This paper presents the dynamic modelling and control technique for a tilt-rotor aerial vehicle operating in bi-rotor mode. This kind of aircraft combines two flight envelopes, making it ideal for scenarios that require hovering, vertical take-off/landing and fixed-wing capabilities. In this work, a detailed mathematical model is derived using Newton-Euler formalism. Based on the obtained model, a new control scheme that incorporates six Proportional-Derivative (PD) controllers is proposed for the attitudes (roll (φ), pitch (θ), yaw (ψ)) and the positions (x, y, z) of the aircraft. Then, intelligent Particle Swarm Optimization (PSO) and conventional Reference Model (RM) techniques are applied for optimal tuning of the controllers' parameters. The stability analysis is developed using the Lyapunov approach and its application to the tilt-rotor system in the case of intelligent and conventional PD controllers. Numerical results of two scenarios prove the efficiency of the controllers tuned using the PSO method. Indeed, its ability to track the desired trajectories is demonstrated through 3D path tracking simulations, even in the presence of wind disturbances. Finally, experimental tests of stabilization and trajectory tracking are carried out on our prototype. These testing showed that our tilt-rotor was stable and suitably follows the imposed trajectories.