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Chapter 3 describes the same new dead-beat control law for three-phase interior permanent magnet synchronous motors with armature reaction, based on the motor discrete-time state-space equation system, using the eigenvalues of the transition matrix. The algebraic calculation of the control voltage vector takes account of d-q axis motor parameters, motor current measures, torque, flux and current set-points, and torque, voltage, flux and current limits. The general algebraic solution for minimizing the current for a given torque is presented. A real-time implementation of algorithms without position sensor is proposed with a Kalman observer. The total uncoupling between torque and flux controls is shown, as well as the torque accuracy and dynamics. The PWM and sampling periods can be chosen regardless of control law, in order to optimize inverter switching frequency and motor current shape factor.