In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability criteria in the International Maritime Organization (IMO). The advantage of this extended Melnikov's method is it overcomes the limitation of small damping that is intrinsic to the implementation of the standard Melnikov's method. The extended Melnikv's method is first applied to two published roll motion models. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is a model with a biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of the extended Melnikov's method is demonstrated. Then this method is used to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. A reference ITTC ship is used here by way of example and the result is compared to that obtained from previously published standard analysis as well as numerical simulations. Because the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, a 'best fit'approximation is given for the extended Melnikov numerically predicted result. The extended Melnikov's method for slowly varying system is applied to a roll-heave-sway coupled ship model. The Melnikov's functions are calculated based on a fishing boat model. And the results are compared with those from standard Melnikov's method. This work is a preliminary research on the application of Melnikov's method to multi-degree-of-freedom ship dynamics. In the last part of the dissertation, the method of manufactured solution is applied to systems with chaotic behavior. The purpose is to identify points with potential numerical discrepancies, and to improve computational efficiency. The numerical discrepancies may be due to the selection of error tolerances, precisions, etc. Two classical chaotic models and two ship capsize models are examined. The current approach overlaps entrainment in chaotic control theory. Here entrainment means two dynamical systems have the same period, phase and amplitude. The convergent region from control theory is used to give a rough guideline on identifying numerical discrepancies for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models. / Ph. D.

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No. of bitstreams: 1 outa_r_dr_ilha.pdf: 8826970 bytes, checksum: 2d87ce6b0e50b1304328308f0df4e3bb (MD5) Previous issue date: 2017-10-27 / O objetivo deste trabalho é a elaboração de um controlador linear ótimo, que possa reduzir um sinal caótico do rotor dinâmico, em um sinal controlado. Para se obter o resultado esperado foi necessário desenvolver atividades ligadas à caracterização do experimento; análise de estabilidade pelo método de Lyapunov; aplicação da função de Lyapunov; análise da sensibilidade das condições iniciais utilizando o expoente de Lyapunov; desenvolvimento do projeto do controle ótimo linear. O resultado final mostra o desempenho da aplicação do controle linear ótimo no sinal caótico, cujo sinal foi reduzido para um comportamento estável e controlado. / The aim of this work is the elaboration of an optimal linear controller that can reduce a chaotic dynamic rotor signal in a controlled signal. To obtain the expected result, it was necessary to develop activities related to the characterization of the experiment; stability analysis by the Lyapunov method; application of the Lyapunov function; sensitivity analysis of the initial conditions by the Lyapunov exponent; development of linear optimum control. The result shows the performance of the optimal linear control in the chaotic signal, whose signal was reduced to a stable and controlled behavior.

Orientador: Fábio Roberto Chavarette / Resumo: O objetivo deste trabalho é a elaboração de um controlador linear ótimo, que possa reduzir um sinal caótico do rotor dinâmico, em um sinal controlado. Para se obter o resultado esperado foi necessário desenvolver atividades ligadas à caracterização do experimento; análise de estabilidade pelo método de Lyapunov; aplicação da função de Lyapunov; análise da sensibilidade das condições iniciais utilizando o expoente de Lyapunov; desenvolvimento do projeto do controle ótimo linear. O resultado final mostra o desempenho da aplicação do controle linear ótimo no sinal caótico, cujo sinal foi reduzido para um comportamento estável e controlado. / Abstract: The aim of this work is the elaboration of an optimal linear controller that can reduce a chaotic dynamic rotor signal in a controlled signal. To obtain the expected result, it was necessary to develop activities related to the characterization of the experiment; stability analysis by the Lyapunov method; application of the Lyapunov function; sensitivity analysis of the initial conditions by the Lyapunov exponent; development of linear optimum control. The result shows the performance of the optimal linear control in the chaotic signal, whose signal was reduced to a stable and controlled behavior. / Doutor