A major drawback hinders the application of Model Predictive Control (MPC) to the regulation of electromechanical systems or, more generally, systems with fast dynamics: the time needed for the online computation of the control is often too long with respect to the sampling time. This paper shows how this problem can be overcome by suitably implementing the MPC technique. The main idea is to compute the control law using the discrete-time Euler Auxiliary System (EAS) associated with the continuous-time plant, and apply the control obtained for the discrete-time system to the continuous-time system. In this way the implementation sampling time can be much smaller than the EAS time parameter, which leads to significant savings in computation time. Theoretical results guarantee stabilisation, constraint satisfaction and robustness of such a control strategy, which is applied to the control of an electric drive and a cart-pendulum system.