This paper presents a general control framework for multicopters equipped with tiltable rotors (tilting multicopters). Differently from classical flat multicopters, tilting multicopters can be fully actuated systems able to decouple position and attitude control. The proposed framework has been transparently integrated into the widely used PX4 control stack, an open-source controller for ground and aerial systems, to fully exploit its high-level interfaces and functionalities and, at the same time, simplify the creation of new devices with tilting propellers. Simulation tools have been also added to the PX4 simulation framework, based on its Software-In-The-Loop (SITL) system and a set of simulated experiments in a dynamic robotic simulator have been carried out to demonstrate the effectiveness of this system. Moreover, to demonstrate the usability of the proposed framework, initial experiments with a real platform have been carried out.