In this paper we describe the design and implementation of a current controller for a reluctance synchronous machine based on continuous set nonlinear model predictive control. A computationally efficient grey box model of the flux linkage map is employed in a tracking formulation which is implemented using the high-performance framework for nonlinear model predictive control acados. The resulting controller is validated in simulation and deployed on a dSPACE real-time system connected to a physical reluctance synchronous machine. Experimental results are presented where the proposed implementation can reach sampling times in the range typical for electrical drives and can achieve large improvements in terms of control performance with respect to state-of-the-art classical control strategies.