This dissertation examines the effects of instantaneous constant-power loads (CPLs) on power converters. These CPLs are prevalent in distributed power architectures and are also present in certain motor-drive applications. CPLs introduce a destabilizing nonlinear effect on power converters through an inverse voltage term that leads to significant oscillations in the main bus voltage or to its collapse. Boundary control is studied in order to stabilize dc-dc converters with instantaneous CPLs. The three basic topologies are studied: buck, boost, and buck-boost. Converter dynamics are analyzed in both switching states and the various operating regions of switch interaction with a first-order switching surface are identified. The analysis reveals important characteristics of CPLs. For non-minimum phase converters, in order to avoid issues related with the fact that the closed-loop state-dependent switching function is undefined on the switching surface, reflective mode solutions to both converter systems are defined in the sense of Filippov. Sufficient conditions for large-signal stability of the closed loop converter operating points are established. It is shown that first-order switching surfaces with negative slopes achieve large-signal stability, while positive slopes lead to instability. In particular, for the boost converter it is illustrated via simulations and experiments that positive slopes may lead to another closed-loop limit cycle. It is also shown that instability as well as system-stalling, which is termed the invariant-set problem, may still occur in reflective mode. However, a hysteresis band that contains the designed boundary may be used to prevent system-stalling, and also allow for a practical implementation of the controller by avoiding chattering. Regulation is also achieved. The dynamic behavior of single-phase full-wave uncontrolled rectifiers with instantaneous CPLs is also explored. Stable operation is shown to be dependent on initial condition and circuit parameters, which must fall within reasonable ranges that validate a CPL model. A necessary condition for stable operation of the rectifier system is thus derived. Furthermore, input and output characteristics of the rectifier with a CPL are investigated, and comparisons are made with the resistive case. A more complete model for the rectifier system that incorporates line-voltage distortion is also utilized to study the rectifier system. Simulations and experimental results are included for verification. / text

Many high-dimensional time-varying signals can be modeled as a sequence of noisy nonlinear observations of a low-dimensional dynamical process. Given high-dimensional observations and a distribution describing the dynamical process, we present a computationally inexpensive approximate algorithm for estimating the inverse of this mapping. Once this mapping is learned, we can invert it to construct a generative model for the signals. Our algorithm can be thought of as learning a manifold of images by taking into account the dynamics underlying the low-dimensional representation of these images. It also serves as a nonlinear system identification procedure that estimates the inverse of the observation function in nonlinear dynamic system. Our algorithm reduces to a generalized eigenvalue problem, so it does not suffer from the computational or local minimum issues traditionally associated with nonlinear system identification, allowing us to apply it to the problem of learning generative models for video sequences.

This thesis proposes a novel method for locating a p-dimensional invariant torus of an n-dimensional map. A set of non-linear equations is formulated and solved using the Newton-Raphson scheme. The method requires a set of sampled points on a guess invariant torus. An interpolant is passed through these points to compute the pointwise shift on the invariant torus, which is used to formulate the equation of invariance for the torus under the given map. The principal application of this method is to locate invariant tori of continuous systems. These tori occur for continuous dynamical systems having quasiperiodic orbits in state space. The discretization of the continuous system in terms of a map is accomplished in terms of its flow function. Results for one-dimensional invariant tori in two and three-dimensional state space and for two-dimensional invariant tori in three and four-dimensional maps are presented. / Master of Science

Identification of thermoacoustic dynamics that exhibit limit cycle behavior is needed to gain a better intuitive feel of the system, to design complex control strategies, and to validate modeling efforts. Limit cycle oscillations arise in thermoacoustic systems due to the coupling between a nonlinear heat release process and the acoustic dynamics of the combustor. This response arises in lean premixed gaseous power generating turbines and is a concern due to the detrimental effect of the pressure oscillations on the structural integrity of the combustor. Due to the volatile environment intrinsic in the combustor, multiple sensing apparatuses are not available. Therefore, in the current study, an identification approach is assessed considering only a single output from the thermoacoustic system. As a means to further investigate the thermoacoustic limit cycle behavior, a scaled version of the industry-based turbine was constructed. By anchoring a flame halfway from end-to-end of a closed-open tube, a similar nonlinear response is achieved. A harmonic balance technique that linearly incorporates the nonlinearity is developed which uses frequency entrainment to offer sufficient information for the identification. Its validity is assessed on a model, which is based on known dynamics of the thermoacoustic system. The structure of the identification algorithm is based on a two-mode acoustic model with both dynamics and nonlinearity in the feedback loop. The limitations of using only a two-mode identification structure for a system with more than two modes is discussed as well as future efforts that may alleviate this problem. / Master of Science

No / The key equations of BiCGStab are summarised to show its connections with Pade and vector-Pade approximation. These considerations lead naturally to stabilised vector-Pade approximation of a vector-valued function (VPAStab), and an algorithm for the acceleration of convergence of a linearly generated sequence of vectors. A generalisation of this algorithm for the acceleration of convergence of a nonlinearly generated system is proposed here, and comparative numerical results are given.

The linear source-filter model (LSFM) has been used as a primary model for speech processing since 1960 when G. Fant presented acoustic speech production theory. It assumes that the source of voiced speech sounds, glottal flow, is independent of the filter, vocal tract. However, acoustic simulations based on the physical speech production models show that, especially when the fundamental frequency (F0) of source harmonics approaches to the first formant frequency (F1) of vocal tract filter, the filter has significant effects on the source due to the nonlinear coupling between them. In this thesis, as an alternative to linear source-filter model, nonlinear interactive source-filter models are proposed for voiced speech. This thesis has two parts, in the first part, a framework for the coupling of the source and the filter is presented. Then, two interactive system models are proposed assuming that glottal flow is a quasi-steady Bernoulli flow and acoustics in vocal tract is linear. In these models, instead of glottal flow, glottal area is used as a source for voiced speech. In the proposed interactive models, the relation between the glottal flow, glottal area and vocal tract is determined by the quasi-steady Bernoulli flow equation. It is theoretically shown that linear source-filter model is an approximation of the nonlinear models. Estimation of ISFM&rsquo / s parameters from only speech signal is a nonlinear blind deconvolution problem. The problem is solved by a robust method developed based on the acoustical interpretation of the systems. Experimental results show that ISFMs produce source-filter coupling effects seen in the physical simulations and the parameter estimation method produce always stable and better performing models than LSFM model. In addition, a framework for the incorporation of the source-filter interaction into classical source-filter model is presented. The Rosenberg source model is extended to an interactive source for voiced speech and its performance is evaluated on a large speech database. The results of the experiments conducted on vowels in the database show that the interactive Rosenberg model is always better than its noninteractive version. In the second part of the thesis, LSFM and ISFMs are compared by using not only the speech signal but also HSV (High Speed Endocopic Video) of vocal folds in a system identification approach. In this case, HSV and speech are used as a reference input-output data for the analysis and comparison of the models. First, a new robust HSV processing algorithm is developed and applied on HSV images to extract the glottal area. Then, system parameters are estimated by using a modified version of the method proposed in the first part. The experimental results show that speech signal can contain some harmonics of the fundamental frequency of the glottal area other than those contained in the glottal area signal. Proposed nonlinear interactive source-filter models can generate harmonics components in speech and produce more realistic speech sounds than LSFM.

Le travail de la thèse traite le problème de suivi de trajectoires des systèmes non linéaires incertains,dont le modèle nominal est construit à l’aide d’un système flou TS (Takagi-Sugeno) de type-2. Cedernier, exploite les modèles locaux du système obtenus par linéarisation autour de certains pointsde fonctionnement. La commande développée est basée sur les modes glissants d’ordre deux avecSuper-Twisting. Nous avons proposé deux systèmes flous type-2 adaptatifs, qui ont comme uniqueentrée la surface de glissement, pour résoudre le problème du calcul de la valeur optimale des gainsde la commande. Des résultats de simulation ont permis de comparer les performances de l’approcheproposée avec la méthode classique. Ensuite, nous avons introduit le concept de l’intégral sliding modepour imposer à priori le temps d’arrivée sur la surface de glissement. Les approches proposées sontgénéralisées aux cas des systèmes multivariables. Plusieurs résultats par simulation et implémentationen temps réel sont présentés pour illustrer les performances des approches développées / This work deals with a fuzzy tracking control design for uncertain nonlinear dynamic system withexternal disturbances and using a TS (Takagi-Sugeno) fuzzy model description. The control is basedon the Super-Twisting algorithm, which is among of second order sliding mode control. Moreover, twoadaptive fuzzy type-2 systems have been introduced to generate the two Super-Twisting signals toavoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upperbounds. These adaptive fuzzy type-2 systems has only one input : the sliding surface, and one output :the optimale values of the control gains, which are hard to compute with the original algorithm.Simulation results are obtained in order to compare the performances of the proposed method tothat given by Levant. Then, we have introduced the integral sliding mode concept to impose inadvance the convergence time and the arrival on the sliding surface. The proposed approaches aregeneralized to the case of multivariable systems. Several results in simulation and in real time usinga benchmark are obtained to validate and to confirm the performances of our contributions.

Ce doctorat est centré sur trois objectifs principaux. Le premier est le développement d’une stratégie de construction de retours d’état sans terme à retard qui stabilisent globalement asymptotiquement uniformément l’origine de systèmes variant dans le temps non linéaires ayant un retard distribué dans la commande. Le deuxième est l’adaptation de la célèbre technique de construction de lois de commande appelée backstepping au cas de systèmes non linéaires de forme feedback ayant dans la commande un retard ponctuel constant. Le troisième est la résolution d’un problème de stabilisation pratique pour une famille de systèmes non linéaires ayant un retard ponctuel dans l’entrée constant et ayant des commandes échantillonnées dont les instants d’échantillonnage dépendent de la valeur de la variable d’état du système. Chacun de ces trois objectifs est atteint au moyen de technique qui utilisent certains opérateurs d’un nouveau type. Des résultats de robustesse de type Input-to-State-Stability sont établis au moyen de fonctionnelles de Lyapunov-Krasovskii. / This PhD thesis is focused on three main objectives. The first goal is to develop a method of construction of state feedbacks without retarded terms that render the origin of timevarying nonlinear systems with a distributed input delay globally uniformly asymptotically stable.The second objective is the adaptation of the celebrated technique of construction of state feedbacks called ’backstepping’ to the case of nonlinear systems in feedback form with a pointwise constant delay in the input. The third aim of this thesis is to solve a problem of practical stabilization for a family of nonlinear systems with sampled retarded state feedbacks whose sampling instants depend on the value of the state variable of the system. Each of these three goals relies on the introduction of operators of a new type. Robustness results of Input-to-State-Stability type are established by using Lyapunov-Krasovskii functionals.

Submitted by João Rafael Alves null (joao.rafa.alves@gmail.com) on 2017-03-21T02:27:39Z No. of bitstreams: 1 Dissertação_15mar2017_Final.pdf: 12263333 bytes, checksum: d28726f4d986b72238323c581149a148 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-03-22T14:09:27Z (GMT) No. of bitstreams: 1 alves_jr_me_bauru.pdf: 12263333 bytes, checksum: d28726f4d986b72238323c581149a148 (MD5) / Made available in DSpace on 2017-03-22T14:09:27Z (GMT). No. of bitstreams: 1 alves_jr_me_bauru.pdf: 12263333 bytes, checksum: d28726f4d986b72238323c581149a148 (MD5) Previous issue date: 2017-01-31 / Quatro configurações de circuito elétrico são estudadas como opções de ligação em dispositivos eletromecânicos: puramente resistivo, RL em série, RLC em série e RLC em série com indutância de variação não linear. Respostas em frequência, diagramas de bifurcação, históricos no tempo, planos de fase, mapas de Poincaré e espectros de frequência são utilizados nas análises. Os três circuitos lineares explorados na dissertação revelam algumas diferenças em termos da transmissibilidade de deslocamento. O sistema com circuito puramente resistivo tem as mesmas características de um sistema puramente mecânico e viscosamente amortecido, mas a resistência elétrica e o fator de amortecimento viscoso se relacionam de forma inversamente proporcional. As respostas dos circuitos RL e RLC, ambos em série, apresentam aspectos mais comportados. A principal diferença entre os sistemas com circuitos RL e RLC em série está principalmente na transmissibilidade para baixas frequências. Embora com uma pequena diferença, a transmissibilidade do sistema com circuito RLC é menor do que a do sistema com circuito RL, para baixas frequências. Para o sistema não linear, nas respostas em frequência e diagramas de bifurcação percebem-se regiões de resposta desordenada para valores baixos de resistência elétrica em determinadas faixas de frequência. Com a análise das respostas, notam-se as presenças dos comportamentos dinâmicos periódico, quasi-periódico e caótico. Para valores baixos de resistência elétrica, a escolha do valor da capacitância é de suma importância para a classificação do tipo de comportamento dinâmico do sistema. Pequenas variações do valor da capacitância representam saltos enormes da dinâmica do sistema. Muitas vezes, mesmo dentro do campo de tolerância especificado pelos fornecedores de componentes elétricos, o valor da capacitância pode resultar em comportamentos caóticos indesejados. / Four configurations of electrical circuit are studied as options of electromechanical devices: purely resistive, RL in series, RLC in series e RLC in series with nonlinear inductance. Frequency responses, bifurcation diagrams, time series, phase plane, Poincaré maps and frequency spectrum are used in analysis. The three linear circuits explored in this dissertation reveal some differences in terms of displacement transmissibility. The system with purely resistive circuit has the same characteristics of a purely viscous damped, but the electrical resistance and the damping factor are inversely proportional. Responses of circuits RL and RLC, both in series, present behaving aspects. The main difference between the systems with RL and RLC circuits is related to the transmissibility for low frequencies. Although with a small difference, the transmissibility of RLC circuit system is smaller than the RL circuit system, for low frequencies. For the nonlinear system, it is possible to perceive disordered response regions for small values of electrical resistance on certain frequency bands. After response analisys, it is noted the presence of periodic, quasi-periodic and chaotic behaviors. For small values of electrical resistance, the choice of capacitance value is very important to determine the type of the dynamic behavior. Small differences of the capacitance values mean significant changes in the system dynamics. It is not rare that even inside the tolerance of electrical components, the capacitance value can result in chaotic behaviors.

This thesis investigates Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closed-loop time-delay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the time-delay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of time-delay systems. Furthermore, the method of Saturated-Root Locus (S-RL) is extended to nonlinear time-delay systems. It turns out that, in a time-delay system, S-RL always terminates prematurely as opposed to a delay-free system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. The impact of increasing the time-delay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the efficacy of the approach.