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A new deadbeat type of direct torque control (DTC) is proposed, analyzed, and experimentally verified in this paper. The control is based on stator and rotor flux as state variables. This choice of state variables allows a graphical representation which is transparent and insightful. The graphical solution shows the effects of realistic considerations such as voltage and current limits. A position- and speed-sensorless implementation of the control, based on the self-sensing signal injection technique, is also demonstrated experimentally for low-speed operation. The paper first develops the new deadbeat DTC methodology and graphical representation of the new algorithm. It then evaluates feasibility via simulation and experimentally demonstrates performance of the new method with a laboratory prototype including the sensorless methods.