Stability Analysis and Control of Supercavitating Vehicles With Advection Delay

Abstract

A pitch-plane model of a supercavitating vehicle is developed to account for the time delay in the propagation of the cavitator action from the vehicle nose to the vehicle aft. This time delay is an advection delay, which is on the order of the vehicle length divided by its speed. Unlike previous models with time-delay effects, in the present model, the effect of cavity rotation during forward motion is incorporated. Stability analyses and feedback control designs are carried out using this model. It is found that the open-loop system with and without the time delay is unstable. Feedback control laws that stabilize the delay-free system model are found to be ineffective in the presence of the time delay. The authors show that the delay leads to destabilization of the supercavitating vehicle dynamics in the sense that an operation at a stable trim condition is replaced by a stable limit-cycle motion that is commonly referred to as tail-slap. Feedback control designs are carried out by taking into account the time delay, and it is demonstrated that the supercavitating vehicle can be stabilized at trim conditions inside and outside the cavity. By using numerical studies of the nonlinear delay-dependent pitch-plane model of the supercavitating vehicle, the effectiveness of the new control designs are demonstrated.