In this paper a switched Model Predictive Control strategy is applied for the speed regulation of a powertrain system composed of an electrical motor connected to a rotating load through an elastic shaft and a gear, which introduces backlash. The system is described through a piecewise-affine model and a different control law is designed for each system dynamics, which allows obtaining very simple controllers, suitable for digital implementation in embedded systems. A switched Kalman filter is employed in order to estimate the unmeasurable system states. The proposed control strategy is tested through both simulations and experiments, and is compared against a traditional proportional-integral controller.