"RF excited CO2 lasers are widely used in industry. They provide relatively high power discharge levels while maintaining compactness, simplicity, and durability with respect to other competing laser technologies. To attain high power levels in the range of 5-10 KW, lasers with large electrode areas have to be designed. Unfortunately, due to the large electrode length requirements, transmission line effects make the discharge loading nonlinear, adversely affecting the efficiency of the CO2 laser. A standard approach to linearize the discharge loading is to introduce shunt inductors across the length of the electrodes in an effort to counter the capacitive nature of the discharge behavior. This thesis investigates and improves the theoretical models found in the literature in an effort to predict the discharge non-uniformity and allow for multiple shunt inductors installation. Specifically, we discuss the coupling of a CO2 laser discharge model with an electrical circuit solving scheme and how it can be characterized as one dimensional (1-D) and two dimensional (2-D) systems. The 1-D system is modeled using transmission line (TL) theory, where as the 2-D system is modeled using a finite difference time domain (FDTD) scheme. All our models were implemented in standard MATLAB code and the results are compared with those found in the literature with the goal to analyze and ascertain model limitations."

Submitted by Maicon Juliano Schmidt (maicons) on 2015-06-03T12:32:25Z No. of bitstreams: 1 Joâo Cândido Moraes Neves_.pdf: 1725890 bytes, checksum: 3ca8d300deeac94f8bd1dc3faf2e4d4a (MD5) / Made available in DSpace on 2015-06-03T12:32:25Z (GMT). No. of bitstreams: 1 Joâo Cândido Moraes Neves_.pdf: 1725890 bytes, checksum: 3ca8d300deeac94f8bd1dc3faf2e4d4a (MD5) Previous issue date: 2015-02-02 / IFRS - Instituto Federal do Rio Grande do Sul / A presente tese tem como objetivo problematizar um dos enunciados que integram o discurso da Educação Matemática Escolar: “Os alunos não aprendem Matemática por ‘falta de base”’. O estudo utiliza as seguintes noções foucaultianas: enunciado, discurso, verdade e regimes de verdade. O material de pesquisa analisado é constituído por enunciações de um grupo de bolsistas do Programa Institucional de Bolsa de Iniciação à Docência (Pibid), que emergiram de entrevistas, diário de campo e seus relatórios finais; e também por teses, dissertações e artigos acadêmicos do período de 1994 a 2013, disponíveis no portal da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) e na mídia, que remetem ao enunciado objeto do estudo. A análise do material de pesquisa mostrou: 1) a recorrência de enunciações que vinculam a dificuldade em aprender matemática à “falta de base” dos estudantes; 2) O enunciado “Os alunos não aprendem Matemática por ‘falta de base’” está entrelaçado com dois outros enunciados presentes no discurso pedagógico: a) A matemática escolar é constituída por um conjunto hierarquizado de conhecimentos (que tem estreitos vínculos com o enunciado O conhecimento matemático apresenta-se hierarquizado); b) O currículo escolar é hierarquizado, isto é, segue uma ordenação linear. / This thesis aims to discuss one of the statements that is part of the discourse of School Mathematics Education: "The students do not learn Mathematics by 'lack of basic skills'”. The study uses the following Foucault’s notions: statement, discourse, truth and regimes of thruth. The research material analized consists of utterances of a college group of the Teacher Induction Program (Pibid), which emerged from interviews, field diary, and their final reports; and also for theses, dissertations and scholarly articles from the period of 1996 to 2014, available on the website of Coordination for the Improvement of Higher Education Personnel portal (CAPES) and the media, referring to the statement object of the study. The analysis of the research material showed: 1) the recurrence of utterances that link the difficulty in learning Mathematics to "lack of basic skills" of students; 2) The statement "The students do not learn Mathematics by 'lack of basic skills' " is interlaced with two other statements presented in the pedagogical discourse: a) The scholar Mathematics is consisted of a hierarchical set of knowledges (which has close ties with the statement - The mathematical knowledge is hierarchical); b) The school curriculum is hierarchical, thus, follows a linear ordering.

Cette thèse étudie l'approche LPV pour la commande robuste des systèmes non linéaires. Son originalité est de proposer pour la première fois un cadre rigoureux permettant de résoudre efficacement des problèmes de synthèse non linéaire. L'approche LPV a été proposée comme une extension de l'approche H-infini dans le contexte des systèmes LPV (« Linéaires à Paramètres Variant dans le temps »), voire non linéaires. Quoique prometteuse, cette approche pour la commande des systèmes non linéaires restait peu utilisée. En effet, au-delà même de certaines limitations théoriques, la nature des solutions obtenues semblait inadéquate. Cette question ouverte est notre point de départ. Nous montrons tout d'abord que la faible variation des correcteurs constatée est due avant tout à la nature du schéma informationnel utilisé traditionnellement lors de la synthèse LPV, et que sous des hypothèses raisonnables, le cadre LPV peut permettre de recouvrir des stratégies de type « linéarisation par bouclage ». Ce point étant acquis, une deuxième difficulté réside dans l'obtention effective de correcteurs non linéaires donnant des garanties de performance. Nous proposons un cadre rigoureux permettant de résoudre efficacement un problème de synthèse incrémentale pondérée, par la résolution d'un problème LPV associé à un schéma informationnel spécifique compatible avec celui identifié dans la première partie. Cette étude et son aboutissement à la définition d'un cadre formel et d'une procédure complète d'obtention de correcteurs, incluant des méthodes de réduction de complexité, donnent des arguments puissants en faveur de l'approche LPV pour la commande robuste de systèmes non linéaires. / This thesis studies the LPV approach for the robust control of nonlinear systems. Its originality is to propose for the first time a rigorous framework allowing to solve efficiently nonlinear synthesis problems.The LPV approach was proposed as an extension of the H-infinity approach in the context of LPV (Linear Parameter-Varying) systems and nonlinear systems. Although this approach seemed promising, it was not much used in practise. Indeed, beyond certain theoretical limitations, the nature itself of the obtained solutions did not seem adequate. This open question constitutes the starting point of our work.We first prove that the observed weak variation of the controllers is in fact mostly due to the information structure traditionally used for LPV synthesis, and that under reasonable assumptions, the LPV framework can overlap feedback linearization strategies. This point having been resolved, a second difficulty lies in the actual achievement of nonlinear controllers yielding performance guarantees. We propose a rigorous framework allowing to solve efficiently an incremental synthesis problem, through the resolution of an LPV problem associated to a specific information structure compatible with the one identified in the first part.This study and its corollary description of a formal framework and of a complete controller synthesis procedure, including complexity reduction methods, provide powerful arguments in favor of the LPV approach for the robust control of nonlinear systems.

abstract: Unmanned aerial vehicles (UAVs) are widely used in many applications because of their small size, great mobility and hover performance. This has been a consequence of the fast development of electronics, cheap lightweight flight controllers for accurate positioning and cameras. This thesis describes modeling, control and design of an oblique-cross-quadcopter platform for indoor-environments. One contribution of the work was the design of a new printed-circuit-board (PCB) flight controller (called MARK3). Key features/capabilities are as follows: (1) a Teensy 3.2 microcontroller with 168MHz overclock –used for communications, full-state estimation and inner-outer loop hierarchical rate-angle-speed-position control, (2) an on-board MEMS inertial-measurement-unit (IMU) which includes an LSM303D (3DOF-accelerometer and magnetometer), an L3GD20 (3DOF-gyroscope) and a BMP180 (barometer) for attitude estimation (barometer/magnetometer not used), (3) 6 pulse-width-modulator (PWM) output pins supports up to 6 rotors (4) 8 PWM input pins support up to 8-channel 2.4 GHz transmitter/receiver for manual control, (5) 2 5V servo extension outputs for other requirements (e.g. gimbals), (6) 2 universal-asynchronous-receiver-transmitter (UART) serial ports - used by flight controller to process data from Xbee; can be used for accepting outer-loop position commands from NVIDIA TX2 (future work), (7) 1 I2C-serial-protocol two-wire port for additional modules (used to read data from IMU at 400 Hz), (8) a 20-pin port for Xbee telemetry module connection; permits Xbee transceiver on desktop PC to send position/attitude commands to Xbee transceiver on quadcopter. The quadcopter platform consists of the new MARK3 PCB Flight Controller, an ATG-250 carbon-fiber frame (250 mm), a DJI Snail propulsion-system (brushless-three-phase-motor, electronic-speed-controller (ESC) and propeller), an HTC VIVE Tracker and RadioLink R9DS 9-Channel 2.4GHz Receiver. This platform is completely compatible with the HTC VIVE Tracking System (HVTS) which has 7ms latency, submillimeter accuracy and a much lower price compared to other millimeter-level tracking systems. The thesis describes nonlinear and linear modeling of the quadcopter’s 6DOF rigid-body dynamics and brushless-motor-actuator dynamics. These are used for hierarchical-classical-control-law development near hover. The HVTS was used to demonstrate precision hover-control and path-following. Simulation and measured flight-data are shown to be similar. This work provides a foundation for future precision multi-quadcopter formation-flight-control. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2018

Dans le cadre des applications sans fil à 60GHz, l’amplificateur de puissance reste un des composants les plus compliqués à implémenter en technologie CMOS. Des modulations à enveloppe non constante obligent à concevoir des circuits hautement linéaires, conduisant à une consommation statique importante. La recherche de topologies et de techniques de linéarisation viables aux fréquences millimétriques fait l’objet de cette thèse. Dans un premier temps, un état de l’art des différents amplificateurs de puissance à 60GHz est dressé, afin d’en extraire l’ensemble des verrous technologiques limitant leurs performances. Suite à l’analyse des phénomènes physiques impactant les composants passifs, plusieurs structures d’amplificateurs élémentaires sont conçues dans les technologies 65nm et 28nm Bulk. Les topologies les plus pertinentes sont déduites de cette étude. Enfin, deux amplificateurs intégrant des techniques de combinaison de puissance et de linéarisation sont implémentés dans les technologies 65nm et 28nm FD-SOI. Ces deux circuits présentent les plus hauts facteurs de mérite ITRS publiés à ce jour. Le circuit en 28nm FD-SOI atteint en outre le meilleur compromis linéarité/consommation de l’état de l’art. / The CMOS 60GHz power amplifier (PA) remains one of the most design-challenging components. Indeed, a high linearity associated with a large back-off range are required due to complex modulated signals.In this context, this work focuses on the design of architectures and linearization techniques which are usable at millimeter-wave frequencies. First, a CMOS PA state of the art is presented to define all bottlenecks. Then, the physical phenomena impacting on passive device performances are described. Elementary PAs are implemented in CMOS 65nm and 28nm Bulk and the most suitable topologies are selected. Finally, two highly linear circuits are designed in 65nm Bulk and 28nm FD-SOI. They achieve the highest ITRS figures of merit reported to this day. In addition, the 28nm FD-SOI PA exhibits the best linearity/consumption tradeoff.

In this thesis, dynamic modeling and nonlinear control of autonomous underwater vehicle manipulator systems are presented. Mainly, two types of systems consisting of a 6-DOF AUV equipped with a 6-DOF manipulator subsystem (UVMS) and with an 8-DOF redundant manipulator subsystem (UVRMS) are modeled considering hydrostatic forces and hydrodynamic effects such as added mass, lift, drag and side forces. The shadowing effects of the bodies on each other are introduced when computing the hydrodynamic forces. The system equations of motion are derived recursively using Newton&ndash / Euler formulation. The inverse dynamics control algorithms are formulated and trajectory tracking control of the systems is achieved by assigning separate tasks for the end effector of the manipulator and for the underwater vehicle. The proposed inverse dynamics controller utilizes the full nonlinear model of the system and consists of a linearizing control law that uses the feedback of positions and velocities of the joints and the underwater vehicle in order to cancel off the nonlinearities of the system. The PD control is applied after this complicated feedback linearization process yielding second order error dynamics. The thruster dynamics is also incorporated into the control system design. The stability analysis is performed in the presence of parametric uncertainty and disturbing ocean current. The effectiveness of the control methods are demonstrated by simulations for typical underwater missions.

In this thesis, dynamic modeling and nonlinear control of autonomous underwater vehicle manipulator systems are presented. Mainly, two types of systems consisting of a 6-DOF AUV equipped with a 6-DOF manipulator subsystem (UVMS) and with an 8-DOF redundant manipulator subsystem (UVRMS) are modeled considering hydrostatic forces and hydrodynamic effects such as added mass, lift, drag and side forces. The shadowing effects of the bodies on each other are introduced when computing the hydrodynamic forces. The system equations of motion are derived recursively using Newton&ndash / Euler formulation. The inverse dynamics control algorithms are formulated and trajectory tracking control of the systems is achieved by assigning separate tasks for the end effector of the manipulator and for the underwater vehicle. The proposed inverse dynamics controller utilizes the full nonlinear model of the system and consists of a linearizing control law that uses the feedback of positions and velocities of the joints and the underwater vehicle in order to cancel off the nonlinearities of the system. The PD control is applied after this complicated feedback linearization process yielding second order error dynamics. The thruster dynamics is also incorporated into the control system design. The stability analysis is performed in the presence of parametric uncertainty and disturbing ocean current. The effectiveness of the control methods are demonstrated by simulations for typical underwater missions.

In this thesis we mainly focused on the usage of the Conditional Value-at-Risk (CVaR) in risk management and on the pricing of the arithmetic average basket and Asian options in the Black-Scholes framework via a new log-normal sum approximation method. Firstly, we worked on the linearization procedure of the CVaR proposed by Rockafellar and Uryasev. We constructed an optimization problem with the objective of maximizing the expected return under a CVaR constraint. Due to possible intermediate payments we assumed, we had to deal with a re-investment problem which turned the originally one-period problem into a multiperiod one. For solving this multi-period problem, we used the linearization procedure of CVaR and developed an iterative scheme based on linear optimization. Our numerical results obtained from the solution of this problem uncovered some surprising weaknesses of the use of Value-at-Risk (VaR) and CVaR as a risk measure. In the next step, we extended the problem by including the liabilities and the quantile hedging to obtain a reasonable problem construction for managing the liquidity risk. In this problem construction the objective of the investor was assumed to be the maximization of the probability of liquid assets minus liabilities bigger than a threshold level, which is a type of quantile hedging. Since the quantile hedging is not a perfect hedge, a non-zero probability of having a liability value higher than the asset value exists. To control the amount of the probable deficient amount we used a CVaR constraint. In the Black-Scholes framework, the solution of this problem necessitates to deal with the sum of the log-normal distributions. It is known that sum of the log-normal distributions has no closed-form representation. We introduced a new, simple and highly efficient method to approximate the sum of the log-normal distributions using shifted log-normal distributions. The method is based on a limiting approximation of the arithmetic mean by the geometric mean. Using our new approximation method we reduced the quantile hedging problem to a simpler optimization problem. Our new log-normal sum approximation method could also be used to price some options in the Black-Scholes model. With the help of our approximation method we derived closed-form approximation formulas for the prices of the basket and Asian options based on the arithmetic averages. Using our approximation methodology combined with the new analytical pricing formulas for the arithmetic average options, we obtained a very efficient performance for Monte Carlo pricing in a control variate setting. Our numerical results show that our control variate method outperforms the well-known methods from the literature in some cases.

La tesi è organizzata come segue: nella prima parte viene presentato il background matematico necessario per studiare il modello, introducendo la nozione di sistema dinamico (capitolo 2). Succesivamente viene introdotto il background economico, con il concetto di determinatezza sia dal punto di vista tecnico, con esempio applicativo, che dal punto di vista dei modelli presenti in letteratura in cui viene impiegato. Nella seconda parte viene presentato il framework analitico, basato sul modello di Woodford. In seguito, si passa studiare il modello con lo strumento della loglinearizzazione, fornendo le relazioni di equilibrio attorno allo stato stazionario. Poi si specifica il modello in un caso particolare e si prosegue per ottenere la versione non lineare del modello, introducendo nuove ipotesi compatibili con il framework analitico, in modo da poter studiare la determinatezza dell'equilibrio. / The thesis is organized as follow: we start presenting, in the first part, the mathematical background we need to study our model, introducing at first the notion of dynamical system, more specifically in the discrete time, as our model required (Chapter 2). Afterwards, for the economical background (Chapter 3-4), the concept of determinacy of the equilibrium is analyzed from the technical point of view for linear models, providing the analytical conditions that let us obtain a unique and determinate equilibrium. Once explored the techniques, we give an exhaustive example that allows us to better understand from the mathematical point of view the concept of determinacy and how it is linked to the concept of stability. After that, a brief survey of the models that involved the study of determinacy is exposed, showing the several fields of application. Then, since in our model of monetary policy we imply different interest-rate policy rules in order to study the stability of the macroeconomic system, we provide a short preamble of the rules for the operating target interest rate set by Central Bank. In the second part the analytical framework is presented. The starting point is a model for price level determination in a cashless economy, where nominal rigidities are introduced, based on Woodford's work and we give the equilibrium relations of the model in the implicit form (Chapter 5). Afterwards, we build the model in a particular case (Chapter 6), by specifying the functions involved in the model by using utility function of C.R.R.A. type and linear production function, compatible with the analytical characterization. In this way we get the components of a general economic equilibrium model, consistent with the optimizing behavior of households and firms. The results obtained after the specification of the functions are the same we can find in the analysis proposed by Walsh. At this point, we obtain the log-linearized version of the model that is the starting point for the study of the stability of the system in the linear case. This procedure let us find a two equations forward-looking and rational-expectations model for inflation and the output gap. Then we briefly present the different policy regimes used in the analysis according to our framework, providing the interest-rate relations that close the model Since our intention is to find a nonlinear version of the model, the step of using the log-linearization is essential in order to understand and to underline how this tool is useful not only for studying the equations around the steady-state but also to make these relations more treatable from a mathematical point of view: in fact it is important in order to figure out the obstacles we faced to build the nonlinear model and to find the solutions proposed in this work. In the third part (Chapter 7), to reach our purpose to go beyond the log-linearized and simplified version of the model, we try, under some assumption compatible with the behavior of the agents, to provide nonlinear conditions for this model. This is meaningful in order to avoid loss of informations due to the limited analysis around a neighborhood of the steady-state. Once illustrated the nonlinear model and the equilibrium relation, we study the determinacy of the equilibrium, using the techniques shown in the first part, under two different interest rate specifications that close the model. Chapter 8 concludes.

Heavy load equipment, such as tractors, shovels, cranes, airplanes, etc, often employ fluid power (i.e. hydraulic) systems to control their loads by way of valve adjustment in a pump-valve control configuration. Most of these systems have low energy efficiency as a consequence of pressure losses across throttle valves. Much of the energy is converted into heat energy which can have determinantal effects on component life and the surrounding environment. From an energy efficiency point of view, an ideal hydraulic system is one that does not include any throttling valve. One such circuit is made of a variable pump and motor load (pump/motor configuration). The velocity of the load is controlled by manipulating the pump displacement or by changing the rotary speed of the pump shaft. In such a system, the transient response of the load is often unsatisfactory because it is difficult to quickly and accurately manipulate the pump displacement or change shaft speed. Thus circuit design must be a compromise between the energy efficiency of the pump/motor system and the controllability of a pump/valve/motor combination. One possible compromise is to use a pump-valve configuration which reduces energy losses across the valve. One way to achieve this is by controlling the pressure drop across the valve and limiting it to a small value, independent of load pressure. Based on this idea, a type of hydraulic control system, usually called load-sensing (LS), has recently been used in the flow power area. This type of system, however, is complex and under certain operating conditions exhibits instability problems. Methods for compensating these instabilities are usually based on a trial-and-error approach. Although some research has resulted in the definition of some instability criterion, a comprehensive and verifiable approach is still lacking. This research concentrates on identifying the relationship between system parameters and instability in one particular type of LS system. Due to the high degree of non-linearity in LS systems, the instabilities are dependent on the steady state operating point. The study therefore concentrates first on identifying all of the steady state operating points and then classifying them into three steady state operating regions. A dynamic model for each operating region is developed to predict the presence of instabilities. Each model is then validated experimentally. This procedure, used in the study of the LS system, is also applied to a pressure compensated (PC) valve. A PC valve is one in which the flow rate is independent in variations to load pressure. A system which combines a LS pump and a PC valve (for the controlling orifice) is called a load sensing pressure compensated (LSPC) system. This research, then, examines the dynamic performance of the LSPC system using the operating points and steady state operating regions identified in the first part of the research. The original contributions of this research include: (a) establishment of three steady state operating conditions defined as Condition I, II & III, which are based on the solution of steady state non-linear equations; (b) the provision of an empirical model of the orifice discharge coefficient suitable for laminar and turbulent flow, and the transition region between them; (c) and the development of an analytical expression for orifice flow which makes it possible to accurately model and simulate a hydraulic system with pilot stage valve or pump/motor compensator. These contributions result in a practical and reliable method to determine the stability of a LS or LSPC system at any operating point and to optimize the design of the LS or LSPC system.