A control method implemented in a variable speed drive for determining the flux and torque inductances (Ld, Lq) of a permanent magnet synchronous machine comprising three phases (a, b, c), each oriented in a direction, a stator and a rotor, characterized in that said method includes steps of: - applying, in the direction of each phase (a, b, c) of a voltage vector (V1, V3, V5) in the positive direction and of a voltage vector (V2, V4, V6) in the negative direction for a predetermined duration, for a phase, the application of the voltage vector in the positive direction and of the voltage vector in the negative direction entailing applying a voltage sequence comprising a positive voltage slot of a predetermined pulse width (Tp), followed by a negative voltage slot having two times the predetermined pulse width (Tp), followed by a positive voltage slot of the predetermined pulse width (Tp), - measuring a current response in each phase after applying the voltage vectors in the two directions, the current response comprising, for each phase, a positive peak and a negative peak, - recovering, for each phase and at the same instants, two distinct current values (Ia1+, Ia2+, Ib1+, Ib2+, Ic1+, Ic2+) on the positive current peak, in its upward phase and two distinct current values (Ia1-, Ia2-, Ib1-, Ib2-, Ic1-, Ic2-) on the negative current peak, in its downward phase, - determining the following values: Δ Ia ave = | δ I a + | + | δ I a − | 2 Δ Ia diff = | δ I a + | − | δ I a − | 2 Δ Ib ave = | δ I b + | + | δ I b − | 2 Δ Ib diff = | δ I b + | − | δ I b − | 2 Δ Ic ave = | δ I c + | + | δ I c − | 2 Δ Ic diff = | δ I c + | − | δ I c − | 2 in which δI a+, δI a-, δI b+, δI b-, δI c+, δI c- represent, for each phase, the current variations calculated on the basis of the current values recovered on the positive current peak and on the negative current peak that are obtained. - determining an angle (θr) for the position of the rotor in relation to the stator on the basis of the following relation: Δ I diff = Δ Ia diff + Δ Ib diff e j 2 π / 3 + Δ Ic diff e j 4 π / 3 et θ r = arctan Δ I diff - determining the flux (Ld) and torque (Lq) inductances of the machine as a function of the determined angle (θ r). - applying, in the direction of each phase (a, b, c) of a voltage vector (V1, V3, V5) in the positive direction and of a voltage vector (V2, V4, V6) in the negative direction for a predetermined duration, for a phase, the application of the voltage vector in the positive direction and of the voltage vector in the negative direction entailing applying a voltage sequence comprising a positive voltage slot of a predetermined pulse width (Tp), followed by a negative voltage slot having two times the predetermined pulse width (Tp), followed by a positive voltage slot of the predetermined pulse width (Tp), - measuring a current response in each phase after applying the voltage vectors in the two directions, the current response comprising, for each phase, a positive peak and a negative peak, - recovering, for each phase and at the same instants, two distinct current values (Ia1+, Ia2+, Ib1+, Ib2+, Ic1+, Ic2+) on the positive current peak, in its upward phase and two distinct current values (Ia1-, Ia2-, Ib1-, Ib2-, Ic1-, Ic2-) on the negative current peak, in its downward phase, - determining the following values: Δ Ia ave = | δ I a + | + | δ I a − | 2 Δ Ia diff = | δ I a + | − | δ I a − | 2 Δ Ib ave = | δ I b + | + | δ I b − | 2 Δ Ib diff = | δ I b + | − | δ I b − | 2 Δ Ic ave = | δ I c + | + | δ I c − | 2 Δ Ic diff = | δ I c + | − | δ I c − | 2 in which δI a+, δI a-, δI b+, δI b-, δI c+, δI c- represent, for each phase, the current variations calculated on the basis of the current values recovered on the positive current peak and on the negative current peak that are obtained. - determining an angle (θr) for the position of the rotor in relation to the stator on the basis of the following relation: Δ I diff = Δ Ia diff + Δ Ib diff e j 2 π / 3 + Δ Ic diff e j 4 π / 3 et θ r = arctan Δ I diff - determining the flux (Ld) and torque (Lq) inductances of the machine as a function of the determined angle (θ r).