A family of passivity-based controllers for dynamic positioning of ships is presented. The authors exploit the idea of shaping the energy function of the closed-loop system to obtain different formulations of the passivity-based control law using the interconnection and damping assignment-passivity-based control (IDA-PBC) methodology. A salient feature of this study is that the proposed control laws are output feedback controllers and the relative velocity measurement is not required. First, we design and analyse two static controllers which can be seen as a non-linear version of the conventional proportional-derivative (PD) controllers. In presence of unknown disturbances, these controllers do not provide the desired regulation properties. To remove this discrepancy we propose, also in the context of the IDA-PBC technique, a dynamic extension of the system and obtain two new controllers that have the desired regulation properties. These new control laws can be seen as a non-linear version of the conventional proportional-integral-derivative (PID) controllers. Simulations are included to validate the theoretical results.