High speed machine tooling allows to increase productivity and product quality, but presents new challenges for the control system. To meet them, this paper proposes to review the conventional control structure, restating the control problem in terms of a constrained finite horizon optimization problem, which can be solved efficiently with a MPC-QDMC algorithm. This approach is shown to allow to enhance significantly the precision attainable with a fixed actuator choice. The model necessary for MPC is determined at best using a black box model identification.