Dynamic loss of stability in depth control of submersible vehicles

Abstract

Control of a modern submarine is a multi-dimensional dynamical problem coupling considerations of initial static stability, hydrodynamic performance, and control system response. In this work, the loss of stability at moderate-to-high speeds is examined using a nonlinear Hopf bifurcation analysis. Complete linear state feedback is used for demonstration purposes for depth control at level attitude and for a fixed nominal speed. The control time constant, the nominal and actual speeds, the metacentric height, and the stern-to-bow-plane ratio are used as the main bifurcation parameters. A complete local bifurcation mapping provides a systematic method for evaluating the bounds of controllability for the control system design parameters for a vehicle with a given set of hydrodynamic coefficients. The submarine and its potential design modifications are verified with direct numerical simulations.