Catastrophe characteristics and control of pitching supercavitating vehicles at fixed depths

•In this study, the Least-squares method is exploited to approximate the nonlinear planing force.•The simplified model of the pitching supercavitating vehicles at fixed depths is established.•The cusp catastrophe potential function is built.•A dynamic washout filter-aided feedback is used to control the catastrophe phenomena.

The existence of the cavity and of a nonlinear planing force results in catastrophe phenomena and causes an instant loss of stability for the supercavitating vehicle during the travel process. To analyze the catastrophe characteristics, the least-squares method is exploited in order to approximate the nonlinear planing force, and the simplified model of the pitching supercavitating vehicle at fixed depths is established. According to the splitting lemma, the cusp catastrophe potential function is built for the pitching supercavitating vehicle at fixed depths and the critical condition of the catastrophe is obtained. A dynamic washout filter-aided feedback is used to control the catastrophe phenomena of the vehicle, and the simulation result shows that the control method is effective and feasible.