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To effectively reject the influence of speed detection on system stability and precision for a bearingless induction motor, this paper proposes a novel speed observation scheme using artificial neural network (ANN) inverse method. The inherent subsystem consisting of speed and torque winding currents is modeled, and then its inversion is implemented by the ANN. The speed is successfully observed via cascading the original subsystem with its inversion. The observed speed is fed back in the speed control loop, and thus, the speed-sensorless vector drive is realized. The effectiveness of this proposed strategy has been demonstrated by experimental results.