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Previous issue date: 2014-01-28 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico - CNPq / O comportamento ca?tico tem sido amplamente observado na natureza, tanto em fen?menos f?sicos e qu?micos quanto em sistemas biol?gicos, aparecendo tamb?m em diversas aplica??es de engenharia, se manifestando tanto em simples osciladores mec?nicos quanto nos mais avan?ados sistemas de comunica??o. No que concerne aos sistemas mec?nicos, comumente os efeitos das n?o-linearidades sobre o comportamento din?mico do sistema s?o de car?ter indesej?vel, o que tem motivado o desenvolvimento de estrat?gias de compensa??o. No entanto, recentemente tem-se verificado a exist?ncia de situa??es nas quais a riqueza da din?mica n?o-linear torna-se atraente. Devido a sua grande sensibilidade ?s condi??es iniciais, os sistemas ca?ticos podem sofrer mudan?as consider?veis por meio de pequenas varia??es em seus par?metros, o que ? extremamente favor?vel quando desejamos dar maior flexibilidade ao sistema controlado. Nesse sentido, analisaremos as varia??es apresentadas pelo oscilador de Duffing, em especial de suas ?rbitas peri?dicas inst?veis e se??o de Poincar? frente a altera??es percentuais de $\pm$ 5, $\pm$ 1 e +10 \% no valor nominal do param?tro que multiplica o termo c?bico. Em seguida, sabendo que o gasto de energia para estabilizar OPIs ? m?nimo, analisaremos o esfor?o de controle necess?rio para controlar e estabilizar tais ?rbitas, que pertencem a modelos diferentes do oscilador de Duffing nominal. Devido a sua robustez a incertezas par?metricas utilizaremos um controlador por modos deslizantes com fun??o de satura??o e compensa??o adaptativa por s?rie de Fourier. / The chaotic behavior has been widely observed in nature, from physical and
chemical phenomena to biological systems, present in many engineering applications
and found in both simple mechanical oscillators and advanced communication
systems. With regard to mechanical systems, the effects of nonlinearities on the
dynamic behavior of the system are often of undesirable character, which has motivated
the development of compensation strategies. However, it has been recently
found that there are situations in which the richness of nonlinear dynamics becomes
attractive. Due to their parametric sensitivity, chaotic systems can suffer considerable
changes by small variations on the value of their parameters, which is extremely
favorable when we want to give greater flexibility to the controlled system. Hence,
we analyze in this work the parametric sensitivity of Duffing oscillator, in particular
its unstable periodic orbits and Poincar?e section due to changes in nominal value of
the parameter that multiplies the cubic term. Since the amount of energy needed to
stabilize Unstable Periodic Orbits is minimum, we analyze the control action needed
to control and stabilize such orbits which belong to different versions of the Duffing
oscillator. For that we will use a smoothed sliding mode controller with an adaptive
compensation term based on Fourier series.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/19376 |
| Date | 28 January 2014 |
| Creators | Rebou?as, Geraldo Francisco de Souza |
| Contributors | 05362438751, http://lattes.cnpq.br/3256782908311485, Ara?jo, Aldayr Dantas de, 10829741453, http://lattes.cnpq.br/3165031680223608, Costa J?nior, Jo?o Carlos Arantes, 42364973368, http://lattes.cnpq.br/5028446242533356, Savi, Marcelo Amorim, 83037497734, http://lattes.cnpq.br/1224532648969159, Bessa, Wallace Moreira |
| Publisher | Universidade Federal do Rio Grande do Norte, P?S-GRADUA??O EM ENGENHARIA MEC?NICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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