In power electronics, multiphase machines have been recently proposed, where most sensorless algorithms applied to electrical drives are represented through a mathematical representation of the physical system which includes the electrical and mechanical parameters of the motor. However, in electrical drive applications, the rotor current cannot be measured, so it must be estimated. This paper deals with the speed sensorless control of five-phase induction machines by using an inner loop of model-based predictive control (MPC). The MPC is obtained from the mathematical model of the machine, using a state-space representation where the two state variables are the stator and rotor currents, respectively. The rotor current is estimated using a reduced order optimal estimator based on a Kalman filter. Simulation results are provided to show the efficiency of the proposed sensorless speed control algorithm.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCI