鱼雷定深航行稳定性的分叉分析

鱼雷定深运动方程含有诸多的非线性项，用传统的分析方法对其稳定性进行研究有较大难度。运用非线性科学中的分叉理论，选定鱼雷定深运动方程中的某一流体动力系数扰动值为分叉参数，系统地分析在经典比例微分深度控制系统作用下，鱼雷在退化平衡点处的航行稳定性。利用中心流形定理，推导出系统状态变量解析表达式，对系统 Hopf分叉进行分析，并进行仿真验证。结果表明，流体动力系数变化使定深航行产生 Hopf分叉，并给出了确保鱼雷稳定航行的流体动力参数取值范围。

Bifurcation analysis for depthkeeping sailing stability of torpedo

There are several nonlinear elements in the equations of torpedo depthkeeping movements. It is difficult to analyze its stability with traditional methods. A hydrodynamic parameter interference is chosen as bifurcation parameter at first. Then the sailing stability of torpedo with proportional-derivative controller is analyzed by bifurcation theory. The center manifold theory is used to get the expression of system state parameters. And the Hopf bifurcation of system is analyzed. The result is verified by numerical simulations. It shows that the hydrodynamic parameter's changing will bring Hopf bifurcation for depthkeeping sailing. And the range of hydrodynamic parameter value that insures torpedo sailing stability is given.