Usually, each phase of the direct reluctance motor is fed separately by its own inverter producing a squarewave phase current depending on the rotor position. In the present work, a star-connection of the three stator phases is used and the direct reluctance motor is fed by a three-phase switched inverter. The space phasor theory shows that three-phase sinewave currents can produce a constant electromagnetic torque. In this case, the rotating reference frame rotates at half of the rotor speed and in the opposite direction. This command strategy allows to reduce the stator deformation due to the electromagnetic radial force which is very high in this type of motor and which is mainly responsible for the acoustic noise. The electromagnetic torque control is realised by a sliding mode control of the three phase currents. In the rotating reference frame, it is possible to show that the eight commutation states of the switched inverter are placed around an ellipse in the complex plane of the derivatives of the space phasor of the phase current. A study of this ellipse has allowed to determine the maximal torque as a function of the speed for a given continuous voltage. It is important to insure that the torque reference will never exceed this limitation in order to avoid a pullout phenomenon, highly unwanted in the speed control. Despite the fact that the resolver inside the casing of the direct reluctance motor produces a small periodic error, it is accurate enough for the position measurement and to produce the three current references. However, the derivative of the position measurement provides a speed evaluation with such a ripple that the speed control cannot be outstanding. So, for the speed measurement, an additional laser rotary encoder is used. The experimental study in the steady-state mode of the speed control shows the presence of an electromagnetic torque ripple. This is a residual ripple caused by the dissimilarity between the stator poles teeth-shapes and the magnetic saturation effect. Although this torque ripple is rather low compared with the usual command strategy, two methods are proposed in order to compensate it. The first method is based on the use of a correction factor depending on the tooth angle. First, in steady-state conditions, the correction factor is stored off-line in a table. Then it is used in-line as a feedforward disturbance compensation. The second method of reducing the residual torque ripple consists in implementing an observer of variable disturbance. This is a disturbance observer able to determine the frequency content of the torque ripple. For instance, in order to observe the continuous component, the fundamental wave as well as the harmonics 2, 3, and 6, the observer must have ten poles. The main difficulty to deal with such an observer is the fact that each pole moves quickly as a function of the motor speed. So, in order to guarantee the observer stability over a large range of speed, the poles are located dynamically regarding to the motor speed by the way of a discontinuous adaptation of the feedforward coefficients. The theoretical study and the numerical simulation have allowed to formulate some criteria about the way of locating the poles. Experimental results confirm the efficiency of the observer of variable disturbance in order to reduce the electromagnetic torque ripple.