Torpedo Movement Analysis Based On Catastrophe Theory

The birth of Catastrophe theory created an effective way to discuss nonlinear science problems. 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 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 equilibria, or eliminate and restrain harmful catastrophe, to remain the system's stability.On the basis of Catastrophe theory, this thesis introduces seven catastrophe models and also gives application ways of these catastrophe models. Especially, Washout filter based on feedback catastrophe control method is introducecd in detail, it is not only preserve the original equilibrium even under model uncertainty, but also can simplify the controller, to expand the range of control parameter. First, Washout filter based on feedback catastrophe control method is applied the fisrt time to the analysis of catastrophe of torpedo vertical movement in this thesis, and catastrophe point of torpedo vertical movement is discussed, then nonlinear controller is put forward to control the point; Second, Torpedo attitude may be sudden changed when wave works, we call it catastrophe. The result of this catastrophe is unpredictable and this situation is not our hope when we launch torpedoes. So to this point, cusp catastrophe model is used to analyse the catastrophe.