Control of an underwater vehicle in irregular waves

In an effort to account for wave forcing in underwater vehicle dynamics, a model derived from Lagrangian mechanics is implemented. The model is first specialized to the case of an underwater vehicle operating in plane progressive waves. A comparison is made between the model in plane progressive waves and an exact solution derived from potential flow theory, revealing that the model accurately captures Froude-Krylov excitation forces. Plane progressive waves are then used to approximate the Pierson-Moskowitz wave energy spectrum as a means to simulate a natural seaway. A proportional derivative (PD) controller is devised to simultaneously maintain a desired depth and heading angle for an underactuated, underwater vehicle to demonstrate the capability of the proposed model.