was developed for three-phase induction motors. A bond graph model was developed and verified with experiments. Nonlinear observability based on Lie derivatives identified the most observable configuration of sensors and parameters. Continuous-discrete Extended Kalman Filter (EKF) technique was used for parameter tuning to detect stator and rotor faults, bearing friction, and mechanical loads from currents and speed signals. A dynamic process noise technique based on the validation index was implemented for EKF. Complex step Jacobian technique improved computational performance of EKF and observability analysis. Results suggest that motor faults, bearing rotational friction, and mechanical load of induction motors can be detected using model-based diagnostics as long as the configuration of sensors and parameters is observable. / text

There is significant uncertainty in our knowledge of the Martian atmosphere and the aerodynamics of the Mars entry, descent, and landing (EDL) systems. These uncertainties result in conservatism in the design of the EDL vehicles leading to higher system masses and a broad range of performance predictions. Data from flight instrumentation onboard Mars EDL systems can be used to quantify these uncertainties, but the existing dataset is sparse and many parameters of interest have not been previously observable. Many past EDL reconstructions neither utilize statistical information about the uncertainty of the measured data nor quantify the uncertainty of the estimated parameters. Statistical estimation methods can blend together disparate data types to improve the reconstruction of parameters of interest for the vehicle. For example, integrating data obtained from aeroshell-mounted pressure transducers, inertial measurement unit, and radar altimeter can improve the estimates of the trajectory, atmospheric profile, and aerodynamic coefficients, while also quantifying the uncertainty in these estimates. These same statistical methods can be leveraged to improve current engineering models in order to reduce conservatism in future EDL vehicle design. The work in this thesis presents a comprehensive methodology for parameter reconstruction and uncertainty quantification while blending dissimilar Mars EDL datasets. Statistical estimation methods applied include the Extended Kalman Filter, Unscented Kalman Filter, and Adaptive Filter. The estimators are applied in a manner in which the observability of the parameters of interest is maximized while using the sparse, disparate EDL dataset. The methodology is validated with simulated data and then applied to estimate the EDL performance of the 2012 Mars Science Laboratory. The reconstruction methodology is also utilized as a tool for improving vehicle design and reducing design conservatism. A novel method of optimizing the design of future EDL atmospheric data systems is presented by leveraging the reconstruction methodology. The methodology identifies important design trends and the point of diminishing returns of atmospheric data sensors that are critical in improving the reconstruction performance for future EDL vehicles. The impact of the estimation methodology on aerodynamic and atmospheric engineering models is also studied and suggestions are made for future EDL instrumentation.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-03T14:55:18Z No. of bitstreams: 1 Arquivototal.pdf: 864117 bytes, checksum: a54f5341fc1386510bbc10ef32cee483 (MD5) / Made available in DSpace on 2018-05-03T14:55:18Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 864117 bytes, checksum: a54f5341fc1386510bbc10ef32cee483 (MD5) Previous issue date: 2017-07-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work presents Carleman estimates to a class of degenerate parabolic problems over a square (in the two dimensional case) or a bounded interval (in the one dimensional case). We consider a differential operator that degenerate only in a part of the boundary. Using semigroup theory, we prove well posedness results. Then, using suitables weight functions, we prove Carleman estimates and, as application, results on multi-objective controllability. / Neste trabalho apresentamos estimativas de Carleman para uma classe de problemas parabólicos degenerados sobre um quadrado (no caso bidimensional) ou sobre um intervalo limitado (no caso unidimensional). Consideramos um operador diferencial que degenera apenas em uma parte da fronteira. Provamos resultados de existência, unicidade e estimativas de energia via teoria do semigrupo. Em seguida usamos funções peso adequadas para obter estimativas de Carleman e, como aplicações, resultados de controlabilidade multi-objetivo.

Para obter-se uma operação segura dos sistemas elétricos de potência (SEP), é imprescindível uma estimação de estado (EE) confiável, pois, as ações de controle e operação, em tempo real, dos SEP se baseiam no banco de dados obtido pelo processo de EE. O primeiro passo, para o sucesso do processo de EE, é a obtenção de um plano de medição confiável, ou seja, um plano de medição que garanta a observabilidade do sistema e a não presença de medidas críticas e dos conjuntos críticos de medidas. Entretanto, tendo em vista a possibilidade de ocorrer, durante a operação de um SEP, de problemas causando a perda de medidas, a obtenção de um plano de medição confiável é uma condição necessária, mas não suficiente, para o sucesso do processo de EE. Face ao exposto, desenvolveu-se neste trabalho um programa computacional que possibilita uma EE confiável mesmo em situação de perda de medidas. O programa proposto permite, de uma forma rápida em termos de velocidade de execução, análise e restauração da observabilidade, identificação de medidas críticas e de conjuntos críticos de medidas, bem como a atualização dessas características qualitativas de conjunto de medidas após a perda de medidas. Como embasamento teórico para o desenvolvimento do programa proposto, foram utilizados dois algoritmos destinados à análise das características qualitativas de conjuntos de medidas, que se baseiam na fatoração triangular da matriz Jacobiana, bem como técnicas de esparsidade e de desenvolvimento de programas computacionais. Para comprovar a eficiência do programa proposto, vários testes foram realizados, utilizando o sistema de 6, 14 e 30 barras do IEEE e 121 barras da ELETROSUL. / To obtain a safe power system (PS) operation, becomes necessary a reliable state estimation (SE), since the real time control actions of a PS are based on the data obtained through the SE process. The first requirement for a successful SE process is the existence of a reliable measurement placement plan, that is, a measurement placement plan that guarantees system observability and the absence of both critical measurements and critical sets. However, considering that during the operation of a PS measurements can be lost decreasing the measurement-redundancy, one can say that although a reliable measurement placement plan is a necessary condition to guarantee a reliable state estimation, it is not sufficient. This dissertation presents a computer program that allows for a reliable SE, even in situations of problems causing loss of measurements. The proposed software allows, in a very fast way in terms of execution time, observability analysis and restoration, identification of critical measurements and critical sets, as well as the updating of these measurement set qualitative characteristics after loss of measurements. As a theoretical background for the development of the software, two algorithms were utilized allowing for the analysis of measurement set qualitative characteristics based on the triangular factorization of the Jacobian matrix, as well as sparsity techniques and techniques for the development of programs. To prove the efficiency of the proposed software, several tests were performed using the system of 6, 14 and 30 buses from IEEE and 121 buses from ELETROSUL.