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Operation of induction machines in the high-speed and/or high-torque range requires field-weakening to comply with voltage and current physical limitations. This paper presents an anti-windup approach to this problem: rather than developing an ad-hoc field weakening strategy in the high-speed region, we equip an unconstrained vector-control design with an anti-windup module that automatically adjusts the current and flux set-points so that voltage and current constraints are satisfied at every operating point. The anti-windup module includes a feedforward modification of the set point aimed at maximizing the available torque in steady-state and a feedback modification of the controller based on an internal model-based antiwindup scheme. This paper includes a complete stability analysis of the proposed solution and presents encouraging experimental results on an industrial drive.