This work shows a mathematic calculation of the hydrodynamic model for the Cormoran-AUV, together with a linear controller which is valid in a certain range of speeds. It also presents the navigation instruments needed to work correctly. The mathematic model has been simplified to three degrees of freedom of movement and the whole system has been simulated using the Matlab Simulink Software. The system has been linearized for different velocities to design a linear control PD for each one of them. The performance of each PD controller is studied, and some limitations in the implementation of the control have been detected. For the case of low speeds, the desired path doesn’t reach the goals of control’s design using the non-linear model. This behavior motivated the search of a valid range of speeds for the nonlinear model. Different paths have been simulated using this control and their results have been compared trhough the performance in the rising time and the establish time.