Fenômenos Não-Lineares e Caóticos em Engenharia
CON10-1906 - ADAPTIVE FUZZY SLIDING MODE CONTROL WITH APPLICATION TO A CHAOTIC PENDULUM
Bessa, Wallace Moreira1; De Paula, Aline Souza2; Savi, Marcelo Amorim3
1Universidade Federal do Rio Grande do Norte; 2Universidade de Brasília; 3Universidade Federal do Rio de Janeiro
Resumo: Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. The idea that chaotic behavior may be controlled by small perturbations of physical parameters allows this kind of behavior to be desirable in different applications. In this work, the application of a variable structure controller to second order nonlinear systems is discussed. The approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling inaccuracies and external disturbances. The general procedure is applied to a nonlinear pendulum and numerical results are presented in order to demonstrate the control system performance. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption. Since noise contamination is unavoidable in experimental data acquisition, it is important to evaluate its effect on chaos control procedures. This work also investigates the effect of noise on the proposed control scheme, verifying the influence on the system stabilization and on the required control action.
Palavras-chave: Adaptive algorithms; Chaos control; Fuzzy logic; Nonlinear pendulum; Noisy signal; Sliding modes.
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CON10-1700 - CHAOS CONTROL IN CARDIAC RHYTHM DYNAMICS
Ferreira, Bianca Borem1; de Paula, Aline Souza2; Savi, Marcelo Amorim1
1COPPE/UFRJ; 2UnB
Resumo: Chaos control methods are applied in order to obtain dynamical systems that may quickly react to some new situation, changing their response. Heart rhythm dynamics constitute a potential application of these methods. Basically, heart rhythms could be either periodic or chaotic and each kind of behavior may be related to both normal or pathological physiological functioning. This article deals of the chaos control applied to cardiac pacemaker modeled by an modified Van der Pol equation. This mathematical equation reproduces the normal and pathological activity of the cardiac pacemaker. The time delayed feedback method is employed for chaos control. Results show the capability of the control procedure to stabilize unstable periodic orbits of the dynamical system eliminating undesired pathological responses of the heart.
Palavras-chave: Chaos; Control; Heart rhythms; Biomechanics.
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CON10-1705 - MODELLING OF STICK-SLIP AND BIT-BOUNCE IN DRILL-STRING DYNAMICS VIA SMOOTHEN FUNCTIONS
Divenyi, Sandor1; Vasconcellos, Mariana N.1; Savi, Marcelo Amorim1; Wiercigroch, Marian2; Pavlovskaia, Ekaterina2
1COPPE/UFRJ; 2University of Aberdeen
Resumo: In this work we model and analyse drill-string vibrations. A special attention is given to the transitions between different phases of motion, which for stick-slip and bit-bounce are normally treated as the non-smooth dynamics. Here we adopt smooth functions which are advantageous in terms of mathematical description and numerical analysis. Our studies have shown that the developed mathematical model is capable of predicting a full range of dynamic responses including the non-smooth behaviour.
Palavras-chave: Oil drilling; Nonlinear dynamics; Nonsmooth systems; Chaos.
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CON10-1701 - NONLINEAR DYNAMICS OF THE DAISYWORLD
Viola, Flavio Maggessi1; Paiva, Susana1; Savi, Marcelo Amorim Savi1; Lopes, Manoela T.1; Brasil Jr., Antonio C.P.2
1COPPE/UFRJ; 2UnB
Resumo: Global warming is the observed increase of the average temperature of the Earths´ atmosphere and oceans. The primary cause of this phenomenon is the greenhouse gases released by burning of fossil fuels, land cleaning, agriculture, among others, leading to the increase of the so-called greenhouse effect. The consequences of this warming is unpredictable. The mathematical modeling of ecological phenomena has an increasing importance in recent years. These models may describe time evolution and spatial distribution and may explain some important characteristics of these systems. Although there are many difficulties related to the system description, their modeling may define at least a system caricature, which may be useful for different goals. This contribution deals with the modeling of the global warming in a dynamical point of view. Mathematical modeling is based on the daisyworld that is able to describe the global regulation that can emerge from the interaction between life and environment. This idea became famous as the Gaia theory of the Earth that establishes self-regulation of the planetary system. In brief, daisyworld represents life by daisy populations while the environment is represented by temperature. Here, two daisy populations are of concern, black and white daisies, and an extra variable related to greenhouse gases is incorporated in the model allowing the analysis of the global warming. Besides, energy equation is considered in order to investigate transients phenomena related to temperature variation. Numerical simulations are carried out presenting a qualitative description of the phenomenon.
Palavras-chave: Global warming; Daisyworld; Nonlinear dynamics; Chaos; Climate change.
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CON10-1699 - ON THE INFLUENCE OF NOISE IN CHAOS CONTROL METHODS
de Paula, Aline Souza1; Savi, Marcelo Amorim2
1UnB; 2COPPE/UFRJ
Resumo: Chaos may be exploited in order to design dynamical systems that may quickly react to some new situation, changing conditions and their response. In this regard, the idea that chaotic behavior may be controlled by small perturbations allows this kind of behavior to be desirable in different applications. Chaos control may be understood as a two stage technique: the first one is known as the learning stage where the unstable periodic orbits (UPOs) embedded in chaotic attractor are identified and system characteristics are evaluated; after that, the control stage stabilizes desired UPOs. This paper presents an overview of chaos control methods classified as follows: OGY methods - that includes discrete and semi-continuous approaches; multiparameter methods - that also includes discrete and semi-continuous approaches; and time-delayed feedback methods that are continuous approaches. These methods are employed in order to stabilize some desired UPOs establishing a comparative analysis of all methods. Essentially, a control rule is of concern and each controller needs to follow this rule in the presence of observed noise. The main goal is to establish a comparative analysis of chaos control methods focusing on the control procedures robustness.
Palavras-chave: Chaos; Control; Nonlinear dynamics; Nonlinear pendulum.
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CON10-1721 - PLASTIC STRAIN LOCALIZATION PROMOTED BY THERMOMECHANICAL COUPLING IN METALLIC MATERIALS
Rodríguez, Natalie P.1; Pacheco, Pedro Manuel Calas Lopes1; Chimisso, Fulvio Enrico Giacomo2
1CEFET/RJ; 2FURG
Resumo: Thermomechanical coupling is an important phenomenon in different engineering problems. Inelastic cyclic strain promotes heating of metallic structural elements, and a considerable amount of heat can be generated in situations where high loading rates and/or high amplitudes of inelastic strain are of concern. The temperature rise of mechanical component depends on the loading amplitude, frequency and temperature boundary conditions. Nevertheless, traditional low-cycle fatigue models neglect the material temperature variation due to thermomechanical coupling and unreal life predictions may be obtained. Indeed, there are situations where such couplings cannot be neglected and a physically more realistic model must take it into account. In this paper, a continuum mechanics model with internal variables is proposed to study the thermomechanical coupling effects of metallic components subjected to inelastic loadings. A thermodynamic approach allows a proper identification of the thermomechanical coupling in the mechanical and thermal equations. A numerical procedure is developed based on an operator split technique associated with an iterative numerical scheme in order to deal with the non-linearities in the formulation. With this assumption, coupled governing equations are solved involving three uncoupled problems: thermal, thermoelastic and elastoplastic behaviors. Numerical simulations of steel plates with a stress concentrator subjected to inelastic loadings are presented and analyzed. Results suggest that the proposed model is capable of capturing important localization phenomena related to plastic strain localization due thermomechanical coupling.
Palavras-chave: Thermomechanical Coupling; Modeling; Numerical Simulation; Elastoplasticity.
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CON10-1066 - ROBÔ DE COMBATE A INCÊNDIOS: TRAJETÓRIAS CAÓTICAS E VISÃO INTELIGENTE.
TAVERA, MAGDA JUDITH MORALES1; LENGERKE, OMAR2; DUTRA, MAX SUELL1; GONZALEZ ACUÑA, HERNAN3
1COPPE-UFRJ; 2COPPE-UFRJ, UNAB - Colombia; 3UNAB - Colombia
Resumo: A vigilância e combate a incêndios é conhecida como uma missão arriscada, situação que os bombeiros enfrentam perigosamente quando estão extinguindo o fogo ou resgatando as vitimas; sendo esta uma parte inerente à profissão. Em contraste, um robô pode funcionar autonomamente ou controlado desde uma distância segura para executar este tipo de labores sem colocar em risco a vida do bombeiro, sendo esta a motivação do presente artigo, onde um robô dotado de visão inteligente recebendo sinais de sensores especializados e um controle caótico poderia reduzir prejuízos humanos, materiais e ambientais. Neste artigo, é proposto implementar natureza caótica a um robô móvel, com o objetivo de realizar inspeção de um ambiente com trajetórias não determinadas, auxiliadas com sistemas de sensores e visão inteligente. O caos caracteriza um dos comportamentos mais ricos e misteriosos dos sistemas dinâmicos não lineares, caracterizados pela topologia transitiva e a dependência nas condições iniciais. O comportamento caótico do robô móvel proposto se consegue incorporando nas equações cinemáticas do robô a equação de Arnold sendo uma equação conhecida que apresenta comportamento caótico.
Palavras-chave: Caos; Visão Estéreo; Robôs de combate a incêndios.
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