H ∞ robust control for underwater supercavitating vehicle with time delay

Abstract

According to Logvinovich cavity dependent expansion principle, a cavity developed by cavitator has memory effect, which arises cavity deformation at aft part of a supercavitating vehicle and leads time delay of travel state. This delay affects the dynamic behavior through changing hydrodynamic and moment on the control surface, and even induces instability. This paper focuses on the time delay effect of the underwater supercavitating vehicle, and a simplified dynamic model of underwater supercavitating vehicle with delay was established. First, a planing force was simplified in straight level state, then a simplified model of supercavitating vehicle with delay in longitude plane was obtained. Taking depth, pitch angle, vertical speed and pitch rate as state variant, $\mathit{H}\infty$ state feedback controller was designed by linear matrix inequality (LMI) and Lyapunov stable theory was exploited to prove the asymptotic stability of the system. Simulation results show that, the controlled system is effectiveness for both simplified model and non-simplified model and it can track reference command signal.