Research On Catastrophe Control Mechanism And It's Application On Nonlinear Ship Roll Motion

The history course of human cognize and transform the objective world is a process which experience from lower to higher, simple to complex, outside to the inside, either the control area. For demanding higher accuracy in actual production process and the increasing complexity of the controlled object, the original linear control theory has been unable to meet the needs of people. So, a series of nonlinear control method were born in succession, such as variable structure control, adaptive control, robust control, etc.Catastrophe control theory is a kind of nonlinear control theory, which main purpose is to control the output's jumping problem of the system when inputs are smooth. This article will explore how to make the catastrophe theory combined with the control technology to create a set of catastrophe control methods, and tentatively applied to the ship rolling motion and stability control.The main work are the as follows:First, for a nonlinear system which potential energy function has multi-input and single-output style, catastrophe model can be built according to the numbers of input variables.They are fold, cusp, swallowtail and butterfly catastrophe models. And in accordance with the different characteristics of each system, linear controller, nonlinear controller and washout controller were designed to control the catastrophe phenomena.Second, fold catastrophe model was introduced into the capsizing of nonlinear ship roll movement, then multi-scale method was used to get the amplitude frequency response equation, and the catastrohe characteristics were proved by numerical simulation. Finally, linear and nonlinear controllers were designed to control the catastrophe phenomena, and the effectiveness was proved by simulation.Third, cusp catastrophe model was made to analyse the course of ship roll motion without damping in hydrostatic water, and the process of ship capsize caused by parameters changes were discussed in detail. Critical conditions were also discussed and the catastrophe cause was clarified. Finally, nonlinear controller and washout controller were designed.At last, the ship's nonlinear rolling motion under excition by longitudinal wave was fitted into butterfly catastrophe model, and the multi-scale method was used to get the catastrohe characteristics. Then the linear feedback controller was designed to restrain the catastrophe, and the result was great by simulation.