Cable Interactions in a Depth Controlled Submersibler

The interaction of a long towing cable with a depth controlled submersible is studied from the point of view of the eifect of cable motion on the stability of the vertical motion of the submersible. The planar dynamics of a submerged vehicle towed at constant speed by a long cable are analyzed subject to simplified models of the hydrodynamics. The coupled motions of the vehicle and cable are treated for small perturbations about the towed equilibrium configuration in which the system translates as a whole at the towing speed. In the special case of a straight towed equilibrium state, the modes and frequencies of vibration of the linearized equation governing the cable are derived and the interaction between the vehicle and the massive heavily damped cable is studied. The conditions for stability of the system are determined by the Parameter Plane method whereby the values of two disposable control system parameters which yield stable operation are displayed. It is determined that a relatively small amount of damping opposing the vehicle's motion is adequate to guarantee stability for a broad range of the system gains. The method of analysis presented is applicable to the case of an arbitrary steady state configuration where the modes of vibration about equilibrium are obtained in other than closed form.