Nonlinear Ship Rolling Analysis Based On Catastrophe Theory

The birth of Catastrophe theory created an effective way to discuss nonlinear science problems. Undergo decades of development and improve, it has been widely applied to the domain of engineering and scientific researches and has been made a lot of achievements. With the complication of controlled object and the desire of performance index on controlled system becomes higher and higher, the controlling problem of complex system is an austere challenge the traditional control theory has to be faced with, one of the reasons is that there are catastrophic characteristics in them, while analysis to these characteristics is the first step. So, the combination of catastrophe theory and control will be a trend.The combination of catastrophe theory and control theory is just in its first stages and needs to be developed. This dissertation starts with the investigation of catastrophe phenomena, catastrophe theory is introduced to control and stability analysis of system, which takes advantage of the systematic precise control. The major purpose of combination of catastrophe theory and control technology is to create new beneficial catastrophe while preserve all initial characters, or eliminate and restrain harmful catastrophe, to remain the system's stability.When ships navigate in waves, there will be large amplitude rolling which contains complex nonlinear phenomena, such as, multi-valued, bifurcation. The serious nonlinear rolling, acted by outside forces or other factors, will lead ships to capsizing. In this paper, the method of multiple scales is used to get the approximate analytical solution of ship rolling nonlinear differential equation. Then, catastrophe theory is applied to establish cusp catastrophe model of rolling and to analyze occurring condition and harmful effects of catastrophe phenomena in ship rolling. The cause of ship singular capsize is explained from a new aspect. Aiming to counter impact of catastrophe, it was proposed that Catastrophe Control theory is applied in ship nonlinear rolling control, and state feedback controller is designed to reduce catastrophe, the simulation curves show that the desired results are attained. It's proved that catastrophe control is a helpful supplement to rolling control.