A challenging task in automotive electrical traction drives is to control the speed of synchronous machines due to the existing physical and computational constraints. The goal of this paper is to find a control solution which can answer this problem. To this end, a multirate predictive cascade speed control structure suitable for real-time implementation is proposed. The focus in this paper is only on the design of the outer-loop controller. First, a suitable mathematical model for the outer-loop plant which includes also the dynamics of the inner control loop is obtained. Second, a one-step-ahead state-feedback model predictive controller based on flexible Lyapunov function concept is employed to control the rotor electrical speed. Third, a state and disturbance observer is employed to estimate the load torque and the unmeasured state. This ensures also offset-free operation of the closed-loop system. To illustrate its effectiveness, the proposed control solution is implemented in a real microcontroller and tested in real time on an industrial hardware-in-the-loop test bench and on a real traction test bench.