Eric G. Paterson

An energy-casimir approach to underwater vehicle depth and heading regulation in short crested waves

Conventional underwater vehicle models neglect wave excitation forces and free surface effects, since the vessel is most often deeply submerged where these effects are negligible. For near-surface operations, wave excitation forces significantly affect vessel motion. This paper focuses on depth and heading regulation for a fully actuated underwater vehicle operating in the wave-affected zone. We first construct a non-canonical Hamiltonian model for the nominal system dynamics. We then employ the energy-Casimir method to construct a control law, together with a Lyapunov function, which renders the desired motion asymptotically stable. Finally, using a disturbance model developed in an earlier work, we study the effects of the Froude-Krylov excitation forces on the closed-loop system response.

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.

Evolution of the propeller near-wake and potential energy in a thermally-stratified environment

The unsteady near-wake of a self-propelled body in a linearly stratified environment is studied through the novel use of an actuator-line model. A comparison to experiment at ReL = 1.6×106 shows agreement in wake profiles and the emergence of individual blade-wake structures. Increasing the Reynolds number to ReL = 3.1×108 reveals a delayed vortex breakdown and relative reduction in velocity profile magnitude, in addition to a thinner boundary layer and reduced skin-friction coefficient as predicted by theory. Downstream turbulent-kinetic, mean-kinetic, and potential energies reveal the persistence of swirl and growth of potential energy, which is embodied as a mixed patch. While velocity and turbulent-kinetic energy are axisymmetric in the mixed patch, the temperature field grows into a unique profile that is asymmetric in the azimuthal direction.

Evolution of Stratified Boundary-Free Shear Flows Under Stokes-Ekman Forcing

Three boundary-free shear flows: a net-zero-momentum shear layer, drag shear layer, and jet are simulated in ocean environments using a 2-dimensions-plus-time approximation of the Reynolds-averaged Navier-Stokes equations. Stokes and Ekman forcing are considered over an array of cases in three different stratification environments to consider the effects of waves, wind, and buoyancy. Constant temperature, linearly-varying temperature, and linearly-varying temperature with a pycnocline are considered. Furthermore, wind conditions are varied from calm to increasing intensities. The results reinforce the thought that the wave-induced Stokes force plays a major role in the development of Langmuir-type circulations. Under “calm” to “smooth” conditions, Stokes-Ekman forcing induces minor changes on shear-layer width and height evolution. For “moderate” conditions and higher, simulations indicate significant changes to shear-layer width and height evolution as well as changes in free-surface transverse current features. The manner of change is mostly dependent on the chosen stratification environment, but results also suggest that Ekman forcing accelerates shear layer spreading.