A quadrotor is a type of small unmanned aerial vehicle (UAV) with four rotors. Various control techniques have been successfully applied to the quadrotor. In this thesis, two control methods, including linear quadratic regulator (LQR) and H2-optimal control, are applied to the autonomous navigation and control of a quadorotor named QBall-X4 that is developed by Quanser. The continuous-time dynamic model is established using the Euler-Lagrange approach. Due to the nonlinearities in the quadrotor dynamics, we propose a simplified linear model, which is further used for the controller design in this thesis. According to the simplified quadrotor dynamics, we design an LQR controller to regulate the quadrotor system from its initial position to the desired position. The effectiveness of the controller is verified by simulation studies. However, the LQR control system is operated in the nominal model, and it can not present guaranteed performance when system uncertainties exist. The main emphasis is placed on designing an H2-optimal controller that minimizes the H2-norm of the transfer function. The solution is obtained by using the state-space approach and linear matrix inequality (LMI) method, respectively. In contrast to LQR control method, which is normally applied to a system with no disturbance, the H2-optimal controller takes the form of an observer together with a state feedback control gain to deal with the system uncertainties and disturbances. The simulation results and experimental study verify that the proposed H2-optimal controller is an effective option for the quadrotor with the attendance of uncertainties and disturbances. / Graduate

Unmanned Aerial Vehicles (UAVs) are remotely piloted or self-piloted aircrafts that can carry cameras, sensors, communications equipment or other payloads. Tiltrotor UAVs provide a unique platform that fulfills the needs for ever-changing mission requirements by combining the desired features / hovering like a helicopter and reaching high forward speeds like an airplane. In this work, the conceptual design and aerodynamical model of a realizable small-sized Tiltrotor UAV is constructed, the linearized state-space models are obtained around the trim points for airplane, helicopter and conversion modes, controllers are designed using Linear Quadratic Regulator (LQR) methods and gain-scheduling is employed to obtain a simulation for the whole flight envelope. The ideas for making a real flying model are established according to simulation results.

In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them. / Neste trabalho, é apresentado um sistema de um monociclo com roda de reação, mostrando desde a construção, passando pela modelagem até o projeto e teste dos controladores. Primeiramente, é feito o projeto mecânico por meio de um desenho assistido por computador tridimensional (3D CAD), para auxiliar a construção e, em seguida, a modelagem por meio do método de Lagrange. Naturalmente, o sistema é não linear e os ângulos de arfagem e rolamento são acoplados. Neste trabalho, controladores lineares são projetados e, portanto, a linearização do sistema é feita pelo Jacobiano, ou seja, assumindo pequenas variações em torno do ponto de equilíbrio. Nesta situação, o modelo desacopla os ângulos de arfagem e rolamento. O protótipo é construído fixando os componentes eletrônicos, a bateria, as rodas e os motores a um corpo, de forma a ser totalmente autônomo. O posicionamento das peças precisa ser equilibrado, de forma a manter a posição do centro de massa ao longo dos eixos de simetria vertical e horizontal. Em seguida, é feito um projeto de controle linear para estabilização da planta usando duas técnicas que são validadas via simulações do sistema não linear acoplado. Depois, as técnicas são testadas no protótipo construído. A primeira consiste do controle ótimo LQR que, apesar de ter funcionado, apresentou alguns problemas devidos a incertezas paramétricas. Logo, é usado o controle H2 via LMI, de tal forma que o projeto equivalha ao LQR, mas desta forma é possível inserir incertezas paramétricas e achar um controlador com algum grau de robustez a elas.

During the uniform locomotion of legged robots with compliant legs, the body of the robot exhibits quasi-periodic oscillations that have a disturbing eect on dierent onboard sensors. Of particular interest is the camera sensor which suers from image degradation in the form of motion-blur as a result of this camera motion. The eect of angular disturbances on the camera are pronounced due to the perspective projection property of the camera. The thesis focuses on the particular problem of legged robots exhibiting angular body motions and attempts to analyze and overcome the resulting disturbances on a camera carrying platform (head). Although the full problem is in 3D with three independent axes of rotation, a planar analysis provides signicant insight into the problem and is the approach taken in the thesis. A carefully modeled planar version of an actual camera platform with realistic mechanical and actuator selections is presented. Passive (ltering) and active (controller) approaches are discussed to compensate/cancel motion generated disturbances. We consider and comparatively evaluate PID and LQR based active control. Since PID has the limitation of controlling only one output, PID-PID control is considered to iv control two states of the model. Due to its state-space formulation and the capability of controlling an arbitrary number of states, LQR is considered. In addition to standard reference signals, Gyroscope measured disturbance signals are collected from the actual robot platform to analyze the bandwidth and test the performance of the controllers. Inverted pendulum control performance is evaluated both on a Matlab-Simulink as well as a precise electro-mechanical test setup. Since construction of the planar head test setup is in progress, tests are conducted on simulation.

Extremely large telescopes (ELTs) are the next generation of ground-based reflecting telescopes of optical wavelengths. ELTs possess an aperture of more than 20 meters and share a number of common features, particularly the use of a segmented primary mirror and the use of adaptive optics systems. In 2005, the European Southern Observatory introduced a new giant telescope concept, named the European Extremely Large Telescope (E-ELT), which is scheduled for operation in 2018. The E-ELT will address key scientific challenges and will aim for a number of notable firsts, including discovering Earth-like planets around other stars in the ``habitable zones'' where life could exist, attempting to uncover the relationship between black holes and galaxies, measuring the properties of the first stars and galaxies, and probing the nature of dark matter and dark energy. In 2009, a feasibility study, conducted by National Instruments, proved the feasibility of the real-time (RT) control system architecture for the E-ELT's nearly 1,000 mirror segments with 3,000 actuators and 6,000 sensors. The goal of the RT control system was to maintain a perfectly aligned field of mirrors at all times with a loop-time of 1 ms. The study assumed a prescribed controller algorithm. This research report prescribes the optimal controller algorithms for large segmented telescopes. In this respect, optimal controller designs for the primary mirror of the E-ELT, where optimality is formulated in the [H-2] and [H-infinity] frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance metrics are met. / text

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos. / This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos. / This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them. / Neste trabalho, é apresentado um sistema de um monociclo com roda de reação, mostrando desde a construção, passando pela modelagem até o projeto e teste dos controladores. Primeiramente, é feito o projeto mecânico por meio de um desenho assistido por computador tridimensional (3D CAD), para auxiliar a construção e, em seguida, a modelagem por meio do método de Lagrange. Naturalmente, o sistema é não linear e os ângulos de arfagem e rolamento são acoplados. Neste trabalho, controladores lineares são projetados e, portanto, a linearização do sistema é feita pelo Jacobiano, ou seja, assumindo pequenas variações em torno do ponto de equilíbrio. Nesta situação, o modelo desacopla os ângulos de arfagem e rolamento. O protótipo é construído fixando os componentes eletrônicos, a bateria, as rodas e os motores a um corpo, de forma a ser totalmente autônomo. O posicionamento das peças precisa ser equilibrado, de forma a manter a posição do centro de massa ao longo dos eixos de simetria vertical e horizontal. Em seguida, é feito um projeto de controle linear para estabilização da planta usando duas técnicas que são validadas via simulações do sistema não linear acoplado. Depois, as técnicas são testadas no protótipo construído. A primeira consiste do controle ótimo LQR que, apesar de ter funcionado, apresentou alguns problemas devidos a incertezas paramétricas. Logo, é usado o controle H2 via LMI, de tal forma que o projeto equivalha ao LQR, mas desta forma é possível inserir incertezas paramétricas e achar um controlador com algum grau de robustez a elas.

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos. / This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17883号 / 工博第3792号 / 新制||工||1580(附属図書館) / 30703 / 京都大学大学院工学研究科建築学専攻 / (主査)教授 中島 正愛, 教授 川瀬 博, 教授 竹脇 出 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM