This paper deals with the full dynamic modeling and control of a flying architecture called a flying parallel robot (FPR). This architecture, which can be seen as a parallel robot whose actuators have been replaced by drones, offers novel possibilities for robotic and aerial manipulation. Over the last decade, many prototypes have been developed in the field of aerial manipulation, like attaching a gripper or a manipulator to the drone. Nevertheless, the proposed approaches suffer from several drawbacks such as a limitation of payload, autonomy constraints and also a manipulability impacted by the quadrotor underactuation, if standard underactuated quadrotors are used. To overcome these limitations, the FPR concept has several advantages: all possible DoF of the end-effector can be controlled; by sharing the efforts over several drones, and by using no additional embedded motors, the payload capability is enhanced. In this paper, the generic dynamic model is established, whatever are the legs topologies and number of drones used. It is shows that a decoupling property of the dynamic model can be established, which can be then exploited for the design of a cascade controller handling the underactuation of the FPR. The proposed modelling approach and control strategy have been applied in order to perform real experiments with a proof-of-concept prototype belonging to the category of flying parallel robots made of three drones and three legs.