: A minimum-time torque control strategy for permanent-magnet ac motor drives is presented. The proposed solution is obtained by an ad-hoc procedure based on the computation of reachability and controllability sets which in turn requires solving iteratively a fourth-degree polynomial equation. For its efficient implementation an algorithm based on Sturm sequences is proposed. The algorithm has been implemented on a laboratory prototype and the experimental results, showing the effectiveness of the proposed technique, are included in the paper. Copyright c 2005 IFAC