Nesta dissertação é apresentada a comparação do desempenho de três estimadores - o Filtro de Kalman Estendido, o Filtro de Kalman Unscented e o Filtro de Partículas - aplicados para estimar a postura de um robô diferencial. Uma câmera foi fixa no teto para cobrir todo o campo operacional do robô durante os experimentos, a fim de extrair o mapa e gerar o ground truth. Isso permitiu realizar uma análise do erro de forma precisa a cada instante de tempo. O desempenho de cada um dos estimadores foi avaliado sistematicamente e numericamente para duas trajetórias. Os resultados desse primeiro experimento demonstram que os filtros proporcionam grandes melhorias em relação à odometria e que o modelo dos sensores é crítico para obter esse desempenho. O Filtro de Partículas mostrou um desempenho melhor em relação aos demais nos dois percursos. No entanto, seu elevado custo computacional dificulta sua implementação em uma aplicação de tempo real. O Filtro de Kalman Unscented, por sua vez, mostrou um desempenho semelhante ao Filtro de Kalman Estendido durante a primeira trajetória. Porém, na segunda trajetória, a qual possui uma quantidade maior de curvas, o Filtro de Kalman Unscented mostrou uma melhora significativa em relação ao Filtro de Kalman Estendido. Foi realizado um segundo experimento, em que o robô planeja e executa duas trajetórias. Os resultados obtidos mostraram que o robô consegue chegar a um determinado local com uma precisão da mesma ordem de grandeza do que a obtida durante a estimação de estados do robô. / In this dissertation, the performance of three nonlinear-model based estimators - the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter - applied to pose estimation of a differential drive robot is compared. A camera was placed above the operating field of the robot to record the experiments in order to extract the map and generate the ground truth so the evaluation of the error can be done at each time step with high accuracy. The performance of each estimator is assessed systematically and numerically for two robot trajectories. The first experimental results showed that all estimators provide large improvements with respect to odometry and that the sensor modeling is critical for their performance. The particle filter showed a better performance than the others on both experiments, however, its high computational cost makes it difficult to implement in a real-time application. The Unscented Kalman Filter showed a similar performance to the Extended Kalman Filter during the first trajectory. However, during the second one (a curvier path) the Unscented Kalman Filter showed a significant improvement over the Extended Kalman Filter. A second experiment was carried out where the robot plans and executes a trajectory. The results showed the robot can reach a predefined location with an accuracy of the same order of magnitude as the obtained during the robot pose estimation.

Nesta dissertação é apresentada a comparação do desempenho de três estimadores - o Filtro de Kalman Estendido, o Filtro de Kalman Unscented e o Filtro de Partículas - aplicados para estimar a postura de um robô diferencial. Uma câmera foi fixa no teto para cobrir todo o campo operacional do robô durante os experimentos, a fim de extrair o mapa e gerar o ground truth. Isso permitiu realizar uma análise do erro de forma precisa a cada instante de tempo. O desempenho de cada um dos estimadores foi avaliado sistematicamente e numericamente para duas trajetórias. Os resultados desse primeiro experimento demonstram que os filtros proporcionam grandes melhorias em relação à odometria e que o modelo dos sensores é crítico para obter esse desempenho. O Filtro de Partículas mostrou um desempenho melhor em relação aos demais nos dois percursos. No entanto, seu elevado custo computacional dificulta sua implementação em uma aplicação de tempo real. O Filtro de Kalman Unscented, por sua vez, mostrou um desempenho semelhante ao Filtro de Kalman Estendido durante a primeira trajetória. Porém, na segunda trajetória, a qual possui uma quantidade maior de curvas, o Filtro de Kalman Unscented mostrou uma melhora significativa em relação ao Filtro de Kalman Estendido. Foi realizado um segundo experimento, em que o robô planeja e executa duas trajetórias. Os resultados obtidos mostraram que o robô consegue chegar a um determinado local com uma precisão da mesma ordem de grandeza do que a obtida durante a estimação de estados do robô. / In this dissertation, the performance of three nonlinear-model based estimators - the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter - applied to pose estimation of a differential drive robot is compared. A camera was placed above the operating field of the robot to record the experiments in order to extract the map and generate the ground truth so the evaluation of the error can be done at each time step with high accuracy. The performance of each estimator is assessed systematically and numerically for two robot trajectories. The first experimental results showed that all estimators provide large improvements with respect to odometry and that the sensor modeling is critical for their performance. The particle filter showed a better performance than the others on both experiments, however, its high computational cost makes it difficult to implement in a real-time application. The Unscented Kalman Filter showed a similar performance to the Extended Kalman Filter during the first trajectory. However, during the second one (a curvier path) the Unscented Kalman Filter showed a significant improvement over the Extended Kalman Filter. A second experiment was carried out where the robot plans and executes a trajectory. The results showed the robot can reach a predefined location with an accuracy of the same order of magnitude as the obtained during the robot pose estimation.

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Un signal GPS est modulé par une porteuse et est étalé par un code pseudo aléatoire. Sa puissance, qui est portée en dessous du niveau du bruit, ne peut pas être directement mesurée. Les estimateurs classiques de la littérature utilisent les paramètres statistiques du maximum de la corrélation, obtenus après le désétalement du signal pour mesurer la puissance du signal reçu. Ces estimateurs nécessitent une longue période d'intégration pour être précis. De plus, ils ne tiennent pas compte de l'effet de la fréquence Doppler et du nombre de satellites visibles sur la statistique du maximum de la corrélation. Ces effets perturbateurs faussent l'estimation de la valeur C/N0 et limitent les applications qui utilisent cette grandeur telle que la réflectométrie des signaux GNSS. Ce travail de thèse propose un estimateur du rapport signal à bruit propre à chaque satellite, à partir d'un signal GPS L1. Pour présenter cet estimateur, nous avons adopté une approche en deux étapes. On suppose dans la première étape que le signal GPS est numérisé sur 1 bit, et on établit une fonction reliant l'amplitude du signal reçu au maximum de corrélation. Cette fonction non linéaire est déduite de l'architecture radio du récepteur GPS et des paramètres du signal qui sont : la fréquence Doppler et le déphasage du signal reçu. En effet, le rapport signal à bruit est une mesure relative, et pour pouvoir estimer l'amplitude du signal, on suppose que le bruit est blanc, gaussien, centré et de variance unitaire. La fonction proposée étant fortement non linéaire, nous proposons dans une deuxième étape, un estimateur dynamique de l'amplitude du signal, qui utilise le filtrage d'état non linéaire et les observations du maximum de la corrélation. Deux filtres sont évalués à cet effet ; le friltrage de Kalman sans parfum et le filtrage particulaire. / A gps signal es modulated by a carrier and is spreaded by a pseudo random code. Its power, which is carried below the level of noise, can't be directly measured. Conventional estimators literature using the statistical parameters of the maximum of the correlation, obtained after despreading of the signal to measure the received signal strength. These estimators require a long period of integration to be precise. Moreover, they do not take into account the effect of the Doppler frequency and the number of visible satellites on the statistical maximum of the correlation. These disruptive effects falsify the estimated value of C/N0 and limit the applications of the reflectometry. This thesis proposes an estimator of the signal to noise ratio own to each satellite, from a GPS L1 signal. To present this estimator, we have adopted a two-step approach. it is assumed in the first stage that the GPS signal is digitized on 1 bit, and sets a function relating the amplitude of the signal received to maximum correlation knowing the parameters of the GPS signal which are : the Doppler frequency and the phase shift of the received signal. indeed, the signal to noise ratio is a relative measure, and to estimate the signal amplitude is assumed that the noise is white, Gaussian, centered and unit variance. The proposed function is highly non-linear. We propose in a second step a dynamic estimator of the signal amplitude, which uses the non-linear state filter and the observations of the maximum correlation. Two filters are assessed in this case the Unscented Kalman filter and a particle filter.

Power quality has become one of major concerns in the power industry. It can be described as the reliability of the electric power to maintain continuity operation of end-use equipment. Power quality problems are defined as deviation of voltage or current waveforms from the ideal value. The expansion plan of wind power generation has raised concern regarding how it influences the voltage and current signals. The variability nature of wind energy and the requirements of wind power generation increase the potential problems such as frequency and harmonic distortions. In order to analyze and mitigate problems in wind power generation, it is important to monitor power quality in wind farm. Therefore, the more accurate and reliable parameter estimation methods suitable for wind power generation are needed. Three parameter estimation methods are proposed in this thesis to estimate the unknown parameters, i.e. amplitude and phase angle of fundamental and harmonic components, DC component and system frequency, during the dynamic change in wind farm. In the first method, a self-tuning procedure is introduced to least square method to increase the immunity of the algorithm to noise. In the second method, nonrecursive Newton Type Algorithm is utilised to estimate the unknown parameters by obtaining the left pseudoinverse of Jacobian matrix. In the last technique, unscented transformation is used to replace the linearization procedure to obtain mean and covariance which will be used in Kalman filter method. All of the proposed methods have been tested rigorously using computer simulated data and have shown their capability to track the unknown parameters under extreme distortions. The performances of proposed methods have also been compared using real recorded data from several wind farms in Europe and have demonstrated high correlation. This comparison has verified that UKF requires the shortest processing time and STLS requires the longest.

A permanent magnet synchronous motor is a type of motor that is used in several different application areas, not least in an autonomous robots where it is the motor that drives the wheels. Today, many actors choose simulation as a tool to save money and time when product tests are performed. This thesis covers both the process of modeling a permanent magnet synchronous motor and regulating it at low speeds, in a simulation environment. As previously mentioned, the motor is a permanent magnet synchronous motor and is a direct-driven outrunner, which means that the motor and the wheel are combined and that the rotor is spinning outside the stator. On current robots in production, there is a gear ratio between the motor and wheels to be able to regulate the motor at higher speeds and thus generate a torque. The gearing contributes to losses and is an extra cost, so the examination of a direct-drive motor is interesting. The direct-drive motor has a lower working speed and is therefore by some reasons more difficult to regulate when applying torque load to the motor. The motor is equipped with current sensors and a position sensor, which has a certain resolution. The position sensor is speed-dependent in the sense that at lower RPMs fewer measurements are obtained, which is a problem when regulating the motor. The thesis examines two different control strategies, one of which is a more classic PI control that is often used on the market in various systems and the other is model predictive control (MPC). The latter is an online optimization where, with the help of information about the system, an optimal input signal is calculated and applied. Two different non-linear Kalman filters are also examined, which are implemented with the two different control strategies, to estimate the speed with the help of the measurements from current and the position sensor. The conclusion is an ideal motor model that mimics the physical motor. MPC is able to regulate the motor between 0-50 RPM, both with and without applied torque and even better with speed estimation from a Kalman filter. The PI controller is not able to regulate the motor at 2 RPM but for speeds at 10 RPM and greater, however with over-/undershoot after an acceleration.

When operating an aircraft, inaccurate measurements can have devastating consequences. For example, when measuring airspeed using a pitot tube, icing effects and other faults can result in erroneous measurements. Therefore, this master thesis aims to create an alternative method which utilizes known flight mechanical equations and sensor fusion to create an estimate of the airspeed during flight. For validation and generation of flight data, a simulation model developed by SAAB AB, called ARES, is used.  Two models are used to describe the aircraft behavior. One of which is called the dynamic model and utilizes forces acting upon the aircraft body in the equations of motion. The other model, called the kinematic model, instead describes the motion with accelerations of the aircraft body. The measurements used are the angle of attack (AoA), side-slip angle (SSA), GPS velocities, and angular rates from an inertial measurement unit (IMU). The dynamic model assumes that engine thrust and aerodynamic coefficients are already estimated to calculate resulting forces, meanwhile the kinematic model instead uses body fixed accelerations from the IMU. These models are combined with filters to create estimations of the airspeed. The filters used are the extended Kalman filter (EKF) and unscented Kalman filter (UKF). These are combined with the two models to create in total four methods to estimate the airspeed.  The results show no major difference in the performance between the filters except for computational time, for which the EKF has the fastest. Further, the result show similar airspeed estimation performance between the models, but differences can be seen. The kinematic model manages to estimate the wind with higher details and to converge faster, compared to the dynamic model. Both models suffer from an observability problem. This problem entails that the aircraft needs to be maneuvered to excite the AoA and SSA in order for the estimation methods to evaluate the wind, which is crucial for accurate airspeed estimation. The robustness of the dynamic model regarding errors in engine thrust and aerodynamic coefficients are also researched, which shows that the model is quite robust against errors in these values.

Nesta tese de doutorado é proposta uma abordagem para estimar a velocidade angular de geradores síncronos conectados em um sistema elétrico de potência, a partir de sinais que podem ser facilmente mensurados, tais como a corrente e a tensão na barra do lado de alta tensão do transformador que conecta o gerador em análise ao restante do sistema. Uma vez que informações precisas sobre o comportamento dinâmico do sistema são de elevada importância para um controle efetivo do SEP, especialmente com o aumento da complexidade da rede, a abordagem proposta nesta tese fornece uma estimativa do sinal de velocidade que pode ser aplicada no estudo da estabilidade a pequenas perturbações para mitigar os problemas inerentes a presença das oscilações eletromecânicas mal amortecidas nos SEPs. A abordagem desenvolvida é composta por dois métodos sendo cada um deles aplicável dependendo das características do problema a ser resolvido e das informações disponíveis para tanto. No primeiro método, uma técnica de sensibilidade da trajetória é aplicada ao sinal de diferença entre a resposta obtida pelo modelo simulado e aquela fornecida por dados amostrados no sistema real emulado. A partir desse sinal de erro e das curvas de sensibilidade, a técnica possibilita calibrar os coeficientes de um modelo linear do SEP e, consequentemente, descrever de forma precisa a resposta da velocidade do gerador em análise. No segundo método, uma técnica de filtragem é utilizada (filtro de Kalman Unscented) a qual fornece uma estimativa adequada para a velocidade angular do rotor mesmo quando elevadas discrepâncias são observadas entre a saída do modelo simulado e a resposta amostrada no sistema real. Os resultados obtidos sobre diferentes sistemas testes evidenciam a eficiência da abordagem proposta. / In this thesis, an approach is proposed to estimate the rotor speed of synchronous generators connected to an electric power system (EPS), from signals that can be easily sampled by measuring equipment, such as current and voltage in high voltage side of the step-up transformer of the power plant. Accurate information about the dynamic behavior of system is essential for effective control and reliable operation of EPS, especially with the increasing complexity of the grid. Hence, the main aim of this work is to provide an estimate of the rotor speed signal that can be applied in the area of small-signal stability, in order to mitigate the detrimental effects of poorly damped electromechanical oscillations in EPSs. The developed approach is composed of two methods, where each of them is applicable depending on the characteristics of the problem to be solved and the available information. In the first method, a trajectory sensitivity technique is applied on the mismatch between the simulated output in the system linear model and the response of the real system. Using this error signal and the sensitivity curves, this method allows to identify and to calibrate some coefficients of the linear model and, consequently, to adequately describe the speed response of the generator under analysis. In this second method, a filtering technique is used, the Unscented Kalman Filter, which provides an adequate estimate for rotor speed even when high discrepancies are observed between the linear model and the sampled response of real system. The results obtained on test systems with different characteristics show the efficiency of the proposed approach.

The simplified models of synchronous generators, widely used in stability studies of large electric power systems, are not completely suitable for the stability analysis and the design of controllers of distributed synchronous generators, generally connected to typically unbalanced branches. To more accurately analyze the systems with distributed generation, it is necessary to utilize synchronous generator models that consider frequency variation in their electrical equations. Furthermore, this model must represent possible unbalanced three-phase voltages at the generator terminals as well. Nonetheless, to provide reliable responses, the parameters of this more detailed model should be known. Thus, this work assesses the influence of the parameters on the responses of a detailed synchronous generator model, suitable to depict unbalanced operating conditions, and proposes an approach for the estimation of its most important parameters. In the proposed structure, we first employ Trajectory Sensitivity Functions to evaluate the dependency of the responses of this model with respect to its parameters and, from that, we rank them according to their importance. Subsequently, we apply an estimation process that utilizes the Unscented Kalman Filter with the aid of a genetic algorithm to estimate the main parameters of this synchronous generator model under unbalanced operating conditions. To obtain the results and, therefore, assess the proposed estimation approach, we make use of a system which comprises a synchronous generator connected to a three-phase unbalanced load. In addition to the unbalanced operation of the test system, we also consider noises due to the constant load switching, typical of distribution systems. The estimations performed for three operating conditions of the generator were very satisfactory, which demonstrates the efficiency of the proposed approach to obtain adequate models for the description of synchronous generator operation under unbalanced operating conditions. / Os modelos simplificados de geradores síncronos, amplamente utilizados em estudos de estabilidade de grandes sistemas elétricos de potência, não são completamente adequados para a análise de estabilidade e projetos de controladores dos geradores síncronos distribuídos, geralmente conectados a sistemas tipicamente desequilibrados. Para que os sistemas com geração distribuída possam ser analisados mais fidedignamente, é necessária a utilização de um modelo de gerador síncrono que considere a variação de frequência em suas equações elétricas. Além disso, esse modelo também deve ser capaz de representar possíveis tensões trifásicas desequilibradas nos terminais do gerador. Entretanto, para que esse modelo mais detalhado possa fornecer respostas coerentes com a realidade, deve-se conhecer seus parâmetros. Dessa forma, este trabalho avalia a influência dos parâmetros nas respostas de um modelo de gerador síncrono mais detalhado, adequado para representar operações desbalanceadas, e propõe uma abordagem para a estimação de seus parâmetros mais importantes. Nessa estrutura, inicialmente empregam-se as Funções de Sensibilidade de Trajetória para avaliar a dependência das respostas desse modelo em relação aos seus parâmetros e, a partir disso, ordená-los conforme sua importância. Em seguida, aplica-se um processo de estimação que utiliza o Filtro de Kalman Unscented com o auxílio de um algoritmo genético para estimar os principais parâmetros desse modelo de gerador síncrono em condições de desbalanço. Para a obtenção dos resultados e consequente avaliação da abordagem de estimação proposta, utiliza-se um sistema composto por um gerador síncrono conectado a uma carga trifásica desbalanceada. Além da operação desbalanceada desse sistema teste, também são considerados ruídos devidos ao constante chaveamento de cargas, típicos de sistemas de distribuição. As estimações realizadas para três condições de operação do gerador foram bem satisfatórias, indicando a eficiência da abordagem proposta na obtenção de modelos adequados para descrever a operação de geradores síncronos em condições de desbalanço.

Nesta tese de doutorado é proposta uma abordagem para estimar a velocidade angular de geradores síncronos conectados em um sistema elétrico de potência, a partir de sinais que podem ser facilmente mensurados, tais como a corrente e a tensão na barra do lado de alta tensão do transformador que conecta o gerador em análise ao restante do sistema. Uma vez que informações precisas sobre o comportamento dinâmico do sistema são de elevada importância para um controle efetivo do SEP, especialmente com o aumento da complexidade da rede, a abordagem proposta nesta tese fornece uma estimativa do sinal de velocidade que pode ser aplicada no estudo da estabilidade a pequenas perturbações para mitigar os problemas inerentes a presença das oscilações eletromecânicas mal amortecidas nos SEPs. A abordagem desenvolvida é composta por dois métodos sendo cada um deles aplicável dependendo das características do problema a ser resolvido e das informações disponíveis para tanto. No primeiro método, uma técnica de sensibilidade da trajetória é aplicada ao sinal de diferença entre a resposta obtida pelo modelo simulado e aquela fornecida por dados amostrados no sistema real emulado. A partir desse sinal de erro e das curvas de sensibilidade, a técnica possibilita calibrar os coeficientes de um modelo linear do SEP e, consequentemente, descrever de forma precisa a resposta da velocidade do gerador em análise. No segundo método, uma técnica de filtragem é utilizada (filtro de Kalman Unscented) a qual fornece uma estimativa adequada para a velocidade angular do rotor mesmo quando elevadas discrepâncias são observadas entre a saída do modelo simulado e a resposta amostrada no sistema real. Os resultados obtidos sobre diferentes sistemas testes evidenciam a eficiência da abordagem proposta. / In this thesis, an approach is proposed to estimate the rotor speed of synchronous generators connected to an electric power system (EPS), from signals that can be easily sampled by measuring equipment, such as current and voltage in high voltage side of the step-up transformer of the power plant. Accurate information about the dynamic behavior of system is essential for effective control and reliable operation of EPS, especially with the increasing complexity of the grid. Hence, the main aim of this work is to provide an estimate of the rotor speed signal that can be applied in the area of small-signal stability, in order to mitigate the detrimental effects of poorly damped electromechanical oscillations in EPSs. The developed approach is composed of two methods, where each of them is applicable depending on the characteristics of the problem to be solved and the available information. In the first method, a trajectory sensitivity technique is applied on the mismatch between the simulated output in the system linear model and the response of the real system. Using this error signal and the sensitivity curves, this method allows to identify and to calibrate some coefficients of the linear model and, consequently, to adequately describe the speed response of the generator under analysis. In this second method, a filtering technique is used, the Unscented Kalman Filter, which provides an adequate estimate for rotor speed even when high discrepancies are observed between the linear model and the sampled response of real system. The results obtained on test systems with different characteristics show the efficiency of the proposed approach.