Dynamics and Control of Supercavitating Vehicles

Analytical and numerical investigations into the dynamics and control of dive-plane dynamics of supercavitating vehicles are presented. Dominant nonlinearities associated with planing forces are taken into account in the model. Two controllers are proposed to realize stable inner-loop dynamics, a linear state feedback control scheme and a switching control scheme. Through numerical simulations and estimation of the region of attraction, it is shown that effective feedback schemes can be constructed. In comparison to existing control schemes, the feedback schemes proposed in this work can stabilize a supercavitating vehicle with a large region of attraction around the trim condition instead of just stabilization around the limit cycle motion. In particular, the achieved stability is robust to modeling errors in the planing force. This robustness is especially important for supercavitating vehicles because the underlying planing force physics is complicated and not yet fully understood. Compared to the linear feedback control scheme, the switching control scheme is seen to increase the region of attraction with reduced control effort, which can be useful for avoiding saturation in magnitude. Analytical tools, including the describing function method and the circle criterion, are applied to facilitate understanding of the closed-loop system dynamics and assist in the controller design. This work provides a basis for interpreting the tail-slap phenomenon of a supercavitating body as a limit cycle motion and for developing control methods to achieve stable inner-loop dynamics in the full model.