Dissertations / Theses on the topic 'Linear quadratic regulator (LQR) controller'

Orientador: Edvaldo Assunção<br>Resumo: Neste trabalho é proposta a resolução do problema do regulador linear quadrático (Linear Quadratic Regulator - LQR) via desigualdades matriciais lineares (Linear Matrix Inequalities - LMIs) para sistemas lineares e invariantes no tempo sujeitos a incertezas politópicas, bem como para sistemas lineares sujeitos a parâmetros variantes no tempo (Linear Parameter Varying - LPV). O projeto dos controladores é baseado na realimentação derivativa. A escolha da realimentação derivativa se dá devido à sua fácil implementação em certas aplicações como, por exemplo, no controle de vibrações. Os sinais usados na realimentação são aceleração e velocidade, sendo obtidos por meio de acelerômetros. Por meio do método proposto é possível obter condições LMIs para a síntese de controladores que garantam a estabilização do sistema em malha fechada, sendo que os controladores possuem desempenho otimizado. Para a formulação das condições LMIs, uma função de Lyapunov do tipo quadrática é utilizada. Exemplos teóricos e simulações são utilizados como forma de validação dos métodos propostos, além de mostrar que os novos resultados apresentam condições menos conservadoras. Além disso, ao final é apresentada uma implementação prática em um sistema de suspensão ativa, produzida pela Quanser®.<br>Abstract: The resolution of linear quadratic regulator (LQR) problem via linear matrix inequalities (LMIs) for linear time-invariant systems subject to polytopic uncertainties, as linear systems subjects to linear parameter varying (LPV), is proposed in this work. The controllers' designs are based on the state derivative feedback. The aim to the choice of the state derivative feedback is your easy implementation in a class of mechanical systems, such as in vibration control, for example. The signals used for feedback are acceleration and velocity, it is obtained by means of accelerometers. Through the proposed method it is possible to obtain LMIs conditions for the synthesis of controllers that guarantee the stabilisation of the closed-loop system, being that the controllers have optimised performance. For the LMIs conditions formulations, a Lyapunov function of type quadratic is used. As a form of validation, theoretical examples and simulations are performed, besides to show that the new results are less conservative. Furthermore, a practical implementation in an active suspension system, produced by Quanser®, is performed.<br>Mestre

"Maintaining an efficient and reliable infrastructure requires continuous monitoring and control. In order to accomplish these tasks, algorithms are needed to process large sets of data and for modeling based on these processed data sets. For this reason, computationally efficient and accurate modeling algorithms along with data compression techniques and optimal yet practical control methods are in demand. These tools can help model structures and improve their performance. In this thesis, these two aspects are addressed separately. A principal component analysis based adaptive neuro-fuzzy inference system is proposed for fast and accurate modeling of time-dependent behavior of a structure integrated with a smart damper. Since a smart damper can only dissipate energy from structures, a challenge is to evaluate the dissipativity of optimal control methods for smart dampers to decide if the optimal controller can be realized using the smart damper. Therefore, a generalized deterministic definition for dissipativity is proposed and a commonly used controller, LQR is proved to be dissipative. Examples are provided to illustrate the effectiveness of the proposed modeling algorithm and evaluating the dissipativity of LQR control method. These examples illustrate the effectiveness of the proposed modeling algorithm and dissipativity of LQR controller."

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-08-14T18:28:45Z No. of bitstreams: 1 FabioSilva.pdf: 1098466 bytes, checksum: a72dcced91748fe6c54f3cab86c19849 (MD5)<br>Made available in DSpace on 2017-08-14T18:28:45Z (GMT). No. of bitstreams: 1 FabioSilva.pdf: 1098466 bytes, checksum: a72dcced91748fe6c54f3cab86c19849 (MD5) Previous issue date: 2008-06-20<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ)<br>Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA)<br>We present in this work the results about two neural networks methods to solve the algebraic Riccati(ARE), what are used in many applications, mainly in the Linear Quadratic Regulator (LQR), H2 and H1 controls. First is showed the real symmetric form of the ARE and two methods based on neural computation. One feedforward neural network (FNN), that de¯nes an error as function of the ARE and a recurrent neural network (RNN), which converts a constrain optimization problem, restricted to the state space model, into an unconstrained convex optimization problem de¯ning an energy as function of the ARE and Cholesky factor. A proposal to chose the learning parameters of the RNN used to solve the ARE, by making a surface of the parameters variations, thus we can tune the neural network for a better performance. Computational experiments related with the plant matrices perturbations of the tested systems in order to perform an analysis of the behavior of the presented methodologies, that are based on homotopies methods, where we chose a good initial condition and compare the results to the Schur method. Two 6th order systems were used, a Doubly Fed Induction Generator(DFIG) and an aircraft plant. The results showed the RNN a good alternative compared with the FNN and Schur methods.<br>Apresenta-se nesta dissertação os resultados a respeito de dois métodos neuronais para a resolução da equação algébrica de Riccati(EAR), que tem varias aplicações, sendo principalmente usada pelos Regulador Linear Quadrático(LQR), controle H2 e controle H1. É apresentado a EAR real e simétrica e dois métodos baseados em uma rede neuronal direta (RND) que tem a função de erro associada a EAR e uma rede neuronal recorrente (RNR) que converte um problema de otimização restrita ao modelo de espaço de estados em outro de otimização convexa em função da EAR e do fator de Cholesky de modo a usufruir das propriedades de convexidade e condições de otimalidade. Uma proposta para a escolha dos parâmetros da RNR usada para solucionar a EAR por meio da geração de superfícies com a variação paramétrica da RNR, podendo assim melhor sintonizar a rede neuronal para um melhor desempenho. Experimentos computacionais relacionados a perturbações nos sistemas foram realizados para analisar o comportamento das metodologias apresentadas, tendo como base o princípio dos métodos homotópicos, com uma boa condição inicial, a partir de uma ponto de operação estável e comparamos os resultados com o método de Schur. Foram usadas as plantas de dois sistemas: uma representando a dinâmica de uma aeronave e outra de um motor de indução eólico duplamente alimentado(DFIG), ambos sistemas de 6a ordem. Os resultados mostram que a RNR é uma boa alternativa se comparado com a RND e com o método de Schur.

Made available in DSpace on 2016-08-17T14:53:01Z (GMT). No. of bitstreams: 1 Fabio Nogueira da Silva.pdf: 1098466 bytes, checksum: a72dcced91748fe6c54f3cab86c19849 (MD5) Previous issue date: 2008-06-20<br>FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO<br>We present in this work the results about two neural networks methods to solve the algebraic Riccati(ARE), what are used in many applications, mainly in the Linear Quadratic Regulator (LQR), H2 and H1 controls. First is showed the real symmetric form of the ARE and two methods based on neural computation. One feedforward neural network (FNN), that de¯nes an error as function of the ARE and a recurrent neural network (RNN), which converts a constrain optimization problem, restricted to the state space model, into an unconstrained convex optimization problem de¯ning an energy as function of the ARE and Cholesky factor. A proposal to chose the learning parameters of the RNN used to solve the ARE, by making a surface of the parameters variations, thus we can tune the neural network for a better performance. Computational experiments related with the plant matrices perturbations of the tested systems in order to perform an analysis of the behavior of the presented methodologies, that are based on homotopies methods, where we chose a good initial condition and compare the results to the Schur method. Two 6th order systems were used, a Doubly Fed Induction Generator(DFIG) and an aircraft plant. The results showed the RNN a good alternative compared with the FNN and Schur methods.<br>Apresenta-se nesta dissertação os resultados a respeito de dois métodos neuronais para a resolução da equação algébrica de Riccati(EAR), que tem varias aplicações, sendo principalmente usada pelos Regulador Linear Quadrático(LQR), controle H2 e controle H1. É apresentado a EAR real e simétrica e dois métodos baseados em uma rede neuronal direta (RND) que tem a função de erro associada a EAR e uma rede neuronal recorrente (RNR) que converte um problema de otimização restrita ao modelo de espaço de estados em outro de otimização convexa em função da EAR e do fator de Cholesky de modo a usufruir das propriedades de convexidade e condições de otimalidade. Uma proposta para a escolha dos parâmetros da RNR usada para solucionar a EAR por meio da geração de superfícies com a variação paramétrica da RNR, podendo assim melhor sintonizar a rede neuronal para um melhor desempenho. Experimentos computacionais relacionados a perturbações nos sistemas foram realizados para analisar o comportamento das metodologias apresentadas, tendo como base o princípio dos métodos homotópicos, com uma boa condição inicial, a partir de uma ponto de operação estável e comparamos os resultados com o método de Schur. Foram usadas as plantas de dois sistemas: uma representando a dinâmica de uma aeronave e outra de um motor de indução eólico duplamente alimentado(DFIG), ambos sistemas de 6a ordem. Os resultados mostram que a RNR é uma boa alternativa se comparado com a RND e com o método de Schur.

Made available in DSpace on 2016-08-17T14:52:59Z (GMT). No. of bitstreams: 1 Joaquim Gomes Brito Filho.pdf: 577773 bytes, checksum: 0d9ad903ecdf123ced443b5b094e37aa (MD5) Previous issue date: 2006-05-31<br>In this work is presented a method to solve the Eigenstructure Allocation pro- blem for multivariable dynamic systems by means of Robust Controllers Design Linear Quadratic Gaussian, LQG/LTR Loop transfer Recovery and Hierarchical Genetic Algorithm in three levels. It shows an uni¯ed method for controllers ro- bust design that are one systematical of the three stages of LQG/LTR methodo- logy. The evolutionary computation is used in the primary level that is the gain controller optimal determination to guarantee the terms of robust stability. The intermediary level, consists in the utilization of a AG to determine the Kalman state observer gain. The last level of this hierarchy consists of recovery the ro- bustness properties of the LQR design which were lost due to inclusion of the LQG loop by means of a GA. The method is veri¯ed in a dynamic system which represents an aircraft in cruzeiro speed, a LQG/LQR-hierarchic design perfor- mance analysis in the frequency domain and of time show the commitments that should be taken over in applications of the real world systems.<br>Apresenta-se um método para resolver o problema de Alocação de Auto-estrutura para sistemas dinâmicos multivariáveis por meio do Projeto de Controladores Ro- busto Gaussiano Linear Quadrático, Recuperação da Malha de Transferência e Algoritmo Genético Hierárquico em três níveis. Mostra-se um método unificado para o projeto de controladores robustos que são uma sistematização das três etapas da metodologia LQG/LTR. A computação evolutiva é utilizada no nível primário que é a determinação dos ganhos do controlador ótimo para garantir as condições de estabilidade robusta. O nível intermediário, consiste na utilização de um AG para determinar os ganhos de Kalman do observador de estado. O último nível desta hierarquia consiste da recuperação das propriedades de ro- bustez do projeto LQR que foram perdidas devido a inclusão da malha LQG por meio de um AG. O método é verficado em um sistema dinâmico que re- presenta uma aeronave em velocidade cruzeiro, uma análise de desempenho do projeto LQG/LQR-hierárquico no domínio da frequência e do tempo mostram os compromissos que devem ser assumidos em aplicações de sistemas do mundo real.

Unmanned aerial systems have been widely used for variety of civilian applications over the past few years. Some of these applications require accurate guidance and control. Consequently, Unmanned Aerial Vehicle (UAV) guidance and control attracted many researchers in both control theory and aerospace engineering. Flying wings, as a particular type of UAV, are considered to have one of the most efficient aerodynamic structures. It is however difficult to design robust controller for such systems. This is due to the fact that flying wings are highly sensitive to control inputs. The focus of this thesis is on modeling and control design for a UAV system. The platform understudy is a flying wing developed by SmartPlanes Co. located in Skellefteå, Sweden. This UAV is particularly used for topological mapping and aerial photography. The novel approach suggested in this thesis is to use two controllers in sequence. More precisely, Linear Quadratic Regulator (LQR) is suggested to provide robust stability, and Proportional, Integral, Derivative (PID) controller is suggested to provide reference signal regulation. The idea behind this approach is that with LQR in the loop, the system becomes more stable and less sensitive to control signals. Thus, PID controller has an easier task to do, and is only used to provide the required transient response. The closed-loop system containing the developed controller and a UAV non-linear dynamic model was simulated in Simulink. Simulated controller was then tested for stability and robustness with respect to some parametric uncertainty. Obtained results revealed that the LQR successfully managed to provide robust stability, and PID provided reference signal regulation.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-08-22T13:19:28Z No. of bitstreams: 1 Patricia Moraes Rêgo.pdf: 1511056 bytes, checksum: 21108136b08107eeb212f5d74ed79ef7 (MD5)<br>Made available in DSpace on 2017-08-22T13:19:28Z (GMT). No. of bitstreams: 1 Patricia Moraes Rêgo.pdf: 1511056 bytes, checksum: 21108136b08107eeb212f5d74ed79ef7 (MD5) Previous issue date: 2007-08-03<br>FAPEMA<br>In this work are proposed models and a convergence analysis of a hierarchical genetic algorithm for the linear quadratic regulator design loop recovery through LQG/LTR controllers. Models are oriented to the weighting and covariance matrices searching of the performance indices of the LQR and LQG design, respectively, and to the selection of the matrices for the LQR design loop recovery gain. The convergence analysis aims at promoting the enhancement of the algorithm performance, as well as to generate satisfactory solutions and speed up the convergence time. The algorithm performance is evaluated with respect to the e ects of an elitist strategy embodied into the algorithm and to variations in the values of some given parameters of the algorithm. The proposed methodology is evaluated in a multi-variable dynamical system representing an aircraft.<br>Propõe-se neste trabalho os modelos e a análise de convergência de um algoritmo genético hierárquico para recuperação da malha de projeto do regulador linear quadrático por controladores LQG/LTR (Linear Quadratic Gaussian/Loop Transfer Recovery). Os modelos dedicam-se à busca das matrizes de ponderações e covariâncias dos índices de desempenho dos projetos de controladores LQR (Linear Quadratic Regulator) e LQG (Linear Quadratic Gaussian), respectivamente, e à seleção de matrizes de ajuste para o ganho de recuperação da malha do projeto LQR. O objetivo da análise de convergência é promover melhorias no desempenho do algoritmo no sentido de gerar soluções satisfatórias e acelerar o tempo de convergência. O desempenho do algoritmo é avaliado em relação aos efeitos de uma estratégia elitista incorporada ao algoritmo e à variações nos valores de determinados parâmetros do algoritmo. A metodologia proposta é avaliada em um sistema dinâmico multivariável que representa uma aeronave.

Two controller performances are assessed for generalization in the path following task of autonomously backing up a tractor-trailer. Starting from random locations and orientations, paths are generated to loading docks with arbitrary pose using Dubins Curves. The combination vehicles can be varied in wheelbase, hitch length, weight distributions, and tire cornering stiffness. The closed form calculation of the gains for the Linear Quadratic Regulator (LQR) rely heavily on having an accurate model of the plant. However, real-world applications cannot expect to have an updated model for each new trailer. Finding alternative robust controllers when the trailer model is changed was the motivation of this research. Reinforcement learning, with neural networks as their function approximators, can allow for generalized control from its learned experience that is characterized by a scalar reward value. The Linear Quadratic Regulator and the Deep Deterministic Policy Gradient (DDPG) are compared for robust control when the trailer is changed. This investigation quantifies the capabilities and limitations of both controllers in simulation using a kinematic model. The controllers are evaluated for generalization by altering the kinematic model trailer wheelbase, hitch length, and velocity from the nominal case. In order to close the gap from simulation and reality, the control methods are also assessed with sensor noise and various controller frequencies. The root mean squared and maximum errors from the path are used as metrics, including the number of times the controllers cause the vehicle to jackknife or reach the goal. Considering the runs where the LQR did not cause the trailer to jackknife, the LQR tended to have slightly better precision. DDPG, however, controlled the trailer successfully on the paths where the LQR jackknifed. Reinforcement learning was found to sacrifice a short term reward, such as precision, to maximize the future expected reward like reaching the loading dock. The reinforcement learning agent learned a policy that imposed nonlinear constraints such that it never jackknifed, even when it wasn't the trailer it trained on.

Though multirotor unmanned aerial vehicles (UAVs) have become widely used during the past decade, challenges in autonomy have prevented their widespread use when moving vehicles act as their base stations. Emerging use cases, including maritime surveillance, package delivery and convoy support, require UAVs to autonomously operate in this scenario. This thesis presents improved solutions to both the state estimation and control problems that must be solved to enable robust, autonomous landing of multirotor UAVs onto moving vehicles.Current state-of-the-art UAV landing systems depend on the detection of visual fiducial markers placed on the landing target vehicle. However, in challenging conditions, such as poor lighting, occlusion, or extreme motion, these fiducial markers may be undected for significant periods of time. This thesis demonstrates a state estimation algorithm that tracks and estimates the locations of unknown visual features on the target vehicle. Experimental results show that this method significantly improves the estimation of the state of the target vehicle while the fiducial marker is not detected.This thesis also describes an improved control scheme that enables a multirotor UAV to accurately track a time-dependent trajectory. Rooted in Lie theory, this controller computes the optimal control signal based on an error-state formulation of the UAV dynamics. Simulation and hardware experiments of this control scheme show its accuracy and computational efficiency, making it a viable solution for use in a robust landing system.

In this thesis, application of linear control methods to control the attitude of a Low-Earth Orbit satellite is studied. Attitude control subsystem is first introduced by explaining attitude determination and control components in detail. Satellite dynamic equations are derived and linearized for controller design. Linear controller and linear quadratic regulator are chosen as controllers for attitude control. The actuators used for control are reaction wheels and magnetic torquers. MATLAB-SIMULINK program is used in order to simulate satellite dynamical model (actual nonlinear model) and controller model. In simulations, the satellite parameters are selected to be similar to the actual BILSAT-1 satellite parameters. In conclusion, simulations obtained from different linear control methods are compared within themselves and with nonlinear control methods, at the same time with that obtained from BILSAT-1 satellite log data.

La presente tesis estudia, propone y realiza sus principales aportaciones en el campo del control para el convertidor CC/CA de tres niveles, sobre la topología denominada Neutral-Point-Clamped, aunque se puede extender a otras topologías y/o número de niveles. Se presenta una metodología de modelado que emplea funciones de conmutación de fase, el operador de promediado y la transformación D-Q, tal que los modelos obtenidos en el dominio D-Q contienen una información completa sobre la dinámica del sistema. La estrategia de conmutación se puede entender como una extensión de la estrategia PWM senoidal de dos a tres niveles. Esta estrategia es simple y no realiza el control de ninguna de las variables del sistema. En esta tesis, el controlador se encarga de regular todas las variables del sistema, incluido el equilibrio del bus de continua. Este es un enfoque diferente del convencional, donde el equilibrio del bus de continua se consigue mediante la elección adecuada de los estados redundantes del convertidor en la estrategia de conmutación, mientras que el resto de variables se regulan a través del controlador. Para la realización del controlador, se propone la técnica de control lineal multivariable LQR (Linear Quadratic Regulator), complementada con la técnica de control no lineal adaptativo denominada programación de ganancia (Gain Scheduling). Se presenta, además, una metodología de cálculo del controlador. Este control es versátil, abierto y adaptable. En cualquier caso, el controlador se puede adaptar a las necesidades concretas de cada aplicación. El cálculo del controlador se realiza mediante simulación con MatLab-Simulink. Los modelos matemáticos que emplean las funciones de conmutación del convertidor son aquellos que ofrecen un mejor compromiso entre velocidad de simulación y precisión. Para validar el control propuesto, se ha diseñado y construido un equipo experimental donde el controlador se ha mostrado aplicable, útil y eficaz en la regulación de las distintas cargas y aplicaciones experimentadas, incluso con carga no lineal, bajo diferentes condiciones de trabajo y variables a controlar, tanto en régimen permanente como en procesos transitorios. La rapidez y calidad de la respuesta transitoria es comparable a la de otros sistemas de control publicados. Es especialmente interesante el excelente control conseguido del equilibrio del bus de continua. Además, la robustez del control permite cancelar el error estacionario aunque diferentes parámetros del sistema presenten desviaciones significativas respecto los valores esperados. El uso de la programación de ganancia junto con la técnica LQR se ha mostrado muy efectivo, puesto que permite realizar diferentes tipos de control. Se ha comprobado la congruencia entre simulaciones y resultados experimentales obtenidos, lo que valida los modelos de simulación empleados y el proceso de diseño del controlador mediante simulación.<br>This dissertation study, propose and carry out the main contributions in the field of three-level inverter control, using the topology Neutral-Point-Clamped, although results can be extended to other topologies and/or number of levels. A procedure for modelling is presented, based on line-switching functions, moving average operator and D-Q transformation. Then, the obtained models in D-Q frame contain complete information about system dynamics. Switching strategy is simple and can be considered as an extension of two-level sinusoidal PWM to three level. The system variables are not controlled by the switching strategy. In this work, all the system variables are controlled by the regulator, including DC-link balance. This control approach is different than the conventional one, where DC-link balance is achieved by means of a proper selection of redundant states in the switching strategy, and the other variables are controlled by the regulator. The regulator is based on the multivariable linear control technique LQR (Linear Quadratic Regulator), in combination with the non-linear adaptive control technique Gain Scheduling. Moreover, a methodology for the calculation of the controller is presented. This controller is versatile, open and adaptable. However, the controller can be built depending on the concrete specifications of each application. The controller is calculated by means of simulation using MatLab-Simulink. The mathematical models based on the switching functions of the converter give the best trade-off between simulation speed and precision. In order to validate the proposed controller, an experimental prototype has been designed and implemented. Experimental results show that the controller is useful and effective for the regulation of different loads and applications, even with non-linear loads, different operation points and variables to control, in steady-state and transitory operation. Dynamic response speed and quality are similar to other control systems in the literature. The DC-link balance control achieved is specially interesting. Furthermore, steady-state error is cancelled due to the robustness of the controller, even though significant deviation of different system parameters are present. The use of Gain-Scheduling in combination with LQR is effective, allowing the calculation of regulators with different control strategies. Good agreement between simulations and experimental results has been found. This result validates simulation models and the design method for the controller, based on simulations.

La presente tesis estudia, propone y realiza sus principales aportaciones en el campo del control para el convertidor CC/CA de tres niveles, sobre la topología denominada Neutral-Point-Clamped, aunque se puede extender a otras topologías y/o número de niveles. Se presenta una metodología de modelado que emplea funciones de conmutación de fase, el operador de promediado y la transformación D-Q, tal que los modelos obtenidos en el dominio D-Q contienen una información completa sobre la dinámica del sistema. La estrategia de conmutación se puede entender como una extensión de la estrategia PWM senoidal de dos a tres niveles. Esta estrategia es simple y no realiza el control de ninguna de las variables del sistema. En esta tesis, el controlador se encarga de regular todas las variables del sistema, incluido el equilibrio del bus de continua. Este es un enfoque diferente del convencional, donde el equilibrio del bus de continua se consigue mediante la elección adecuada de los estados redundantes del convertidor en la estrategia de conmutación, mientras que el resto de variables se regulan a través del controlador. Para la realización del controlador, se propone la técnica de control lineal multivariable LQR (Linear Quadratic Regulator), complementada con la técnica de control no lineal adaptativo denominada programación de ganancia (Gain Scheduling). Se presenta, además, una metodología de cálculo del controlador. Este control es versátil, abierto y adaptable. En cualquier caso, el controlador se puede adaptar a las necesidades concretas de cada aplicación. El cálculo del controlador se realiza mediante simulación con MatLab-Simulink. Los modelos matemáticos que emplean las funciones de conmutación del convertidor son aquellos que ofrecen un mejor compromiso entre velocidad de simulación y precisión. Para validar el control propuesto, se ha diseñado y construido un equipo experimental donde el controlador se ha mostrado aplicable, útil y eficaz en la regulación de las distintas cargas y aplicaciones experimentadas, incluso con carga no lineal, bajo diferentes condiciones de trabajo y variables a controlar, tanto en régimen permanente como en procesos transitorios. La rapidez y calidad de la respuesta transitoria es comparable a la de otros sistemas de control publicados. Es especialmente interesante el excelente control conseguido del equilibrio del bus de continua. Además, la robustez del control permite cancelar el error estacionario aunque diferentes parámetros del sistema presenten desviaciones significativas respecto los valores esperados. El uso de la programación de ganancia junto con la técnica LQR se ha mostrado muy efectivo, puesto que permite realizar diferentes tipos de control. Se ha comprobado la congruencia entre simulaciones y resultados experimentales obtenidos, lo que valida los modelos de simulación empleados y el proceso de diseño del controlador mediante simulación.<br>This dissertation study, propose and carry out the main contributions in the field of three-level inverter control, using the topology Neutral-Point-Clamped, although results can be extended to other topologies and/or number of levels. A procedure for modelling is presented, based on line-switching functions, moving average operator and D-Q transformation. Then, the obtained models in D-Q frame contain complete information about system dynamics. Switching strategy is simple and can be considered as an extension of two-level sinusoidal PWM to three level. The system variables are not controlled by the switching strategy. In this work, all the system variables are controlled by the regulator, including DC-link balance. This control approach is different than the conventional one, where DC-link balance is achieved by means of a proper selection of redundant states in the switching strategy, and the other variables are controlled by the regulator. The regulator is based on the multivariable linear control technique LQR (Linear Quadratic Regulator), in combination with the non-linear adaptive control technique Gain Scheduling. Moreover, a methodology for the calculation of the controller is presented. This controller is versatile, open and adaptable. However, the controller can be built depending on the concrete specifications of each application. The controller is calculated by means of simulation using MatLab-Simulink. The mathematical models based on the switching functions of the converter give the best trade-off between simulation speed and precision. In order to validate the proposed controller, an experimental prototype has been designed and implemented. Experimental results show that the controller is useful and effective for the regulation of different loads and applications, even with non-linear loads, different operation points and variables to control, in steady-state and transitory operation. Dynamic response speed and quality are similar to other control systems in the literature. The DC-link balance control achieved is specially interesting. Furthermore, steady-state error is cancelled due to the robustness of the controller, even though significant deviation of different system parameters are present. The use of Gain-Scheduling in combination with LQR is effective, allowing the calculation of regulators with different control strategies. Good agreement between simulations and experimental results has been found. This result validates simulation models and the design method for the controller, based on simulations.

Micro aerial vehicles and other autonomous systems have the potential to truly transform life as we know it, however much of the potential of autonomous systems remains unrealized because reliable navigation is still an unsolved problem with significant challenges. This dissertation presents solutions to many aspects of autonomous navigation. First, it presents ROSflight, a software and hardware architure that allows for rapid prototyping and experimentation of autonomy algorithms on MAVs with lightweight, efficient flight control. Next, this dissertation presents improvments to the state-of-the-art in optimal control of quadrotors by utilizing the error-state formulation frequently utilized in state estimation. It is shown that performing optimal control directly over the error-state results in a vastly more computationally efficient system than competing methods while also dealing with the non-vector rotation components of the state in a principled way. In addition, real-time robust flight planning is considered with a method to navigate cluttered, potentially unknown scenarios with real-time obstacle avoidance. Robust state estimation is a critical component to reliable operation, and this dissertation focuses on improving the robustness of visual-inertial state estimation in a filtering framework by extending the state-of-the-art to include better modeling and sensor fusion. Further, this dissertation takes concepts from the visual-inertial estimation community and applies it to tightly-coupled GNSS, visual-inertial state estimation. This method is shown to demonstrate significantly more reliable state estimation than visual-inertial or GNSS-inertial state estimation alone in a hardware experiment through a GNSS-GNSS denied transition flying under a building and back out into open sky. Finally, this dissertation explores a novel method to combine measurements from multiple agents into a coherent map. Traditional approaches to this problem attempt to solve for the position of multiple agents at specific times in their trajectories. This dissertation instead attempts to solve this problem in a relative context, resulting in a much more robust approach that is able to handle much greater intial error than traditional approaches.

The following is a study of an attitude control system (ACS) for a low earth orbit nanosatellite. Control actuation is applied using three reaction wheels and three mutually orthogonal current-driven magnetorquers which produce torques by interacting with the earth’s magnetic field. Control torques are distributed amongst the actuators allowing them to work together in concert. This type of control is referred to as hybrid magnetic attitude control. To account for the nearly periodic behavior of the earth’s magnetic field, control torques are assigned using periodic and optimal control theory. The primary focus is to apply the time-varying Linear Quadratic Regulator controller to test the stability and energy consumption of the ACS when reaction wheels are removed from the control law, or are simulated to be missing. Other situations studied include the effects of control saturation, introducing uncertainty in the orbital inclination, and observing performance as the number of magnetic coils is increased.

The popularity of distributed generating (DG) sources have been increasing over the past few years. With the increasing penetration of these DGs, the concept of micro grid is becoming popular. A micro grid is a small power system network with distributed generating sources which can operate seamlessly irrespective of the presence of the utility grid. Operating the micro grid in this manner increases system reliability and reduces power interruptions. However, it introduces several control challenges. This thesis aims at analysing the behaviour of a micro grid system during the transition between grid connected mode and islanded mode of operation and address the control challenges through novel schemes. With the presence of grid, the micro grid system variables, such as voltage and frequency, are strictly regulated by the grid. The local sources follow the voltage and frequency reference set by the grid and supply constant power. With the loss of grid, that is when the system is islanded, the network variables need to be regulated by the local sources. The control structures for the inverter-based sources during the two operating modes are detailed in the present work. With the loss of grid, the system should be able to transfer seamlessly to islanded mode without any transients. Similarly, when the grid supply is restored, the micro grid should seamlessly resynchronize to the grid without any transients. This thesis proposes two novel controller schemes for achieving seamless transfer between grid-connected and islanded mode in micro grids. The rst scheme uses an output feedback topology to reduce the transitions during mode transfer. The second scheme uses a Linear Quadratic Regulator (LQR) theory based compensator to achieve seamless transfer. The performance of the proposed schemes have been validated through simulations on a benchmark micro grid network for various operating conditions. An experimental micro grid set-up is developed with a single inverter based DG source. The droop control scheme for islanded mode of operation has been validated on hardware.

The popularity of distributed generating (DG) sources have been increasing over the past few years. With the increasing penetration of these DGs, the concept of micro grid is becoming popular. A micro grid is a small power system network with distributed generating sources which can operate seamlessly irrespective of the presence of the utility grid. Operating the micro grid in this manner increases system reliability and reduces power interruptions. However, it introduces several control challenges. This thesis aims at analysing the behaviour of a micro grid system during the transition between grid connected mode and islanded mode of operation and address the control challenges through novel schemes. With the presence of grid, the micro grid system variables, such as voltage and frequency, are strictly regulated by the grid. The local sources follow the voltage and frequency reference set by the grid and supply constant power. With the loss of grid, that is when the system is islanded, the network variables need to be regulated by the local sources. The control structures for the inverter-based sources during the two operating modes are detailed in the present work. With the loss of grid, the system should be able to transfer seamlessly to islanded mode without any transients. Similarly, when the grid supply is restored, the micro grid should seamlessly resynchronize to the grid without any transients. This thesis proposes two novel controller schemes for achieving seamless transfer between grid-connected and islanded mode in micro grids. The rst scheme uses an output feedback topology to reduce the transitions during mode transfer. The second scheme uses a Linear Quadratic Regulator (LQR) theory based compensator to achieve seamless transfer. The performance of the proposed schemes have been validated through simulations on a benchmark micro grid network for various operating conditions. An experimental micro grid set-up is developed with a single inverter based DG source. The droop control scheme for islanded mode of operation has been validated on hardware.

碩士<br>國立彰化師範大學<br>電機工程學系<br>104<br>Inverted Pendulum System is an extremely unstable system. It’s an important research topic to stabilize upside down control for balancing the inverted pendulum system This thesis studies the system model of an inverted pendulum cart and investigates the design method using linear quadratic regulator (LQR). A Matlab-based LQR controller is designed to simulate system responses and conduct the relationships between the inverted pendulum cart system parameters and the LQR controller gains. In this thesis, the DC servo motors are used to drive the wheels of inverted pendulum, and an embedded system is used for implementation the controller. The tilt sensor in the pendulum cart frame is used to measure the inclination angle of the pendulum cart. The tilt sensor output is read by the embedded controller through an A/D converter. The DC servo motor encoders are used to measuring the inverted pendulum cart position that are read by the embedded controller using the Digital Inputs (DI). The inclination angle and the position of the inverted pendulum cart are the input the LQR controller, control command output to the DC servo motor through the D/A converter to maintain the cart in its inverted state. The simulation results show that the inverted pendulum cart can be controlled by the proposed LQR controller to reach a balancing upright state.