Application of Vector Control to Permanent Magnet Synchronous Motors Using Chaos Control

This paper presents the idea of vector control for permanent magnet synchronous motor (PMSM) based on chaos theorem, using chaos controller. PMSM will demonstrate chaotic phenomena when its parameters fall into a certain area. To achieve this aim, the sub-system of controller has been designed by considering block diagram structure of vector control for PMSM and by applying the setting of Lyapunov exponents method. Also, asymptotical stability of closed loop system with given controller is shown, using the direct Lyapunov method. The performance of designed controller in chaotic mode is compared with conventional vector control methods. Also, the normal mode for PMSM is considered and the performance of controller is compared. Simulation results indicate that not only does this controller eliminate the chaos in chaotic mode and have good performance but also is able to control the system in normal mode by using almost the smaller control signal effort

Evaluación del Efecto de un Retardo y una No Linealidad en Sistemas con Comportamiento Caótico Utilizando Exponentes de Lyapunov

Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis.Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior.Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed.Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system.Language: English  Contexto: Al ser los sistemas realimentados muy comunes y ampliamente usados, se han desarrollado estudios de las características estructurales bajo las cuales se genera comportamiento caótico. Estos pueden ser separados en un sistema no lineal y un sistema lineal por lo menos de tercer orden. Se han usado métodos como la función descriptiva para su análisis.Método: Se propone un sistema realimentado a partir de un sistema lineal, un sistema no lineal y un retardo, con el fin de evaluar su comportamiento utilizando los exponentes de Lyapunov. Se evalúa con tres diferentes sistemas lineales, diferentes valores del retardo y diferentes valores para los parámetros de una característica no lineal, buscando alcanzar un comportamiento caótico.Resultados: Se realizaron cien experimentos para cada uno de los tres sistemas cambiando el valor de algunos parámetros evaluando la influencia de los mismos en la dinámica del sistema. Se realizan y analizan gráficas de contorno que relacionan estos parámetros con el máximo exponente de Lyapunov.Conclusiones: A pesar que la no linealidad es una condición para que exista caos, esto no implica que cualquier característica no lineal genera un sistema caótico, esto se evidencia en las gráficas de contorno mostrando las transiciones entre comportamiento caótico y no caótico del sistema realimentado.Idioma: Inglé

Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications

Taming Crowded Visual Scenes

Computer vision algorithms have played a pivotal role in commercial video surveillance systems for a number of years. However, a common weakness among these systems is their inability to handle crowded scenes. In this thesis, we have developed algorithms that overcome some of the challenges encountered in videos of crowded environments such as sporting events, religious festivals, parades, concerts, train stations, airports, and malls. We adopt a top-down approach by first performing a global-level analysis that locates dynamically distinct crowd regions within the video. This knowledge is then employed in the detection of abnormal behaviors and tracking of individual targets within crowds. In addition, the thesis explores the utility of contextual information necessary for persistent tracking and re-acquisition of objects in crowded scenes. For the global-level analysis, a framework based on Lagrangian Particle Dynamics is proposed to segment the scene into dynamically distinct crowd regions or groupings. For this purpose, the spatial extent of the video is treated as a phase space of a time-dependent dynamical system in which transport from one region of the phase space to another is controlled by the optical flow. Next, a grid of particles is advected forward in time through the phase space using a numerical integration to generate a flow map . The flow map relates the initial positions of particles to their final positions. The spatial gradients of the flow map are used to compute a Cauchy Green Deformation tensor that quantifies the amount by which the neighboring particles diverge over the length of the integration. The maximum eigenvalue of the tensor is used to construct a forward Finite Time Lyapunov Exponent (FTLE) field that reveals the Attracting Lagrangian Coherent Structures (LCS). The same process is repeated by advecting the particles backward in time to obtain a backward FTLE field that reveals the repelling LCS. The attracting and repelling LCS are the time dependent invariant manifolds of the phase space and correspond to the boundaries between dynamically distinct crowd flows. The forward and backward FTLE fields are combined to obtain one scalar field that is segmented using a watershed segmentation algorithm to obtain the labeling of distinct crowd-flow segments. Next, abnormal behaviors within the crowd are localized by detecting changes in the number of crowd-flow segments over time. Next, the global-level knowledge of the scene generated by the crowd-flow segmentation is used as an auxiliary source of information for tracking an individual target within a crowd. This is achieved by developing a scene structure-based force model. This force model captures the notion that an individual, when moving in a particular scene, is subjected to global and local forces that are functions of the layout of that scene and the locomotive behavior of other individuals in his or her vicinity. The key ingredients of the force model are three floor fields that are inspired by research in the field of evacuation dynamics; namely, Static Floor Field (SFF), Dynamic Floor Field (DFF), and Boundary Floor Field (BFF). These fields determine the probability of moving from one location to the next by converting the long-range forces into local forces. The SFF specifies regions of the scene that are attractive in nature, such as an exit location. The DFF, which is based on the idea of active walker models, corresponds to the virtual traces created by the movements of nearby individuals in the scene. The BFF specifies influences exhibited by the barriers within the scene, such as walls and no-entry areas. By combining influence from all three fields with the available appearance information, we are able to track individuals in high-density crowds. The results are reported on real-world sequences of marathons and railway stations that contain thousands of people. A comparative analysis with respect to an appearance-based mean shift tracker is also conducted by generating the ground truth. The result of this analysis demonstrates the benefit of using floor fields in crowded scenes. The occurrence of occlusion is very frequent in crowded scenes due to a high number of interacting objects. To overcome this challenge, we propose an algorithm that has been developed to augment a generic tracking algorithm to perform persistent tracking in crowded environments. The algorithm exploits the contextual knowledge, which is divided into two categories consisting of motion context (MC) and appearance context (AC). The MC is a collection of trajectories that are representative of the motion of the occluded or unobserved object. These trajectories belong to other moving individuals in a given environment. The MC is constructed using a clustering scheme based on the Lyapunov Characteristic Exponent (LCE), which measures the mean exponential rate of convergence or divergence of the nearby trajectories in a given state space. Next, the MC is used to predict the location of the occluded or unobserved object in a regression framework. It is important to note that the LCE is used for measuring divergence between a pair of particles while the FTLE field is obtained by computing the LCE for a grid of particles. The appearance context (AC) of a target object consists of its own appearance history and appearance information of the other objects that are occluded. The intent is to make the appearance descriptor of the target object more discriminative with respect to other unobserved objects, thereby reducing the possible confusion between the unobserved objects upon re-acquisition. This is achieved by learning the distribution of the intra-class variation of each occluded object using all of its previous observations. In addition, a distribution of inter-class variation for each target-unobservable object pair is constructed. Finally, the re-acquisition decision is made using both the MC and the AC

Studies and implementations of chaotic dynamics using reconfigurable analog devices

Orientador: Marconi Kolm MadridDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho teve como principal objetivo estudar a tecnologia baseada em dispositivos Field Programmable Analog Arrays (FPAAs) e identificar os benef'icios quanto ao seu uso em aplicações de identificação de fenômenos inerentes aos sistemas dinâmicos não-lineares, tais como bifurcações e caos. Esses dispositivos permitem que diferentes tipos de circuitos possam ser implementados sem a necessidade de alteração da topologia do circuito, ou seja, existe a possibilidade de que os sistemas possam ser reconfigurados em tempo de execução à medida que novas alterações sejam necessárias. Com base na Teoria do Caos e na Teoria de Sistemas de Controle, foi implementado o sistema conhecido como Circuito de Chua, que serviu para demonstrar os ganhos que se podem obter com o uso da abordagem proposta quando aplicada ao estudo de sistemas dinâmicos operando no caos em relação às técnicas consideradas mais convencionais. Resultados obtidos pela análise de séries temporais de sinais adquiridos, comprovam a grande eficiência dessa abordagem quanto ao tempo de desenvolvimento e ao tempo para a obtenção dos resultados em comparação com implementações de modelos dinâmicos bastante conhecidos na literatura em relação às implementações dos mesmos em computadoresAbstract: This work had as main objective to study the technology based on Field Programmable Analog Arrays (FPAAs) devices and to identify the benefits to use these devices in applications of identification of inherent phenomena to the nonlinear dynamic systems as bifurcations and chaos. These devices allow that different types of circuits can be implemented without the necessity of alteration of the topology of the circuit, that is, the systems implemented in the FPAA can be reconfigured in execution when new alterations are necessary. On the basis of the Chaos Theory and in the Control Systems Theory, was implemented the system known as Chua¿s Circuit which served to demonstrate the profits that can be gotten with the use of the boarding proposal when applied to the study of dynamic systems operating in chaos in relation to the considered techniques conventional. Gotten results, for the analysis of time series of acquired signals, prove the great efficiency of this boarding in the time of development and the time for obtain the results when comparing implementations of dynamic models sufficiently known in literature in relation with the implementations of the same ones in digital computersMestradoAutomaçãoMestre em Engenharia Elétric

Máquina de aprendizagem extrema com otimização por exame de partículas aplicada à previsão de séries temporais

Resumo: Identificação de sistemas é uma área interessada em obter modelos matemáticos de sistemas desconhecidos baseados em dados de leituras sequenciais do sistema. Diversas aplicações do mundo real não tem sua dinâmica completamente compreendida ou são complexas para serem modeladas, para estes casos, a identificação de sistemas é uma ferramenta eficiente para modelagem e previsão. Este trabalho aborda redes neurais artificiais, mais precisamente, redes neurais com uma única camada de neurônios ocultos, em inglês, Single Layer Feedforward Neural Network (SLFN), para previsão de séries temporais. Um algoritmo de aprendizagem proposto recentemente chamado de Máquina de Aprendizagem Extrema, em inglês, Extreme Learning Machine (ELM), é introduzido para a tarefa de aprendizagem da rede neural. O algoritmo ELM é baseado na matriz inversa generalizada de Moore-Penrose, que torna o problema um simples sistema linear. No núcleo do algoritmo ELM, duas funções de ativação diferentes serão testadas, sendo que uma delas é uma função de ativação variável. Para alcançar melhores resultados, um método estocástico de otimização do campo da inteligência de enxame chamado de Otimização por Enxame de Partículas, em inglês, Particle Swarm Optimization (PSO), é validado para otimizar os parâmetros do algoritmo ELM. O PSO consiste em modelar as ações de um bando de pássaros procurando por comida, onde cada pássaro é uma partícula, e cada partícula é uma possível solução para o problema. Neste trabalho é proposta uma nova variação do PSO empregando a função gama invertida. Neste contexto, três conjuntos de dados são usados para testar os algoritmos, um é a leitura de uma fornalha, e dois são obtidos de equações diferenciais com comportamento caótico. Os modelos obtidos através do algoritmo ELM são então validados através de testes de correlação. As previsões realizadas pelo algoritmo ELM são promissoras para todos os conjuntos de dados, revelando que a combinação do algoritmo PSO com o ELM é uma eficiente forma de identificação de sistemas

Computational Intelligence and Complexity Measures for Chaotic Information Processing

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value

Low-frequency noise in downscaled silicon transistors: Trends, theory and practice

By the continuing downscaling of sub-micron transistors in the range of few to one deca-nanometers, we focus on the increasing relative level of the low-frequency noise in these devices. Large amount of published data and models are reviewed and summarized, in order to capture the state-of-the-art, and to observe that the 1/area scaling of low-frequency noise holds even for carbon nanotube devices, but the noise becomes too large in order to have fully deterministic devices with area less than 10nm×10nm. The low-frequency noise models are discussed from the point of view that the noise can be both intrinsic and coupled to the charge transport in the devices, which provided a coherent picture, and more interestingly, showed that the models converge each to other, despite the many issues that one can find for the physical origin of each model. Several derivations are made to explain crossovers in noise spectra, variable random telegraph amplitudes, duality between energy and distance of charge traps, behaviors and trends for figures of merit by device downscaling, practical constraints for micropower amplifiers and dependence of phase noise on the harmonics in the oscillation signal, uncertainty and techniques of averaging by noise characterization. We have also shown how the unavoidable statistical variations by fabrication is embedded in the devices as a spatial “frozen noise”, which also follows 1/area scaling law and limits the production yield, from one side, and from other side, the “frozen noise” contributes generically to temporal 1/f noise by randomly probing the embedded variations during device operation, owing to the purely statistical accumulation of variance that follows from cause-consequence principle, and irrespectively of the actual physical process. The accumulation of variance is known as statistics of “innovation variance”, which explains the nearly log-normal distributions in the values for low-frequency noise parameters gathered from different devices, bias and other conditions, thus, the origin of geometric averaging in low-frequency noise characterizations. At present, the many models generally coincide each with other, and what makes the difference, are the values, which, however, scatter prominently in nanodevices. Perhaps, one should make some changes in the approach to the low-frequency noise in electronic devices, to emphasize the “statistics behind the numbers”, because the general physical assumptions in each model always fail at some point by the device downscaling, but irrespectively of that, the statistics works, since the low-frequency noise scales consistently with the 1/area law

Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms

Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 177-200).The chaotic behavior of dynamical systems underlies the foundations of statistical mechanics through ergodic theory. This putative connection is made more concrete in Part I of this thesis, where we show how to quantify certain chaotic properties of a system that are of relevance to statistical mechanics and kinetic theory. We consider the motion of a particle trapped in a double-well potential coupled to a noisy environment. By use of the classic Langevin and Fokker-Planck equations, we investigate Kramers' escape rate problem. We show that there is a deep analogy between kinetic rate theory and stochastic chaos, for which we propose a novel definition. In Part II, we develop techniques based on Volterra series modeling and Bayesian non-linear filtering to distinguish between dynamic noise and measurement noise. We quantify how much of the system's ergodic behavior can be attributed to intrinsic deterministic dynamical properties vis-a-vis inevitable extrinsic noise perturbations.by Zhi-De Deng.M.Eng.and S.B