$H_{2}$ and $H_{\infty }$ Designs for Diving and Course Control of an Autonomous Underwater Vehicl

H ₂ and H _infin designs applied to the diving and course control of an autonomous underwater vehicle (AUV) considering the presence of wave disturbances are described. The six-degrees-of-freedom equations of motion of the vehicle are described as a linear model and divided into three noninteracting (or lightly interacting) subsystems for speed control, steering, and diving. This work is based on the slender form of the Naval Postgraduate School (NPS, Monterey, CA) AUV, considering that the subsystems can be controlled by means of two single-screw propellers, a rudder, port and starboard bow planes, and a stern plane. A model of the AUV dynamics is presented with the first- and the second-order wave force disturbances, i.e., the Froude-Kriloff and diffraction forces. An algorithm of nonlinear regression for the rationalization of the subsurface sea spectrum is provided in this case study. The obtained results are analyzed and evaluated in the frequency domain comparing the controllers performance considering or not the inclusion of the model of waves.