In this thesis we investigate the problem of designing a control system for a modern bicycle so that the bicycle is stable and follows a path. We propose a multi-loop control architecture, where each loop is systematically designed using linear control techniques. The proposed strategy guarantees that the bicycle asymptotically converges to paths of constant curvature. A key advantage of our approach is that by using linear techniques analysis and controller design are relatively simple. We base our control design on the nonlinear (corrected) Whipple model, which has been previously verified for correctness and experimentally validated. The equations of motion for the nonlinear model are very complicated, and would take many pages to explicitly state. They also have no known closed form solution. To enable analysis of the model we linearize it about a trajectory such that the bicycle is upright and travelling straight ahead. This linearization allows us to arrive at a parameterized linear time-invariant state-space representation of the bicycle dynamics, suitable for analysis and control design. The inner-loop control consists of a forward-speed controller as well as a lean and steer controller. To keep the bicycle at a constant forward speed, we develop a high-bandwidth proportional controller that uses a torque along the axis of the rear wheel of the bicycle to keep the angular velocity of the rear wheel at a constant setpoint. To stabilize the bicycle at this forward speed, lean torque and steer torque are treated as the control signals. We design a state-feedback controller and augment integrators to the output feedback of the lean angle and steer angle to provide perfect steady-state tracking. To arrive at the gains for state feedback, linear-quadratic regulator methods are used. When following a constant-curvature path, a vehicle has a constant yaw rate. Using this knowledge, we begin designing the outer-loop path-following control by finding a map that converts a yaw rate into appropriate lean angle and steer angle references for the inner loop. After the map is completed, system identification is performed by applying a yaw-rate reference to the map and analyzing the response of the bicycle. Using the linear approximation obtained, a classical feedback controller for yaw-rate tracking is designed. In addition to yaw-rate control, to track a path the yaw angle of the bicycle must match that of the path and the bicycle must physically be on the path. To analyze these conditions a linear approximation for the distance between the bicycle to the path is found, enabling construction of a linear approximation of the entire system. We then find that by passing the signal for the difference in yaw rate and the distance through separate controllers, summing their output, and subtracting from the reference yaw rate of the path, the bicycle converges to the path. After developing the general design procedure, the final part of the thesis shows a step by step design example and demonstrates the results of applying the proposed control architecture to the nonlinear bicycle model. We highlight some problems that can arise when the bicycle is started far from the path. To overcome these problems we develop the concept of a virtual path, which is a path that when followed returns the bicycle to the actual path. We also recognize that, in practice, typical paths do not have constant curvature, so we construct more practical paths by joining straight line segments and circular arc segments, representing a practical path similar to a path that would be encountered when biking through a series of rural roads. Finally, we finish the design example by demonstrating the performance of the control architecture on such a path. From these simulations we show that using the suggested controller design that the bicycle will converge to a constant curvature path. Additionally with using the controllers we develop that in the absence of disturbance the bicycle will stay within the intended traffic lane when travelling on a typical rural road.

In this thesis we investigate the problem of designing a control system for a modern bicycle so that the bicycle is stable and follows a path. We propose a multi-loop control architecture, where each loop is systematically designed using linear control techniques. The proposed strategy guarantees that the bicycle asymptotically converges to paths of constant curvature. A key advantage of our approach is that by using linear techniques analysis and controller design are relatively simple. We base our control design on the nonlinear (corrected) Whipple model, which has been previously verified for correctness and experimentally validated. The equations of motion for the nonlinear model are very complicated, and would take many pages to explicitly state. They also have no known closed form solution. To enable analysis of the model we linearize it about a trajectory such that the bicycle is upright and travelling straight ahead. This linearization allows us to arrive at a parameterized linear time-invariant state-space representation of the bicycle dynamics, suitable for analysis and control design. The inner-loop control consists of a forward-speed controller as well as a lean and steer controller. To keep the bicycle at a constant forward speed, we develop a high-bandwidth proportional controller that uses a torque along the axis of the rear wheel of the bicycle to keep the angular velocity of the rear wheel at a constant setpoint. To stabilize the bicycle at this forward speed, lean torque and steer torque are treated as the control signals. We design a state-feedback controller and augment integrators to the output feedback of the lean angle and steer angle to provide perfect steady-state tracking. To arrive at the gains for state feedback, linear-quadratic regulator methods are used. When following a constant-curvature path, a vehicle has a constant yaw rate. Using this knowledge, we begin designing the outer-loop path-following control by finding a map that converts a yaw rate into appropriate lean angle and steer angle references for the inner loop. After the map is completed, system identification is performed by applying a yaw-rate reference to the map and analyzing the response of the bicycle. Using the linear approximation obtained, a classical feedback controller for yaw-rate tracking is designed. In addition to yaw-rate control, to track a path the yaw angle of the bicycle must match that of the path and the bicycle must physically be on the path. To analyze these conditions a linear approximation for the distance between the bicycle to the path is found, enabling construction of a linear approximation of the entire system. We then find that by passing the signal for the difference in yaw rate and the distance through separate controllers, summing their output, and subtracting from the reference yaw rate of the path, the bicycle converges to the path. After developing the general design procedure, the final part of the thesis shows a step by step design example and demonstrates the results of applying the proposed control architecture to the nonlinear bicycle model. We highlight some problems that can arise when the bicycle is started far from the path. To overcome these problems we develop the concept of a virtual path, which is a path that when followed returns the bicycle to the actual path. We also recognize that, in practice, typical paths do not have constant curvature, so we construct more practical paths by joining straight line segments and circular arc segments, representing a practical path similar to a path that would be encountered when biking through a series of rural roads. Finally, we finish the design example by demonstrating the performance of the control architecture on such a path. From these simulations we show that using the suggested controller design that the bicycle will converge to a constant curvature path. Additionally with using the controllers we develop that in the absence of disturbance the bicycle will stay within the intended traffic lane when travelling on a typical rural road.

Made available in DSpace on 2014-06-11T19:22:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-27Bitstream added on 2014-06-13T19:28:00Z : No. of bitstreams: 1 sampaio_lp_me_ilha.pdf: 1553174 bytes, checksum: 4a7ad1f1c4400135903509fd327b3112 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho propõe uma nova abordagem na metodologia de operação para o inversor Boost monofásico, como estrutura base para o aproveitamento de fontes alternativas e renováveis de energia elétrica. Considerando-se que equipamentos eletro/eletrônicos convencionais em CA (corrente alternada) necessitam, normalmente, de níveis e formato de tensão diferentes daqueles fornecidos por essas fontes de energia, o inversor proposto é uma estrutura integrada que tem a capacidade de operar como conversor elevador de tensão e inversor, apresentando um número reduzido de componentes e rendimento maior, quando comparado às formas tradicionais de se associar em cascata o conversor elevador com o inversor. O projeto convencional do inversor fonte de corrente (CSI) exige uma indutância elevada de entrada, além disso, o modelo a pequeno sinais do CSI é semelhante ao do conversor Boost no modo de condução contínua, apresentando um zero no semi-plano direito na função de transferência para o controle da tensão de saída, sendo que este zero causa o conhecido efeito de fase não-mínima. Desta forma, uma metodologia especial de projeto é apresentada resultando numa indutância Boost reduzida e numa técnica de controle utilizando um sistema multi-malhas, com alimentação direta, devidamente projetada de forma a possibilitar elevadas dinâmicas de transferência de energia. Adicionalmente, o inversor apresenta tensão de saída com reduzidas distorções harmônicas (DHT), número reduzido de componentes de potência e, consequentemente, elevada densidade de potência. Neste trabalho são apresentadas as análises qualitativa e quantitativa do inversor, a modelagem e técnica de controle proposta, metodologia de projeto, os principais resultados de simulação e experimentais com a finalidade de demonstrar a viabilidade de aplicação da proposta. / This work presents a new methodology for the operation and control of a single-phase current-source Boost Inverter, it is used as base structure for alternative and renewable electric energy sources. The electro/electronics devices normally require eletrical source in AC (alternate current) in different voltage levels and shapes those provided by the alternative and renewable electrical sources. The proposed inverter is an integrated structure able to operate as step-up DC-DC converter and inverter, it presents a reduced number of components, high efficiency when compared with the traditional technique of step-up and inverter for cascade association. The conventional design of current source inverter (CSI) require a large boost inductance, therefore, the small-signal model is similar to continuous-current-mode (CCM) Boost converter, which has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the well-known non-minimum-phase effects. In this context, a special design with small boost inductance and a multi-loop control is proposed in order to assure stability and very fast dynamics. Furthermore, the inverter presents output voltage with very low total harmonic distortion (THD), reduced number of components and high power density. In addition, this work presents the Boost CSI operation, the proposed control technique, the main simulation and experimental results in order to demonstrate the feasibility of the proposal.

Orientador: Carlos Alberto Canesin / Banca: Falcondes Jose Mendes de Seixas / Banca: Denizar Cruz Martins / Resumo: Este trabalho propõe uma nova abordagem na metodologia de operação para o inversor Boost monofásico, como estrutura base para o aproveitamento de fontes alternativas e renováveis de energia elétrica. Considerando-se que equipamentos eletro/eletrônicos convencionais em CA (corrente alternada) necessitam, normalmente, de níveis e formato de tensão diferentes daqueles fornecidos por essas fontes de energia, o inversor proposto é uma estrutura integrada que tem a capacidade de operar como conversor elevador de tensão e inversor, apresentando um número reduzido de componentes e rendimento maior, quando comparado às formas tradicionais de se associar em cascata o conversor elevador com o inversor. O projeto convencional do inversor fonte de corrente (CSI) exige uma indutância elevada de entrada, além disso, o modelo a pequeno sinais do CSI é semelhante ao do conversor Boost no modo de condução contínua, apresentando um zero no semi-plano direito na função de transferência para o controle da tensão de saída, sendo que este zero causa o conhecido efeito de fase não-mínima. Desta forma, uma metodologia especial de projeto é apresentada resultando numa indutância Boost reduzida e numa técnica de controle utilizando um sistema multi-malhas, com alimentação direta, devidamente projetada de forma a possibilitar elevadas dinâmicas de transferência de energia. Adicionalmente, o inversor apresenta tensão de saída com reduzidas distorções harmônicas (DHT), número reduzido de componentes de potência e, consequentemente, elevada densidade de potência. Neste trabalho são apresentadas as análises qualitativa e quantitativa do inversor, a modelagem e técnica de controle proposta, metodologia de projeto, os principais resultados de simulação e experimentais com a finalidade de demonstrar a viabilidade de aplicação da proposta. / Abstract: This work presents a new methodology for the operation and control of a single-phase current-source Boost Inverter, it is used as base structure for alternative and renewable electric energy sources. The electro/electronics devices normally require eletrical source in AC (alternate current) in different voltage levels and shapes those provided by the alternative and renewable electrical sources. The proposed inverter is an integrated structure able to operate as step-up DC-DC converter and inverter, it presents a reduced number of components, high efficiency when compared with the traditional technique of step-up and inverter for cascade association. The conventional design of current source inverter (CSI) require a large boost inductance, therefore, the small-signal model is similar to continuous-current-mode (CCM) Boost converter, which has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the well-known non-minimum-phase effects. In this context, a special design with small boost inductance and a multi-loop control is proposed in order to assure stability and very fast dynamics. Furthermore, the inverter presents output voltage with very low total harmonic distortion (THD), reduced number of components and high power density. In addition, this work presents the Boost CSI operation, the proposed control technique, the main simulation and experimental results in order to demonstrate the feasibility of the proposal. / Mestre

In der Z-Boson-Resonanzphysik sind mehrere Präzisionsobservablen in einem perfekten Zustand, bei dem die theoretische Unsicherheit niedriger ist als die gegenwärtige experimentelle Unsicherheit. Das Konzept für den zukünftigen Teilchenbeschleuniger Future Circular Collider (FCC), will eine Verbesserung der Messungen für die Präzisionsobservablen um ein bis zwei signifikante Stellen erreichen. Damit werden die Vorhersagen des elektroschwachen Standardmodells in eine Situation versetzt, in der vollständige Zweischleifenkorrekturen zusammen mit den führenden Dreischleifenkorrekturen obligatorisch werden. 2016 wurden die vollständigen Zweischleifenkorrekturen für den effektiven schwachen Mischungswinkel für die bottom Quarks sin^2/theta/^b_eff berechnet, indem die fehlenden bosonischen Zweischleifenkorrekturen bereitgestellt wurden. Dabei liegt die Schwierigkeit in der Berechnung der entsprechenden Zwei-Schleifen Vertex-Feynman-Integrale, die mehrere massive Teilchen einschließen. Gegenwärtig ist die analytische Rechnung der meisten dieser Integrale schwierig und deswegen werden rein numerische Techniken, mittels Sektorzerlegungsansatz und der Integralansatz nach Mellin-Barnes, angewandt. Es war bis vor kurzem nicht bekannt, wie Mellin-Barnes-Integraldarstellungen in den minkowskischen Integrationsgebieten numerisch behandelt werden können. Um dieses Problem anzugehen, stellen wir eine Vielzahl von ein- und mehrdimensionaler Techniken vor, die ein Teil des neuen Programms MBnumerics.m sind, welches in dieser Dissertation entwickelt wurde. Der Sektorzerlegungsansatz und der Integralansatz nach Mellin-Barnes sind zusammen ausreichend, um elektroschwache Zweischleifenkorrekturen für die Präzisionsobservablen der Annihilation von e^+e^- in zwei Fermionen in der Z-Bosonresonanz auszurechnen. Aktuell führt dies zu der genauesten Vorhersage für den effektiven elektroschwachen Mischungswinkel für bottom Quarks sin^2/theta/^b_eff = 0.232312. / In the Z-boson resonance physics several precision observables are in a perfect state, where the theory uncertainty is lower than the present experimental uncertainty. The ambitious concepts for the future collider, Future Circular Collider (FCC), aim for an improvement of measurements for the precision observables by one to two significant digits. This will put the Electroweak Standard Model predictions in a situation where complete two-loop corrections together with the leading three-loop corrections will become mandatory. The complete two-loop corrections for effective weak mixing angle for bottom quarks sin^2/theta/^b_eff were reported recently, by providing the missing bosonic two-loop corrections. The difficult task in this computation is the calculation of the corresponding two-loop vertex Feynman integrals which include several massive particles. At present the analytic evaluation for most of these integrals is out of reach and purely numerical techniques were applied. Only two methods, sector decomposition approach and the Mellin-Barnes integral approach, are known to extract infrared and ultraviolet singularities in a systematic way for a general Feynman integral with fully automatized algorithms. It was not known until recently how to treat Mellin-Barnes integral representations in Minkowskian regions numerically. To address this problem we introduce and discuss in detail a variety of one- and multi-dimensional techniques, which are part of a new program MBnumerics.m developed in this thesis work. Two techniques, sector decomposition and Mellin-Barnes integral approach, are together sufficient to treat electroweak two-loop corrections to the precision observables for the e^+e^- annihilation into two fermions at the Z-boson resonance. This leads to the most precise prediction at present for the effective weak mixing angle for bottom quarks: sin^2/theta/^b_eff=0.232312.