This project documents the development of a non-linear controller, estimator and model to be used for dynamic positioning of a shuttle tanker. State-of-the-art methods have been developed by [FG98], which employs a backstepping framework for the control of a supply ship. This project is based on this work, and fosters to improve on the outcome, by including the wave induced motions in the stability analysis.

The estimator is based on the works of [FS99] who develops a wave filtering estimator that is both stable and passive in a Lyapunov sense. The estimator is based on the known non-linear model of the vessel, and through this, provides the controller with an estimate of the position that is better than using raw GPS and compass measurements. The estimator is shown to be exponentially globally stable, and will thus provide an estimate that over time converges to the true measurement. The stability properties and tuning of the filter is achieved using the Kalman-Yakubovich-Popov lemma.

The end result is a uniform globally exponential stable controller that is able to maintain the vessels position whilst under the influence of disturbances. The benchmark of the controller is the linear system used at FORCE TECHNOLOGY to test if various thruster configurations of ships are able to maintain the position under specified disturbances. Results have shown that the non-linear controller outperforms the linear counterpart, and as such could replace the system used at FORCE TECHNOLOGY .

Besides the controller, initial steps to develop an on-line thrust allocating module by solving a quadratic equation have been developed and tested, however, large jumps in the control signal makes the allocating module unstable. The complexity of the optimization problem is evident by the two azimuth thrusters mounted on the vessel, which both requires an angle and an input force, and through this, can be used to produce a force in the x- and y-direction as well as a moment about the z-axis.

To the authors knowledge, no one have included the wave induced motion pa- rameter in the stability analysis of ships - and these findings make way for a deeper investigation into non-linear control of ships and other off-shore vehicles. Proposals to make the system even more robust are discussed in the report.