Induction machines (IMs) are widely used in many applications, e.g., electric vehicles or industrial automation, which motivates efficiency-optimal operation for the sake of energy and cost savings. However, a loss-minimal IM control leads to reduced flux operation at partial load, i.e., achievable torque dynamics after load steps are physically limited due to the IMâ\euro™s large rotor time constant. Hence, designing the IM torque control for minimal settling time is of particular importance to allow both an efficient and sufficiently dynamic drive operation. Against this background, a model predictive control (MPC) framework is proposed, which utilizes a precise model of the IM covering magnetic saturation, iron losses, skin effect and thermal influences. As this model is highly nonlinear, it is iteratively linearized along the predicted control trajectory so that a computationally efficient quadratic program can be defined for the MPC problem. To enable sufficiently long prediction horizons, a hierarchical control structure with the stator currents as the actuation variables of the model predictive torque control is utilized. Thanks to this scalable control approach, the proposed framework can be easily extended to multi-machine drive systems covering higher-dimensional problem spaces. Empirical tests validate the feasibility of the proposed approach both for single as well as multi-machine drive applications.