Aerial manipulation aims at combining the manoeuvrability of aerial vehicles with the manipulation capabilities of robotic arms. This, however, comes at the cost of the additional control complexity due to the coupling of the dynamics of the two systems. In this paper we present a NMPC specifically designed for MAVs equipped with a robotic arm. We formulate a hybrid control model for the combined MAV-arm system which incorporates interaction forces acting on the end effector. We explain the practical implementation of our algorithm and show extensive experimental results of our custom built system performing multiple aerial-writing tasks on a whiteboard, revealing accuracy in the order of millimetres.