Absolute stability control of supercavitating vehicles based on backstepping

In cruise phase of supercavitating bodies, only the cavitator fixed at the head and the fins located at the back of the body contact with water. Existence of the cavity makes the interaction between body surface and outside world a quite complex process. In the vertical plane, this interaction process creates strong nonlinear planing force, which can get high amplitude. Besides, it is also a bad environment for control effort when the body surface gets separated with water. In this paper, by using backstepping, first of all, the original system is transformed into a cascade connection of two subsystems, in which the second part is organized in the form of Lure feedback connections, so that the stability work of the whole system can be solved by analyzing the second subsystem stability problem, through the analysis of the sector bounded conditions of the nonlinear part, a state feedback controller is designed using the circle criterion methods. The simulation results show that the designed controller can get absolute stability of the whole system, and track the given depth signal.