Underwater vehicle depth and attitude regulation in plane progressive waves

Hydrodynamic forces from unsteady and nonuniform flow fields are difficult to capture accurately in control-oriented dynamic models of undersea vehicles. We present an approximate dynamic model for the motion of an underwater vehicle operating below the free surface in waves. The quasi-steady model, derived from potential flow theory, treats the forces and moments generated by the wave as exogenous inputs. The hydrodynamic forces predicted by this maneuvering model compare favorably with an analytical solution for an infinite cylinder in a plane progressive wave. A proportional-derivative (PD) feedback controller is developed to regulate the depth and pitch attitude. Numerical analysis of the trade-off between depth and pitch attitude regulation suggests there is an optimal “look-ahead” distance. A nonlinear control law developed to stabilize a steady motion outperforms the PD controller in numerical simulations.