In this paper a Generalized Predictive Control (GPC) scheme is proposed for the stabilization of a fast mechatronic system. Namely the inertia wheel inverted pendulum, which has two degrees of freedom and one actuator. The proposed control approach should be able to stabilize this system around its unstable equilibrium point and maintain it in this state. The efficiency and performance of the proposed control scheme are firstly illustrated through simulation results, then its robustness is shown through real-time experiments on the prototype of the system in question.