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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Coordinated Variable Structure Switching Attacks for Smart Grid

Liu, Shan 02 October 2013 (has links)
The effective modeling and analysis of large-scale power system disturbances especially those stemming from intentional attack represents an open engineering and research problem. Challenges stem from the need to develop intelligent models of cyber-physical attacks that produce salient disruptions and appropriately describe meaningful cyber-physical interdependencies such that they balance precision, scale and complexity. In our research, we present a foundation for the development of a class of intelligent cyber-physical attacks termed coordinated variable structure switching attacks whereby opponents aim to destabilize the power grid through con- trolled switching sequence. Such switching is facilitated by cyber-attack and corruption of communication channels and control signals of the associated switch(es). We provide methods and theorems to construct such attack models and demonstrate their utility in the simulation of extensive system disturbances. Our proposed class of cyber-physical switching attacks for smart grid systems has the potential to disrupt large-scale power system operation within a short interval of time. Through successful cyber intrusion, an opponent can remotely apply a state- dependent coordinated switching sequence on one or more relays and circuit breakers of a power system to disrupt operation. Existence of this switching vulnerability is dependent on the local structure of the power grid. Variable structure systems theory is employed to effectively model the cyber-physical aspects of a smart grid and determine the existence of the vulnerability and construct the destabilizing switching attack sequence. We illustrate the utility of the attack approach assess its impact on the different power system test cases including the single machine infinite bus power system model and the Western Electricity Coordinating Council (WECC) 3-machine 9-bus system through MATLAB/Simulink and PSCAD simulation environment. The results demonstrate the potential of our approach for practical attack. Moreover, we build on our work in several ways. First, we extend the research to demonstrate an approach to mitigation within the variable structure system frame- work. We demonstrate via small signal analysis how through persistent switching a stable sliding mode can be used to disrupt a dynamical system that seems stable. We also design an approach to vulnerability analysis to assess the feasibility of co-ordinated variable structure switching attacks. Moreover, we study the performance of our attack construction approach when the opponent has imperfect knowledge of the local system dynamics and partial knowledge of the generator state. Based on the system with modeling errors, we study the performance of coordinated variable structure switching attacks in the presence of state estimation. Finally, we illustrate the concepts of attack model within the multiple switching framework, the cascading failure analysis is employed in the New-England 10-machine, 39-bus power system using MATLAB/Simulink and DSATools simulation environment. Our results demonstrate the potential for coordinated variable structure switching attacks to enable large-scale power system disturbances.
2

Sliding mode control of the stand alone wound rotor synchronous generator

Muñoz Aguilar, Raúl Santiago 19 July 2010 (has links)
En esta Tesis ha sido analizado el control de la màquina sincrónica de rotor bobinado actuando en isla. Para esta configuración, la velocidad mecànica determina la frecuencia, y la tensión de rotor se utiliza para fijar la amplitud de la tensión de estator. Debido a que la constante de tiempo eléctrica es mucho más ràpida comparada con la constante de tiempo mecánica, la velocidad mecánica fue considerada constante y externamente regulada y la investigación se enfocó en la regulación de la amplitud de la tensión de estator.Cuatro diferentes controladores basados en técnicas de modos deslizantes fueron diseñados en el marco de referencia dq. Las leyes de control obtenidas regulan la amplitud de la tensión de estator independientemte del valor de la carga. Adicionalmente, sólo las medidas de tensión y posición del rotor (para calcular la transformada dq) son necesarias. La estabilidad de los puntos de equilibrio obtenidos fueron probados al menos utilizando anàlisis de pequeña señal.Se realizó la validación por simulación y experimental de cada controlador en diferentes escenarios. Los resultados obtenidos validan los diseños y muestran las principales ventajas y desventajas de el sistema en lazo cerrado.El capítulo 2 cubre los problemas de modelado de la màquina sincrónica de rotor bobinado. Partiendo de las ecuaciones trifásicas generales, y utilizando la transformada de Park, se encontraron el modelo en dq del generador sincrónico de rotor bobinado (WRSG) en isla, alimentando tanto carga resistiva como inductiva. Los puntos de equilibrio del sistema obtenido fueron analizados y calculados, luego se definió el objetivo de control. Finalmente, se obtuvieron modelos lineales aproximados y sus respectivas funciones de transferencia.Los controladores PI son los más usados en la industria porque ofrecen buen desempeño y son sencillos de implementar. En el capítulo 3, se obtuvieron las reglas de sintonización para el controlador PI, y se analizaron estos resultados con el objetivo de proponer nuevos controladores que mejoraran el desempeño de la clásica aproximación PI.El esquema de control en modos deslizantes para la WRSG conectada a una carga resistiva fue diseñado en el capítulo 4. Éste, también incluye un completo análisis de estabilidad del sistema en lazo cerrado. El capítulo 5 presenta dos diseños basados en modos deslizantes para regular la amplitud de la tensión de estator para el WRSG actuando en isla. Ambos diseños usan la componente d de la tensión de estator en la función de conmutación. El primer caso es un control anidado, donde un lazo externo PI es añadido para proveer la referencia de la componente d de la tensión. En la segunda aproximación un término integral es añadido a la superficie de conmutación.El caso de alimentar una carga inductiva es estudiado en el capítulo 6. El controlador requiere una extensión dinámica debido a que la amplitud de la tensión de estator es una salida de grado relativo cero. Como resultado, un controlador robusto, que no depende de los parámetros de la máquina ni de los valores de carga es obtenido. En el capítulo 7 los resultados de simulación y experimentales para los controladores diseñados para el WRSG actuando en isla son presentados. En primer lugar, una descripción completa del banco es presentada. Esta incluye detalles de la etapa de adquisición de datos y de la DSP utilizada. En segundo lugar, se hace la descripción del procedimiento de simulación. Luego, las simulaciones y experimentos, que contienen diferentes escenarios, con cambios de referencia y variaciones de carga para cada controlador son presentados. / The control of the stand-alone the wound rotor synchronous generator has been analyzed in this dissertation. For this islanded configuration, the mechanical speed determines the frequency, and the rotor voltage is used to set the stator voltage amplitude. Due to the electrical time constant is so fast compared with the mechanical time constants, the mechanical speed was considered constant and externally regulated and the research was focused on the stator voltage amplitude regulation.Four different controllers based on sliding mode control techniques were designed in the dq reference frame. The obtained control laws regulate the stator voltage amplitude irrespectively of the load value. Furthermore, only voltage and rotor position measures (to compute the dq transformation), are required. The stability of the obtained equilibrium points was proved at least using small-signal analysis. Simulation and experimental validation of each controller containing several scenarios were carried out. The obtained results validate the designs and show the main advantages and disadvantages of each closed loop system. Chapter 2 covers the modeling issues of the wound rotor synchronous machine. From the general three-phase dynamical equations, and using the Park transformation, the dq-model of the stand-alone wound rotor synchronous generator feeding both a resistive and an inductive load are obtained. Equilibrium points of the obtained systems are analyzed and, after defining the control objective, the desired equilibrium points are computed.Finally, linear approximated models are obtained and their transfer functions are also presented.PI controllers are the most used in the industry because they offers good performance and are easily implementables. In Chapter 3 we obtain the tuning rule for the PI controller, and we analyze these results in order to propose new controllers which improve the classic PI approach.The sliding mode control scheme for the WRSG connected to a resistive load is designed in Chapter 4. It also includes a complete stability analysis of the closed loop system. Chapter 5 presents two sliding mode designs to regulate the stator voltage amplitude for a stand-alone wound rotor synchronous generator. Both use the stator voltage d-component error in the switching function. The first case is a nested controller, where an outer PI loop is added to provide the proper d-voltage component reference. In the second approach an integral term is added to the switching function. The case of feeding an inductive load is studied in Chapter 6. The controller introduces a dynamic extension because the stator voltage amplitude is a zero relative degree output. As result, a robust controller, which neither depends on the machine parameters nor on the load values, is obtained. In Chapter 7 the simulation and the experimental results of the designed controllers for the stand-alone wound rotor synchronous generator are presented. Firstly, a complete description of the bench is provided. It also includes details of the data acquisition stage and the used DSP card. Secondly, the description of the simulation procedure is commented. Then, the simulation and experiments which contains several scenarios, with reference change and load variations evaluated for each controller are presented.
3

DESIGN OF SERVO CONTROL SYSTEM BY INTEGRAL VARIABLE STRUCTURE MODEL FOLLOWING CONTROL WITH APPLICATION TO ROLLER GEAR CAM AND POWER SYSTEM

Chang, Geeng-Kwei 01 January 2002 (has links)
A robust servo control system based on Integral Variable Structure Model Following Control (IVSMFC) is proposed. The IVSMFC approach comprises a reference model part for specifying the design requirements and an Integral Variable Structure Control (IVSC) part for minimizing the errors between the plant and the model. Sliding mode thus obtained features robustness against external disturbances and parameter variations. Design procedures in both continuous-time and discrete-time have been detailed. The IVSMFC-based servo control system has been successfully applied to a DSP-based brushless DC motor drive for globoidal cam indexing system and to power system. Simulation and experimental results demonstrate that the proposed scheme can achieve fast and robust responses.
4

Controlador adaptativo backstepping a estrutura vari?vel

Queiroz, Kurios Iuri Pinheiro de Melo 20 November 2008 (has links)
Made available in DSpace on 2015-03-03T15:07:31Z (GMT). No. of bitstreams: 1 KuriosIPMQ.pdf: 875895 bytes, checksum: e5d1081ef123fc325214ccd9a2fee411 (MD5) Previous issue date: 2008-11-20 / Neste trabalho, um controlador adaptativo backstepping a estrutura vari?vel (Variable Structure Adaptive Backstepping Controller, VS-ABC) ? apresentado para plantas monovari?veis, lineares e invariantes no tempo com grau relativo unit?rio. Ao inv?s das tradicionais leis integrais para estima??o dos par?metros da planta, leis chaveadas s?o utilizadas com o objetivo de aumentar a robustez em rela??o a incertezas param?tricas e dist?rbios externos, bem como melhorar o desempenho transit?rio do sistema. Adicionalmente, o projeto do novo controlador ? mais intuitivo quando comparado ao controlador backstepping original, uma vez que os rel?s introduzidos apresentam amplitudes diretamente relacionadas com os par?metros nominais da planta. Esta nova abordagem, com uso de estrutura vari?vel, tamb?m reduz a complexidade das implementa??es pr?ticas, motivando a utiliza??o de componentes industriais, tais como, FPGAs (Field Programmable Gate Arrays ), MCUs (Microcontrollers) e DSPs (Digital Signal Processors). Simula??es preliminares para um sistema inst?vel de primeira e segunda ordem s?o apresentadas de modo a corroborar os estudos. Um dos exemplos de Rohrs ? ainda abordado atrav?s de simula??es, para os dois cen?rios adaptativos: o controlador backstepping adaptativo original e o VS-ABC
5

Controlador adaptativo por modelo de refer?ncia e estrutura vari?vel aplicado ao controle de ?ngulo de carga e fluxo de campo de um gerador s?ncrono

Fernandes, Marcus Vin?cius Ara?jo 23 October 2008 (has links)
Made available in DSpace on 2015-03-03T15:07:31Z (GMT). No. of bitstreams: 1 MarcusVAF.pdf: 586875 bytes, checksum: a12bd0bbfec29a70ab1bd62b33fc064d (MD5) Previous issue date: 2008-10-23 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Resumo / Nesta disserta??o de mestrado ? apresentada uma aplica??o do Controlador Adaptativo por Modelo de Refer?ncia e Estrutura Vari?vel em um Gerador S?ncrono conectado a um barramento infinito, para o controle do ?ngulo de carga e fluxo de campo deste gerador. Uma teoria de desacoplamento ? usada no modelo do Gerador S?ncrono para se obter dois subsistemas, onde o ?ngulo de carga e o fluxo de campo podem ser controlados independentemente. A avalia??o da estrat?gia de controle proposta ser? realizada atrav?s de simula??es para o modelo desacoplado do Gerador S?ncrono. Tamb?m ser? feita uma compara??o com os controladores Proporcional Derivativo aplicado ao Gerador S?ncrono desacoplado e Proporcional Integrativo Derivativo aplicado ao Gerador S?ncrono acoplado, sendo este ?ltimo, o sistema vigente hoje no Brasil. Os resultados das simula??es comprovar?o a efici?ncia e robustez desta estrat?gia de controle
6

Controlador adaptativo backstepping a estrutura variavel com Observadores de estado

Amorim, Breno Meira Moura de 12 April 2012 (has links)
Made available in DSpace on 2015-03-03T15:07:34Z (GMT). No. of bitstreams: 1 BrenoMMA_DISSERT.pdf: 2152939 bytes, checksum: 11e98e5a221057a9bd3545dd9b777bb5 (MD5) Previous issue date: 2012-04-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This research aims at developing a variable structure adaptive backstepping controller (VS-ABC) by using state observers for SISO (Single Input Single Output), linear and time invariant systems with relative degree one. Therefore, the lters were replaced by a Luenberger Adaptive Observer and the control algorithm uses switching laws. The presented simulations compare the controller performance, considering when the state variables are estimated by an observer, with the case that the variables are available for measurement. Even with numerous performance advantages, adaptive backstepping controllers still have very complex algorithms, especially when the system state variables are not measured, since the use of lters on the plant input and output is not something trivial. As an attempt to make the controller design more intuitive, an adaptive observer as an alternative to commonly used K lters can be used. Furthermore, since the states variables are considered known, the controller has a reduction on the dependence of the unknown plant parameters on the design. Also, switching laws could be used in the controller instead of the traditional integral adaptive laws because they improve the system transient performance and increase the robustness against external disturbances in the plant input / Esta pesquisa objetiva desenvolver um controlador adaptativo backstepping a estrutura vari?vel (Variable Structure Adaptive Backstepping Controller, VS-ABC) utilizando observadores de estado para plantas monovari?veis, lineares e invariantes no tempo com grau relativo unit?rio. Para isso, os filtros K foram substitu?dos por um Observador Adaptativo de Luenberger e o algoritmo de controle utiliza leis chaveadas. As simula??es apresentadas comparam o desempenho do controlador quando as vari?veis de estado s?o estimadas por um observador, com o caso em que as vari?veis est?o dispon?veis para medic?o. Os controladores adaptativos backstepping mesmo com v?rias vantagens de desempenho, ainda possuem algoritmos muito complexos, principalmente quando n?o s?o medidas as vari?veis de estado do sistema, pois o uso de filtros nos sinais de entrada e sa?da da planta n?o ? algo trivial. Na inten??o de tornar o projeto do controlador mais intuitivo, pode-se utilizar um observador adaptativo em alternativa aos comumente utilizados filtros K. Al?m disso, o controlador tem uma menor depend?ncia dos par?metros desconhecidos da planta na fase de projeto, ja que as vari?veis de estado s?o consideradas conhecidas. E ainda, leis chaveadas podem ser utilizadas no controlador em vez das leis integrais tradicionais porque melhoram o desempenho transit?rio do sistema e aumentam a robustez perante dist?rbios externos na entrada da planta
7

Controlador em modo dual adaptativo robusto - DMARC

Cunha, Caio Dorneles 24 January 2008 (has links)
Made available in DSpace on 2014-12-17T14:54:50Z (GMT). No. of bitstreams: 1 CaioDC.pdf: 2782026 bytes, checksum: ffc0e89b5e796daecc6152d3075b6918 (MD5) Previous issue date: 2008-01-24 / The so-called Dual Mode Adaptive Robust Control (DMARC) is proposed. The DMARC is a control strategy which interpolates the Model Reference Adaptive Control (MRAC) and the Variable Structure Model Reference Adaptive Control (VS-MRAC). The main idea is to incorporate the transient performance advantages of the VS-MRAC controller with the smoothness control signal in steady-state of the MRAC controller. Two basic algorithms are developed for the DMARC controller. In the first algorithm the controller's adjustment is made, in real time, through the variation of a parameter in the adaptation law. In the second algorithm the control law is generated, using fuzzy logic with Takagi-Sugeno s model, to obtain a combination of the MRAC and VS-MRAC control laws. In both cases, the combined control structure is shown to be robust to the parametric uncertainties and external disturbances, with a fast transient performance, practically without oscillations, and a smoothness steady-state control signal / Neste trabalho ? apresentada uma proposta de um controlador, denominado Controlador em Modo Dual Adaptativo Robusto (DMARC), que estabelece uma liga??o entre um controlador adaptativo por modelo de refer?ncia (MRAC) e um controlador adaptativo por modelo de refer?ncia e estrutura vari?vel (VS-MRAC). A id?ia b?sica ? incorporar as vantagens de desempenho transit?rio do controlador VS-MRAC com as propriedades de regime permanente do controlador MRAC convencional. S?o desenvolvidos dois algoritmos b?sicos para o controlador DMARC. No primeiro o ajuste do controlador ? feito, em tempo real, atrav?s da varia??o de um par?metro na lei de adapta??o. No segundo algoritmo a lei de controle ? gerada, utilizando o modelo Takagi-Sugeno da l?gica nebulosa, para obter uma composi??o ponderada das leis de controle do MRAC e do VS-MRAC. Em ambos os casos, o esquema combinado de controle ? mostrado ser robusto ?s incertezas param?tricas e perturba??es externas, al?m de apresentar um desempenho r?pido e pouco oscilat?rio durante o transit?rio e um sinal de controle suave em regime permanente
8

Controle adaptativo robusto para um modelo desacoplado de um rob? m?vel

Dias, Samaherni Morais 01 February 2010 (has links)
Made available in DSpace on 2014-12-17T14:54:54Z (GMT). No. of bitstreams: 1 SamaherniMD_TESE.pdf: 1906280 bytes, checksum: 4c045dfdea855b9b5837f362598733e7 (MD5) Previous issue date: 2010-02-01 / This thesis presents a new structure of robust adaptive controller applied to mobile robots (surface mobile robot) with nonholonomic constraints. It acts in the dynamics and kinematics of the robot, and it is split in two distinct parts. The first part controls the robot dynamics, using variable structure model reference adaptive controllers. The second part controls the robot kinematics, using a position controller, whose objective is to make the robot to reach any point in the cartesian plan. The kinematic controller is based only on information about the robot configuration. A decoupling method is adopted to transform the linear model of the mobile robot, a multiple-input multiple-output system, into two decoupled single-input single-output systems, thus reducing the complexity of designing the controller for the mobile robot. After that, a variable structure model reference adaptive controller is applied to each one of the resulting systems. One of such controllers will be responsible for the robot position and the other for the leading angle, using reference signals generated by the position controller. To validate the proposed structure, some simulated and experimental results using differential drive mobile robots of a robot soccer kit are presented. The simulator uses the main characteristics of real physical system as noise and non-linearities such as deadzone and saturation. The experimental results were obtained through an C++ program applied to the robot soccer kit of Microrobot team at the LACI/UFRN. The simulated and experimental results are presented and discussed at the end of the text / Esta tese apresenta o desenvolvimento de uma nova estrutura de controlador adaptativo robusto aplicado a sistemas rob?ticos m?veis com rodas (rob? m?vel de superf?cie) e restri??es n?o-holon?micas de movimento. Este controlador atua tanto na din?mica como na cinem?tica do rob?, e pode ser dividido em duas partes distintas. A primeira parte controla a din?mica, atrav?s da utiliza??o de controladores adaptativos por modelo de refer?ncia e estrutura vari?vel. A segunda parte controla a cinem?tica do rob? atrav?s de um controlador de posi??o, cujo objetivo ? fazer com que o rob? seja capaz de atingir um ponto qualquer no plano cartesiano, sendo que este controlador cinem?tico ? baseado apenas em informa??es da configura??o do rob?. O trabalho aplica um m?todo de desacoplamento para transformar o modelo linear do rob? m?vel, que ? um sistema com m?ltiplas entradas e m?ltiplas sa?das, em dois sistemas desacoplados com apenas uma entrada e uma sa?da cada um, para reduzir a complexidade do projeto do controlador. Em seguida, aplica-se um controlador adaptativo por modelo de refer?ncia e estrutura vari?vel a cada um dos sistemas resultantes. Um controlador ser? respons?vel pelo posicionamento e o outro pela orienta??o do rob?, sendo que estes controladores utilizam como refer?ncias sinais provenientes do controlador cinem?tico de posi??o. Para comprovar o funcionamento da estrutura proposta, obteve-se resultados simulados e experimentais para o rob? m?vel com acionamento diferencial de um kit de futebol de rob?s. O simulador possui as principais caracter?sticas do sistema f?sico real, dentre as quais podem-se destacar os ru?dos de entradas e as n?o-linearidades como zona morta e satura??o. Os resultados experimentais foram obtidos atrav?s de um programa desenvolvido em C++ e aplicado a um kit de futebol de rob?s da empresa Microrobot no Laborat?rio de Acionamento, Controle e Instrumenta??o da Universidade Federal do Rio Grande do Norte (LACI/UFRN). Os resultados simulados e experimentais s?o apresentados e discutidos ao final da tese
9

Estudo comparativo de estrat?gias de controle aplicadas a um gerador s?ncrono

Jacome, Isac Calistrato 25 June 2012 (has links)
Made available in DSpace on 2015-03-03T15:07:34Z (GMT). No. of bitstreams: 1 IsacCJ_DISSERT.pdf: 1949059 bytes, checksum: dd9548aaca6ef14a8a29ea281a293986 (MD5) Previous issue date: 2012-06-25 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The robustness and performance of the Variable Structure Adaptive Pole Placement Controller are evaluated in this work, where this controller is applied to control a synchronous generator connected to an infinite bus. The evaluation of the robustness of this controller will be accomplished through simulations, where the control algorithm was subjected to adverse conditions, such as: disturbances, parametric variations and unmodeled dynamic. It was also made a comparison of this control strategy with another one, using classic controllers. In the simulations, it is used a coupled model of the synchronous generator which variables have a high degree of coupling, in other words, if there is a change in the input variables of the generator, it will change all outputs simultaneously. The simulation results show which control strategy performs better and is more robust to disturbances, parametric variations and unmodeled dynamics for the control of Synchronous Generator / A robustez e o desempenho do Controlador Adaptativo por Posicionamento de Polos e Estrutura Variavel s?o avaliados neste trabalho, onde este controlador e aplicado para o controle de um Gerador Sncrono conectado a um barramento infi- nito. A avaliac?o da robustez deste controlador sera realizada atraves de simulac?es, onde o algoritmo de controle foi submetido a condic?es adversas, tais como: perturba c?es, variac?es parametricas e din?mica n?o modelada. Tambem foi feita uma comparac?o desta estrategia de controle, com outra utilizando controladores classicos. Nas simulac?es, e utilizado o modelo acoplado do gerador sncrono, onde suas variaveis apresentam um alto grau de acoplamento, ou seja, se houver alterac?o em uma das variaveis de entrada do gerador todas as suas sadas ser?oo alteradas simultaneamente. Os resultados das simulac?es demonstram qual estrategia de controle apresenta melhor desempenho, e e mais robusta a perturbac?es, variac?es parametricas e din?mica n?o modelada para o controle do Gerador S?ncrono
10

Controle adaptativo por modelo de referencia e estrutura vari?vel discreto no tempo

Jacome, Isael Calistrato 05 February 2013 (has links)
Made available in DSpace on 2015-03-03T15:07:35Z (GMT). No. of bitstreams: 1 IsaelCJ_DISSERT.pdf: 3710521 bytes, checksum: ffcd6197d140a1f366f43dd76204f72c (MD5) Previous issue date: 2013-02-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / With the technology progess, embedded systems using adaptive techniques are being used frequently. One of these techniques is the Variable Structure Model- Reference Adaptive Control (VS-MRAC). The implementation of this technique in embedded systems, requires consideration of a sampling period which if not taken into consideration, can adversely affect system performance and even takes the system to instability. This work proposes a stability analysis of a discrete-time VS-MRAC accomplished for SISO linear time-invariant plants with relative degree one. The aim is to analyse the in uence of the sampling period in the system performance and the relation of this period with the chattering and system instability / Com o avanco da tecnologia, sistemas embarcados utilizando t?cnicas adaptativas est?o sendo utilizados com mais frequencia. Uma dessas t?cnicas ? o Controlador adaptativo por Modelo de Referencia e Estrutura Variavel (VS-MRAC). A implementa??o dessa t?cnica em sistemas embarcados, requer a considera??o de um per?odo de amostragem que se n?o for levado em considera??o, pode afetar de maneira negativa a performance do sistema e at? mesmo lev?-lo a instabilizacao. Este trabalho prop?e uma an?lise de estabilidade do VS-MRAC para o caso discreto para uma planta SISO linear, invariante no tempo, de grau relativo unit?rio. O objetivo ? analisar a influ?ncia do per?odo de amostragem no desempenho do sistema, e a rela??o desse per?odo com o fen?meno de "chattering" e instabiliza??o do sistema

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