This thesis focuses on matrix generalizations of Hurwitz polynomials. A real polynomial with all its roots in the open left half plane of the complex plane is called a Hurwitz polynomial. The study of these Hurwitz polynomials has a long and abundant history, which is associated with the names of Hermite, Routh, Hurwitz, Liénard, Chipart, Wall, Gantmacher et al. The direct matricial generalization of Hurwitz polynomials is naturally defined as follows: A p by p matrix polynomial F is called a Hurwitz matrix polynomial if the determinant of F is a Hurwitz polynomial. Recently, Choque Rivero followed another line of matricial extensions of the classical Hurwitz polynomial, called matrix Hurwitz type polynomials. However, the notion “matrix Hurwitz type polynomial” is still irrelative to “Hurwitz matrix polynomial” due to the totally unclear zero location of the former notion. So the main goal of this thesis is to discover the relation between the two notions “matrix Hurwitz-type polynomials” and “Hurwitz matrix polynomials' and provide some criteria to identify Hurwitz matrix polynomials. The central idea is to determine the inertia triple of matrix polynomials in terms of some related matrix sequences. Suppose that F is a p by p matrix-valued polynomial of degree n. We split F into the odd part and the even part, which allow us to introduce an essential rational matrix function of right type G. From the matrix coefficients of the Laurent series of G we construct the (n-1)-th extended sequence of right Markov parameters (SRMP) of F. Then we show that the inertia triple of F can be characterized by a combination of the inertia triples of two block Hankel matrices generated by the (n-1)-th SRMP of F and the number of zeros (counting for multiplicities) of greatest right common divisors of the even part and the odd part of F lying on the left half of the real axis. By an analogous approach we also obtain the dual results for the inertia triple of F in terms of the SLMP of F. Then we demonstrate that F is a Hurwitz matrix polynomial of degree n if and only if the (n − 1)-th SRMP (resp. SLMP) of F is a Stieltjes positive definite sequence. On this account, the two notions “Hurwitz matrix polynomials” and “matrix Hurwitz type polynomials” are equivalent. In addition, we investigate quasi-stable matrix polynomials appearing in the theory of stability, which contain Hurwitz matrix polynomials as a special case. We seek a correspondence between quasi-stable matrix polynomials, Stieltjes moment problems and multiple Nevanlinna-Pick interpolation in the Stieltjes class. Accordingly, we prove that F is a quasi-stable matrix polynomial if and only if the (n − 1)-th SRMP (resp. SLMP) of F is a Stieltjes non-negative definite extendable sequence and the zeros of right (resp. left) greatest common divisors of the even part and the odd part of F are located on the left half of the real axis.:1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Matrix polynomials and greatest common divisors. . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Greatest common divisors of matrix polynomials . . . . . . . . . . . . . . . . . . . . . 8 3 Matrix sequences and their connection to truncated matricial moment problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Matrix fraction description and some related topics . . . . . . . . . . . . . . . . . . 19 4.1 Realization of Matrix fraction description from Markov parameters . . . . . . . 19 4.2 The interrelation between Hermitian transfer function matrices and monic orthogonal system of matrix polynomials . . . . . . . . . . . . . . . . . . . . . . . .27 5 The Bezoutian of matrix polynomials and the inertia problem of matrix polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 5.2 The Anderson-Jury Bezoutian matrices in connection to special transfer function matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 6 Para-Hermitian strictly proper transfer function matrices and their related monic Hurwitz matrix polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7 Solution of matricial Routh-Hurwitz problems in terms of the Markov pa- rameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8 Matrix Hurwitz type polynomials and some related topics . . . . . . . . . . . . . . 67 9 Hurwitz matrix polynomials and some related topics . . . . . . . . . . . . . . . . . . 77 9.1 Hurwitz matrix polynomials, Stieltjes positive definite sequences and matrix Hurwitz type polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 9.2 S -system of Hurwitz matrix polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . 82 10 Quasi-stable matrix polynomials and some related topics . . . . . . . . . . . . 95 10.1 Particular monic quasi-stable matrix polynomials and Stieltjes moment problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 10.2 Particular monic quasi-stable matrix polynomials and multiple Nevanlinna- Pick interpolation in the Stieltjes class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101 10.3 General description of monic quasi-stable matrix polynomials . . . . . . . . .104 List of terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 List of notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Selbständigkeitserklärung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

L’objectif de cette thèse est de fournir une approche générale permettant d’aborder les problèmes de contrôle aéroélastique.Tout d’abord, un modèle d’aile oscillante est développé afin de rendre compte des phénomènes d’hystérésis des charges aérodynamiques et de décrochage dynamique qui peut être observé, particulièrement à fort angles d’attaque ou à faible nombre de Reynolds. Le modèle est alors entraîné et comparé avec succès aux résultats expérimentaux obtenus pour une aile NACA 0018. Ce modèle, comme de nombreux modèles aérodynamiques, souffre d’une complexité inhérente et de non-linéarités qui rendent son analyse et son contrôle complexes. Par conséquent, le modèle a été modifié afin d’inclure les non-linéarités dans une formulation polytopique aux paramètres incertains. S’appuyant sur la théorie de la commande linéaire quadratique et utilisant les inégalités des matrices linéaires, plusieurs théorèmes sont développés, considérant les saturations qui sont un problème majeur et récurent de la dynamique du vol. Les théorèmes sont alors appliqués avec succès au cas du stall flutter en présence de saturations en position et en vitesse. / This thesis aims at providing a general approach for aeroelastic control. First, an aeroelastic model of an oscillating wing is developed to capture the phenomena of hysteresis of aerodynamic load and dynamic stall which can be observed at low Reynolds number or large angles of attack. The model is then trained and successfully compared to experimental data for a NACA 0018 wing. This model, like many aeroelastic models, suffers from its inherent complexity and nonlinearities which make its analysis and control challenging. Consequently, the set of equations is conveniently manipulated to encapsulate the nonlinearities in a polytopic formulation with unknown parameters. Then, based on linear quadratic regulation theory and using framework of linear matrix inequalities, several theorems are developed considering saturations which are a major and recurrent issue in flight control. The theorems are then successfully applied to solve the problem of stall flutter in presence of rate and magnitude saturations.

This report focuses on the utilisation of flight mechanics in the context of aircraftconceptual design to assess stability, control, and motion characteristics. The pri-mary objective is to acquire the equations of motion and implement longitudinalstability and control criteria using Pacelab Aircraft Preliminary Design 8.1, a com-mercial software tool. The equations and criteria employed in this study are derivedfrom an extensive review of relevant literature.By incorporating a dedicated Flight Mechanics chapter within the software, it be-comes possible to evaluate aircraft concepts under varying conditions. To ensureaccuracy and validity, DATCOM+ and OpenVSP were employed for testing andverification purposes.The key aspects covered in this report include flight mechanics, its implementationin Pacelab APD 8.1, determination of aerodynamic derivatives, formulation of equa-tions of motion, and their application to the B747 aircraft model. The emphasis liesin assessing longitudinal stability and control, including specific characteristics suchas the phugoid and short period modes.This report provides valuable insights into the integration of flight mechanics withinthe Pacelab APD 8.1 software for aircraft conceptual design. The results contributeto a better understanding of stability and control parameters and their impact onaircraft performance.

Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network.

No description available.

The study of nonlinear dynamical systems via the spectrum of the Koopman operator has emerged as a paradigm shift, from the Poincaré's geometric picture that centers the attention on the evolution of states, to the Koopman operator's picture that focuses on the evolution of observables. The Koopman operator-theoretic framework rests on the idea of lifting the states of a nonlinear dynamical system to a higher dimensional space; these lifted states are referred to as the Koopman eigenfunctions. To determine the Koopman eigenfunctions, one performs a nonlinear transformation of the states by relying on the so-called observables, that is, scalar-valued functions of the states. In other words, one executes a change of coordinates from the state space to another set of coordinates, which are denominated Koopman canonical coordinates. The variables defined on these intrinsic coordinates will evolve linearly in time, despite the underlying system being nonlinear. Since the Koopman operator is linear, it is natural to exploit its spectral properties. In fact, the theory surrounding the spectral properties of linear operators has well-known implications in electric power systems. Examples include small-signal stability analysis and direct methods for transient stability analysis based on the Lyapunov function. From the applications' standpoint, this framework based on the Koopman operator is attractive because it is capable of revealing linear and nonlinear modes by only applying well-established tools that have been developed for linear systems. With the challenges associated with the high-dimensionality and increasing uncertainties in the power systems models, researchers and practitioners are seeking alternative modeling approaches capable of incorporating information from measurements. This is fueled by an increasing amount of data made available by the wide-scale deployment of measuring devices such as phasor measurement units and smart meters. Along these lines, the Koopman operator theory is a promising framework for the integration of data analysis into our mathematical knowledge and is bringing an exciting perspective to the community. The present dissertation reports on the application of the Koopman operator for identification, estimation, and control of electric power systems. A dynamic state estimator based on the Koopman operator has been developed and compares favorably against model-based approaches, in particular for centralized dynamic state estimation. Also, a data-driven method to compute participation factors for nonlinear systems based on Koopman mode decomposition has been developed; it generalizes the original definition of participation factors under certain conditions. / PHD / Electric power systems are complex, large-scale, and given the bidirectional causality between economic growth and electricity consumption, they are constantly being expanded. In the U.S., some of the electric power grid facilities date back to the 1880s, and this aging system is operating at its capacity limits. In addition, the international pressure for sustainability is driving an unprecedented deployment of renewable energy sources into the grid. Unlike the case of other primary sources of electric energy such as coal and nuclear, the electricity generated from renewable energy sources is strongly influenced by the weather conditions, which are very challenging to forecast even for short periods of time. Within this context, the mathematical models that have aided engineers to design and operate electric power grids over the past decades are falling short when uncertainties are incorporated to the models of such high-dimensional systems. Consequently, researchers are investigating alternative data-driven approaches. This is not only motivated by the need to overcome the above challenges, but it is also fueled by the increasing amount of data produced by today’s powerful computational resources and experimental apparatus. In power systems, a massive amount of data will be available thanks to the deployment of measuring devices called phasor measurement units. Along these lines, the Koopman operator theory is a promising framework for the integration of data analysis into our mathematical knowledge, and is bringing an exciting perspective on the treatment of high-dimensional systems that lie in the forefront of science and technology. In the research work reported in this dissertation, the Koopman operator theory has been exploited to seek for solutions to some of the challenges that are threatening the safe, reliable, and efficient operation of electric power systems.

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.

Orientador: Jose Antenor Pomilio / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-09T17:17:10Z (GMT). No. of bitstreams: 1 Silva_LeonardodeAraujo_D.pdf: 14156071 bytes, checksum: f544bd5c73e51000deee838abcc80fa7 (MD5) Previous issue date: 2007 / Resumo: Nesta tese é introduzida uma nova estratégia de controle que permite a síntese de indutâncias negativas para realização da compensação série de linhas de transmissão. O método, que é baseado na estratégia SDR (Síntese Direta de Reatâncias), opera com realimentação de estados e requer a medição de variáveis locais. Em relação aos métodos tradicionais, usando capacitores, a compensação através de indutância negativa pode ter desempenho superior, pois é possível conseguir sistemas mais estáveis, sem risco de ressonâncias, e com desempenho dinâmico superior, o que permite a realização de outras funções desejáveis, tais como o amortecimento de oscilações eletromecânicas e a compensação de cintilação luminosa. Dada a elevada potência requerida pela aplicação, sugere-se a utilização do Conversor Multinível em Cascata Assimétrico, que apresenta alto rendimento e é capaz de produzir uma tensão de saída de baixo conteúdo harmônico. Para este conversor, foi introduzida uma estratégia de controle que permite uma implementação sem que sejam necessárias fontes CC. Sugere-se também um procedimento para escolha do capacitor de filtragem que permite uma redução da corrente no conversor para uma dada condição de operação. São apresentados alguns estudos sobre a estabilidade da compensação série com indutância negativa. Para a técnica de controle proposta, são realizados estudos de autovalores, que permitem verificar a robustez com variação de parâmetros. Através de simulações, verificasse a estabilidade com a presença de elementos não modelados na planta, como capacitâncias parasitas. Também são apresentados estudos sobre a estabilidade para um modelo de simulação da ressonância subsíncrona, que considera o modelo do gerador e características mecânicas do eixo da turbina. Os resultados obtidos com estes estudos de estabilidade, bem com os resultados experimentais, indicam que a técnica proposta é viável para a aplicação / Abstract: This thesis introduces a new control strategy of realizing negative inductances with static converters for series compensation of transmission lines. The proposed method, which is basedon DRS (Direct Reactance Synthesis) technique, requires state feedback of variables that can be measured locally. The use of negative inductances instead of capacitors may yield performance improvement because there is no risk of resonance and it is possible to obtain higher stability margins and better dynamic performance. Consequently, it is possible to realize some useful functions that are not possible with conventional strategies, just as flicker ompensation and smoothing of electromechanical oscillations. Series compensation requires high power static converters and, due to this, the use of the Asymmetrical Cascaded Multilevel Converters (ACMC) is suggested. This high efficiency power converter is capable of producing a low THD output voltage using less power switches than other topologies. This thesis also introduces a DC control strategy for ACMC, which may allow negative inductance implementation with no DC sources. It is also suggested a design procedure for choosing the filter capacitance that reduces the required current capability of the power converter. Some studies regarding the stability of series compensation with negative inductances were carried on. For the new control strategy, it was possible to perform the eigenvalues analysis, that proved therobustness under some parameters variations. The stability considering elements that were not modeled, just as stray capacitances or generator and turbine shaft, were tested through simulations. The simulations and experimental results corroborate to prove that the control strategy is suitable for this application / Doutorado / Energia Eletrica / Doutor em Engenharia Elétrica

Konsequent betriebener Leichtbau führte und führt weiterhin zu steigender Komplexität in der Blechumformung. Erkenntnisse aus Forschungsaktivitäten zur gezielten Beeinflussung, Regelung und Vollautomatisierung des Tiefziehprozesses konnten jedoch bisher nicht in Großserienpresswerke transferiert werden. Aus diesem Grund wird in dieser Arbeit ein Werkzeugkonzept vorgestellt, welches unter Berücksichtigung der relevanten Randbedingungen eine gezielte lokale Beeinflussung des Umformprozesses ermöglicht. Gleichzeitig gestattet es, mit Hilfe eines neuartigen, optischen Sensorkonzeptes die Geschwindigkeit sowie den Einlaufweg der Platine zu überwachen. Es wird eine methodische Vorgehensweise zur Herstellung von Umformwerkzeugen, auf der neuen Konzeption basierend, beschrieben. Umformsimulationen dienen dabei zur Identifikation von kritischen Bauteilen und deren neuralgischen Zonen. Eine entsprechend angepasste Konstruktion bietet Bauraum für die Implementierung von zusätzlichen Aktuatoren und einem definiert elastischen Einsatz. Abschließende FEM-Analysen mit Volumenmodellen sowie die Kalkulation der Lebensdauer bestätigen eine ausreichende Flexibilität und die erforderliche Dauerfestigkeit. Im Rahmen der experimentellen Analyse konnte eine drastische Verkürzung der Anlaufzeit durch deutlich reduzierten Tuschieraufwand aufgrund der Anpassungsfähigkeit sowie Flexibilität des definiert elastischen Werkzeugkonzeptes nachgewiesen werden. Neben diesem Potential hinsichtlich strukturierter Inbetriebnahmen ermöglicht die Konzeption eine Kompensation von Pressenunterschieden und individuellen Maschinencharakteristika (wie bspw. Stößelverkippungen) wodurch der Transfer von der Einarbeitspresse auf die Produktionsanlage wesentlich weniger Korrekturschleifen hervorruft. Außerdem werden der Qualitätsaufwand (Nachtuschieren) während der laufenden Serienproduktion, Stillstandszeiten und Ausschussquoten stark verringert. Darüber hinaus ergeben sich erweiterte Anwendungsmöglichkeiten bei der Umformung von tailored blanks und aus der Minimierung/Optimierung des Platinenzuschnittes enorme Einsparungs- und Kostenpotentiale. Abschließend werden die Vorteile eines geschlossenen Prozessregelkreises durch die Verknüpfung von Sensorik und Aktorik analysiert. Dabei bestätigt das vorgeschlagene Regelkonzept einer Prozessnachführung die Erhöhung der Prozessstabilität bei schwankenden Prozessparametern durch die gezielte, lokale Verteilung der Flächenpressung. Zuletzt diskutiert der vorliegende Beitrag Transfermöglichkeiten der Verbesserungspotentiale in kommende Serienwerkzeuge vor dem Hintergrund von Kostenrestriktionen und Minimierung des bedientechnischen sowie konstruktiven Aufwandes.