潜艇操纵运动分叉突变特性  

BIFURCATION AND CATASTROPHE CHARACTERISTICS IN SUBMARINE MOTION

作　　者：王晓玢[1] 孙尧[1] 莫宏伟[1] 

机构地区：[1]哈尔滨工程大学自动化学院,哈尔滨150001

出　　处：《工程力学》2009年第10期252-256,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(60672035);高等学校博士学科专项科研基金项目(20050217021)

摘　　要：为研究潜艇失稳现象发生的机理,对潜艇垂直面操纵运动进行非线性建模,并利用分叉与突变理论方法对运动稳定性进行分析。利用中心流形理论将潜艇运动方程约化到包含原系统全部动力学特性的低维系统,分别对静态分叉和动态分叉引发的状态突变进行了分析,并通过数值仿真验证。仿真结果证明:潜艇在垂直面内以高速大舵角作强机动时将发生跨临界分叉和Hopf分叉,并导致系统状态在分叉点处产生突变。此现象揭示了潜艇动力学模型中非线性项的影响,并为操纵控制系统的设计提供了必要理论依据。To study the mechanism of losing stability, the nonlinear submarine maneuvering motion model in dive plane was established. The bifurcation and catastrophe theory methodology was adopted to analyze the motion stability. The motion equations of submarine were reduced to a lower system which contains all dynamic properties of the original system by utilizing center manifold theory. The status catastrophe caused by static bifurcation and dynamic bifurcation was respectively discussed. The numerical simulation results in MATLAB/Simulink program showed that the transcritical bifurcation or Hopf bifurcation occurred in submarine operating motion with high-speed and large rudder angle in dive plane. And bifurcations would lead to status catastrophe at bifurcation points. These catastrophe phenomena reveal the effect of nonlinear terms in submarine dynamic model, and provide necessary theoretical basis for submarine maneuvering control system designing.

关 键 词：潜艇 突变 中心流形理论 跨临界分叉 HOPF分叉 

分 类 号：U661[交通运输工程—船舶及航道工程] TP13[交通运输工程—船舶与海洋工程]