<p>The Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by <i>p</i><i>n</i>^(λ)(<i>x</i>) instead of the standard notation <i>p</i><i>n</i>^(λ) (<i>x</i>/2, <i>π</i>/2), where λ > 0. The limiting case of these sequences of polynomials <i>p</i><i>n</i>⁽⁰⁾ (<i>x</i>) =lim_λ→0 <i>p</i><i>n</i>^(λ)(<i>x</i>), is obtained, and is shown to be an orthogonal sequence in the strip, <i>S</i> = {<i>z</i> ∈ ℂ : −1≤ℭ (<i>z</i>)≤1}.</p><p>From the point of view of Umbral Calculus, this sequence has a special property that makes it unique in the Symmetric Meixner-Pollaczek class of polynomials: it is of convolution type. A convolution type sequence of polynomials has a unique associated operator called a delta operator. Such an operator is found for <i>p</i><i>n</i>⁽⁰⁾ (<i>x</i>), and its integral representation is developed. A convolution type sequence of polynomials may have associated Sheffer sequences of polynomials. The set of associated Sheffer sequences of the sequence <i>p</i><i>n</i>⁽⁰⁾(<i>x</i>) is obtained, and is found</p><p>to be ℙ = {{<i>p</i><i>n</i>^(λ) (<i>x</i>)} =0 : λ ∈ R}. The major properties of these sequences of polynomials are studied.</p><p>The polynomials {<i>p</i><i>n</i>^(λ) (<i>x</i>)}^∞<i>n</i>₌₀, λ < 0, are not orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard’s three term recurrence relation condition. For every λ ≤ 0, an associated nonstandard inner product is defined with respect to which <i>p</i><i>n</i>^(λ)(x) is orthogonal. </p><p>Finally, the connection and linearization problems for the Symmetric Meixner-Pollaczek polynomials are solved. In solving the connection problem the convolution property of the polynomials is exploited, which in turn helps to solve the general linearization problem.</p>

The Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by pn(λ)(x) instead of the standard notation pn(λ) (x/2, π/2), where λ &gt; 0. The limiting case of these sequences of polynomials pn(0) (x) =limλ→0 pn(λ)(x), is obtained, and is shown to be an orthogonal sequence in the strip, S = {z ∈ ℂ : −1≤ℭ (z)≤1}. From the point of view of Umbral Calculus, this sequence has a special property that makes it unique in the Symmetric Meixner-Pollaczek class of polynomials: it is of convolution type. A convolution type sequence of polynomials has a unique associated operator called a delta operator. Such an operator is found for pn(0) (x), and its integral representation is developed. A convolution type sequence of polynomials may have associated Sheffer sequences of polynomials. The set of associated Sheffer sequences of the sequence pn(0)(x) is obtained, and is found to be ℙ = {{pn(λ) (x)} =0 : λ ∈ R}. The major properties of these sequences of polynomials are studied. The polynomials {pn(λ) (x)}∞n=0, λ &lt; 0, are not orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard’s three term recurrence relation condition. For every λ ≤ 0, an associated nonstandard inner product is defined with respect to which pn(λ)(x) is orthogonal. Finally, the connection and linearization problems for the Symmetric Meixner-Pollaczek polynomials are solved. In solving the connection problem the convolution property of the polynomials is exploited, which in turn helps to solve the general linearization problem.

As wireless communication becomes an ever-more important and pervasive part of our everyday life, system capacity and quality of service issues are becoming more critical. In order to increase the system capacity and improve the quality of service, it is necessary that we pay closer attention to bandwidth and power efficiency issues. Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique for high speed data transmission and is generally regarded as bandwidth efficient. However, OFDM signals suffer from high peak-to-average power ratios (PARs) which lead to power inefficiency in the RF portion of the transmitter. Moreover, in OFDM, the well-known pilot tone assisted modulation (PTAM) technique utilizes a number of dedicated training pilots to acquire the channel state information (CSI), resulting in somewhat reduced bandwidth efficiency. In this dissertation, we will address the above mentioned bandwidth and power efficiency issues in wireless transmissions. To avoid bandwidth efficiency loss due to dedicated training, we will first develop a superimposed training framework that can be used to track the frequency selective as well as the Doppler shift characteristics of a channel. Later on, we will propose a generalized superimposed training framework that allows improved channel estimates. To improve the power efficiency, we adopt the selected mapping (SLM) framework to reduce the PARs for both OFDM and forward link Code Division Multiple Access (CDMA). We first propose a dynamic SLM algorithm to greatly reduce the computational requirement of SLM without sacrificing its PAR reducing capability. We propose a number of blind SLM techniques for OFDM and for forward link CDMA; they require no side information and are easy to implement. Our proposed blind SLM technique for OFDM is a novel joint channel estimation and PAR reduction algorithm, for which bandwidth efficiency power efficiency - complexity - bit error rate tradeoffs are carefully considered.

Many communications signal formats are not power efficient because of their large peak-to-average power ratios (PARs). Moreover, in the presence of nonlinear devices such as power amplifiers (PAs) or mixers, the non-constant-modulus signals may generate both in-band distortion and out-of-band interference. Backing off the signal to the linear region of the device further reduces the system power efficiency. To improve the power efficiency of the communication system, one can pursue two approaches: i) linearize the PA; ii) reduce the high PAR of the input signal. In this dissertation, we first explore the optimal nonlinearity under the peak power constraint. We show that the optimal nonlinearity is a soft limiter with a specific gain calculated based on the peak power limit, noise variance, and the probability density function of the input amplitude. The result is also extended to the fading channel case. Next, we focus on digital baseband predistortion linearization for power amplifiers with memory effects. We build a high-speed wireless test-bed and carry out digital baseband predistortion linearization experiments. To implement adaptive PA linearization in wireless handsets, we propose an adaptive digital predistortion linearization architecture that utilizes existing components of the wireless transceiver to fulfill the adaptive predistorter training functionality. We then investigate the topic of PAR reduction for OFDM signals and forward link CDMA signals. To reduce the PAR of the OFDM signal, we propose a dynamic selected mapping (DSLM) algorithm with a two-buffer structure to reduce the computational requirement of the SLM method without sacrificing the PAR reduction capability. To reduce the PAR of the forward link CDMA signal, we propose a new PAR reduction algorithm by introducing a relative offset between the in-phase branch and the quadrature branch of the transmission system.

The nonlinear simulation model of an unmanned aerial vehicle (UAV) in MATLAB&reg / /Simulink&reg / environment is developed by taking into consideration all the possible major system components such as actuators, gravity, engine, atmosphere, wind-turbulence models, as well as the aerodynamics components in the 6 DOF equations of motion. Trim and linearization of the developed nonlinear model are accomplished and various related analyses are carried out. The model is validated by comparing with a similar UAV data in terms of open loop dynamic stability characteristics. Using two main approaches / namely, classical and optimal, linear controllers are designed. For the classical approach, Simulink Response Optimization (SRO) tool of MATLAB&reg / /Simulink&reg / is utilized, whereas for the optimal controller approach, linear quadratic (LQ) controller design method is implemented, again by the help of the tools put forth by MATLAB&reg / . The controllers are designed for control of roll, heading, coordinated turn, flight path, pitch, altitude, and airspeed, i.e., for the achievement of all low-level control functions. These linear controllers are integrated into the nonlinear model, by carrying out gain scheduling with respect to airspeed and altitude, controller input linearization regarding the perturbed states and control inputs, and anti integral wind-up scheme regarding the possible wind-up of the integrators in the controller structures. The responses of the nonlinear model controlled with the two controllers are compared based on the military flight control requirements. The advantages and disadvantages of these two frequently used controllers in industry are investigated and discussed. These results are to be evaluated by the designers themselves based on the design criteria of a project that is worked on.

This thesis deals with the design of an anti-skid brake controller for a generic fighter aircraft. Antiskid brake controllers prevent wheel locking and maximize the coefficient of friction between the tyre and the ground, resulting in lower stopping distance and time. The frictional force is maximized by regulating the slip. A model for the landing gear is first developed, which consists of the translational and rotational motions of the wheel, the equation for the slip and the elastic landing gear strut dynamics. The elastic behaviour of the landing gear is characterized through its modal frequencies, obtained from a Finite element analysis. As the governing equations are nonlinear, with linear elastic deformations of the strut, feedback linearization is used to design the anti-skid controller. The brake controller is found to work well. Its stability is verified through numerical simulations. Both the plant parameters and the sensor measurements are perturbed up to 10% from their nominal values. It is seen that the feedback linearization tolerates these variations quite well. The system is exceptionally tolerant to sensor noises. The torsional stiffness of the strut is found to be more critical than the longitudinal stiffness. Limits on the torsional stiffness that can be tolerated by the controller are found. This determines the limits on the stiffness of the landing gear beyond which gear walk may appear. The thesis concludes with suggestions for future work in this exciting field.

Nowadays the developments of power supplies in military, industrial or commercial applications are growing rapidly, not only to achieve the highest efficiency but also to focus on the size and weight minimization which are playing a major role in this area. Therefore, the research trends in dc-dc, ac-dc, dc-ac, ac-ac topologies are still continuously developing into the direction of new topologies, new control concepts, new materials and devices to achieve highest efficiency and smallest size. The cost per unit is also one of the most important points of power supplies. Also, with new control methods and new ways of manufacturing, for example, the cost per unit might be reduced. Also, a simplified control concept might help to avoid discrete circuits, especially, at low power levels. The last mentioned statement is demonstrated, for instance, by the concept of the Link-Switch of the company Power Integration where an extremely small number of components are necessary. With the target of minimization, this research work explores the possibility to replace conventional electromagnetic transformers considered as the most bulky devices in power supplies by piezoelectric transformers (PT) for innovative off-line power supplies. Several control methods for a load resonant converter focusing on class-E topology utilizing PT, were developed in order to investigate and to select an appropriate control method capable of improving the efficiency and reducing the size of the converter. Efficiency should be understood in this way as maximum reliability at minimum power losses. Different controllers were evaluated for optimizing the effect of disturbances of line and load variations. The ZVS condition for a wide input voltage range and a wide output load range can be achieved by a method called duty-cycle tracking. Further, with an improved design of the PT containing an auxiliary tap, the ZVS condition can be obtained by a method called turn-on synchronization. The controlled output voltage, current or power is achieved by a variable frequency control. Further, the dynamic modeling for open loop and closed loop of load resonant converters, focused on the class-E topology, was introduced. The transient behavior of the output voltage of the open loop against perturbations such as the input voltage change, the switching frequency change, and the output load change is treated by replacing the complete circuit of the class-E converter by simple equivalent circuit models. The results from the analysis of the open loop dynamic behavior are applied to modeling the closed loop class-E converter with several control methods. The methods of linearization for exact solution and heuristic approximation for the steady state analysis were purposed. These models of linearization were implemented with the controller in its topologies to investigate the sufficient accuracy of obtained results of the regulation. Besides, the linearization models were used to observe the stability condition of the proposed control loops. Finally, the evaluation of a well-known classical control such P, I, PI, PD, PID and a simplified controller for a fixed load application by matching an appropriate switching frequency according to the input voltage, into the load resonant converter, considering class-E topology, were presented. Also, the optimum design of the controller for a load resonant converter was discussed and derived. / Die Entwicklung von Stromversorgungen in militärischen, industriellen und kommerziellen Anwendungen nimmt bis heute tendenziell stark zu. Nicht nur zur Erzielung höchster Wirkungsgrade, sondern auch im Hinblick auf Baugrößen- und Gewichtsminimierung, welche eine vorrangige Rolle spielen, ist diese Tendenz zu verzeichnen. Diesbezüglich gehen die Forschungstrends bei DC-DC, AC-DC, DC-AC und AC-AC Topologien in Richtung neuer Topologien, neuer Regelungskonzepte, sowie neuer Materialien und Bauelemente, um den höchsten Wirkungsgrad bei kleinster Baugröße zu erreichen. Die Gerätekosten sind ebenso ein sehr wichtiger Punkt bei Stromversorgungen. Auch durch neue Regelungsmethoden und durch neue Herstellungsverfahren können die Gerätekosten beispielsweise reduziert werden. Ebenso kann ein vereinfachtes Regelungskonzept dazu verhelfen, dass diskrete Schaltungen, speziell im unteren Leistungsbereich, vermieden werden. Letzteres wird beispielsweise beim Konzept des Link-Switch der Firma Power Integration verdeutlicht, indem extern wenige Bauelemente benötigt werden. Mit dem Ziel der Miniaturisierung wird in dieser Forschungsarbeit die Möglichkeit untersucht, konventionelle elektromagnetische Transformatoren, welche in Stromversorgungen als besonders voluminös gelten, durch piezoelektrische Transformatoren (PT) bei der Herstellung innovativer Netzstromversorgungen zu ersetzen. Verschiedene Regelungsmethoden für Lastresonanzkonverter, mit dem Fokus auf eine Klasse- E-Topologie mit PT, wurden hierzu entwickelt. Dies hatte zum Ziel, ein geeignetes Regelungsverfahren zu erarbeiten und auszuwählen, welches eine verbesserte Effizienz bei reduzierter Konverter-Baugröße aufzuweisen hat. Effizienz soll hierbei verstanden werden als maximale Zuverlässigkeit bei minimalen Leistungsverlusten. Verschiedene Reglertypen wurden entworfen um die Effekte der Störungen durch Netzspannungs-und Lastvariationen regelungstechnisch zu optimieren. Die Nullspannungsschaltungsbedingung (ZVS-Bedingung) über einen weiten Bereich der Eingangspannung und einen weiten Lastbereich kann durch einen sogenannte Duty-Cycle-Nachführung mit der Frequenz erreicht werden. Weiterhin kann durch eine verbesserte Ausführung des PT auf Basis einer Hilfsanzapfung die ZVSBedingung durch eine sogenannte Einschaltsynchronisation erreicht werden. Geregelte Ausgangsspannung, Ausgangsstrom oder Ausgangsleistung werden über eine Frequenzstellung erreicht. Die dynamische Modellierung der offenen und geschlossenen Regelschleife eines Lastresonanzkonverters, wieder im Hinblick auf die Klasse-E, wird im weiteren vorgestellt. Das transiente Verhalten der Ausgangsspannung der offenen Regelschleife gegenüber Störungen durch Eingangsspannungsänderung, durch Schaltfrequenzänderung oder durch Ausgangslaständerung, wird durch den Ersatz der Klasse-E-Schaltung durch einfache Äquivalenzmodelle behandelt. Die Ergebnisse der Analyse des Verhaltens des offenenen Regelkreises werden verwendet, um den Klasse-E-Konverter mit geschlossener Regelschleife unter Verwendung verschiedener vorgestellter Regelungsmethoden zu modellieren. Methoden der Linearisierung für die exakte Lösung und für eine heuristische Approximation der statischen Analyse des eingeschwungenen Zustands werden vorgeschlagen. Diese Methoden der Linearisierung werden zusammen mit den Reglermodellen in deren jeweilige Topologie implementiert um die ausreichende Genauigkeit der erhaltenen Resultate des Regelungsverhaltens zu beurteilen. Weiterhin werden diese Linearisierungsmodelle dazu verwendet, die Stabilitätskriterien der vorgeschlagenen Regelschleife zu überwachen. Schlussendlich wird die Bestimmung der bekannten klassischen Regler (P, I, PI, PD, PID), sowie eines vereinfachten Konstantlaststellers durch geeignete Anpassung der Schaltfrequenz an die Eingangsspannung, für Lastresonanzkonverter, wieder mit Blick auf die Klasse-E, vorgestellt. Außerdem wird der optimierte Reglerentwurf für Lastresonanzkonverter diskutiert und abgeleitet.

A novel fuzzy system named as 2-way fuzzy system is developed by combining the intuitionistic fuzzy set theory with the fuzzy systems theory. The developed system is used in modelling and minimizing uncertainty and inconsistency. Uncertainty is the width of the interval introduced by the independent assignment of membership and nonmembership functions of the intuitionistic fuzzy sets / and inconsistency is the violation of the consistency inequality in this assignment. The uncertainty and inconsistency is reduced through a 2 phase training. An evaluation of the degree of reduction of inconsistency is carried out at the end of the rst phase of training by forming the shadowed set patterns of the membership and nonmembership functions. The system is further trained for a second phase in order to reduce uncertainty. There are three dierent methods developed for the stability analysis of fuzzy systems. The rst method is based on the approximating sequences technique, and the design turns into an optimal control problem. In the sec ond analysis, describing function of a 2-way fuzzy system is evaluated analytically, and a systematic design approach is developed using describing function technique. The last analysis technique employs the Lie algebra theory in the stability analysis of Takagi-Sugeno fuzzy systems. The theoretical results are simulated on an application system, which is a exible-joint robot arm system.

[pt] O presente trabalho desenvolve um novo modelo para um problema logístico de remanejamento de placas entre pilhas em um Pátio de Placas de uma Laminação, típico da indústria siderúrgica. Esta abordagem inclui uma nova característica que indica o destino das placas remanejadas. Uma nova metodologia de decisão altera sensivelmente o escopo do problema e traz um novo conceito: o balanço entre a escolha ótima das placas e o possível destino das placas remanejadas, ou seja, deve-se pesar a escolha da placa a ser laminada juntamente com a possibilidade de um bom remanejamento das placas que estão acima da mesma. Esse modelo não linear é linearizado por técnicas de linearização e resolvido através de programação linear inteira. Com isso, o estudo apresenta uma redução no tempo médio de manuseio de placas (TMM) de 5 minutos por placa laminada encontrado na literatura existente, para menos de 4 minutos. Finalmente o modelo proposto incentiva a construção de uma ferramenta de gestão que possa resolver o problema SSS em situações práticas do dia-a-dia através de redução de custo de operação como forma de viabilizar o investimento nesta ferramenta. / [en] This work develops a new model for a typical logistic problem in the steel industry known as slab stack shuffling problem inside a Slab Yard of a Rolling Mill. This new approach includes a new feature that indicates the destination stacks of shuffled slabs. A new decision methodology changes significantly thescope of the problem and introduces a new concept: the balance between optimal choice of the rolled slabs and possible destinations for shuffled slabs which means it must weigh the choice of the slab to be rolled engaged with a low cost shuffle operation for the slabs that are above the chosen slab. This nonlinear model is linearized through specific modeling techniques and solved by integer linear programming. Thus, this work shows a reduction in average handling time (TMM) from 5 minutes per rolled slab found in the literature, to less than 4 minutes. Finally, the proposed model encourages the construction of a management tool that can solve the SSS problem in practical daily situations through operating costs reduction as a payback of investment in this tool.

Submitted by Pablo Aguiar De Maio (pabloamaio@outlook.com) on 2015-09-10T19:50:43Z No. of bitstreams: 1 Pablo Aguiar De Maio - Dissertação - Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo.pdf: 2233029 bytes, checksum: d3ed48936d09fde216e44fb4d688b47d (MD5) / Approved for entry into archive by Janete de Oliveira Feitosa (janete.feitosa@fgv.br) on 2015-09-25T12:16:10Z (GMT) No. of bitstreams: 1 Pablo Aguiar De Maio - Dissertação - Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo.pdf: 2233029 bytes, checksum: d3ed48936d09fde216e44fb4d688b47d (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-09-28T16:51:14Z (GMT) No. of bitstreams: 1 Pablo Aguiar De Maio - Dissertação - Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo.pdf: 2233029 bytes, checksum: d3ed48936d09fde216e44fb4d688b47d (MD5) / Made available in DSpace on 2015-09-28T16:51:50Z (GMT). No. of bitstreams: 1 Pablo Aguiar De Maio - Dissertação - Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo.pdf: 2233029 bytes, checksum: d3ed48936d09fde216e44fb4d688b47d (MD5) Previous issue date: 2015-07-31 / In this work we present a new numerical method with adaptive stepsize based on the local linearization approach, to integrate stochastic differential equations with additive noise. We also propose a computational scheme that allows efficient implementation of this method, properly adapting the algorithm of Padé with scaling-squaring strategy to compute the exponential of matrices involved. To introduce the construction of this method, we briefly explain what stochastic differential equations are, the mathematics that is behind them, their relevance to the modeling of various phenomena, and the importance of using numerical methods to evaluate this kind of equations. A succinct study of numerical stability is also presented on the following pages. With this dissertation, we intend to introduce the necessary basis for the construction of the new method/scheme. At the end, several numerical experiments are performed to demonstrate, in a practical way, the effectiveness of the proposed method, comparing it with other methods commonly used. / Neste trabalho apresentamos um novo método numérico com passo adaptativo baseado na abordagem de linearização local, para a integração de equações diferenciais estocásticas com ruído aditivo. Propomos, também, um esquema computacional que permite a implementação eficiente deste método, adaptando adequadamente o algorítimo de Padé com a estratégia “scaling-squaring” para o cálculo das exponenciais de matrizes envolvidas. Antes de introduzirmos a construção deste método, apresentaremos de forma breve o que são equações diferenciais estocásticas, a matemática que as fundamenta, a sua relevância para a modelagem dos mais diversos fenômenos, e a importância da utilização de métodos numéricos para avaliar tais equações. Também é feito um breve estudo sobre estabilidade numérica. Com isto, pretendemos introduzir as bases necessárias para a construção do novo método/esquema. Ao final, vários experimentos numéricos são realizados para mostrar, de forma prática, a eficácia do método proposto, e compará-lo com outros métodos usualmente utilizados.