Constant torque motors are needed for rotary screw compressors that are used for cooling and other applications. In such systems, the torque demanded by the load is approximately the same over the whole range of mechanical speeds. In this paper, the use of multi-phase induction machines is investigated for this type of application. The requirement of low stator current distortion is considered. A scheduled approach is used to provide the best possible tuning for each operating point, similar to the concept of gain scheduling control. Simulations and laboratory tests are used to assess the proposal and compare it with finite-state predictive control. The experiments show that a trade-off situation appears between the ripple content in stator currents in the torque-producing and harmonic planes. As a consequence, the controller tuning appears as an important step. The proposed method considers various figures of merit with cost function tuning, resulting in a scheduled scheme that provides improved results. It is shown that the approach leads to a reduction in current ripple, which is advantageous for this particular application.