Capable of both vertical take-off and landing and forward flight, tail-sitters are a versatile class of UAVs with a large range of potential applications. A variant of tailsitters using tilt-rotors instead of ailerons for pitch and roll control has been proposed to mitigate the reduced control authority at low to zero velocities. The control of the translational dynamics for this platform is uniquely challenging. The extended flight envelope requires the controller to be able to perform hover and forward flight which are two flight phases with very different dynamics. Additionally, the tilt-rotor mechanism used to control the system is highly nonlinear which adds to the challenge. This paper presents a novel acceleration controller using Nonlinear Model Predictive Control (NMPC) in addition to the use of behavioural cloning to mimic the NMPC using a feedforward neural network. It is shown that behavioural cloning does successfully transfer general flight characteristics but that the performance is degraded with respect to the NMPC. Additionally, a sensitivity analysis was performed to investigate the effects of improper parameter estimation on controller performance. The most interesting result from this analysis is the strong sensitivity of both controllers to changes in centre of gravity location and mass.