# PMSM torque behavior and interpretation

As I know, with field oriented control of a PMSM it is possible to control a constant torque via the dq-axis currents.

I try to understand the behavior of a permanent Magnet synchronous machine when the frequency of the energizing current is not aligned with the rotor speed, i.e., the corresponding fields are not synchronous.

Would in this case the torque varying in time, in other words, the torque cannot be constant? When I simulate a PMSM with sinusoidal coil voltages of fixed frequency, would it be possible at all to create a constant torque, unless the rotor is rotating with the same frequency?

• Constant torque? No. You would get at best very poor starting and extreme torque fluctuation from zero to max torque at the difference frequency between the rotor's d-axis and the stator's field. But absent any control, within a certain load range it would behave as a synchronous machine and the rotor would lock to the stator's field. Sep 25, 2019 at 20:17
• Thanks. Fluctuation means an oscillation like torque profile? Could it also happen that the torque becomes negative, i.e. An oscillation arround the zero axis? Sep 25, 2019 at 21:08
• Yes, the torque would become negative, it would oscillate around the zero axis. I should have said between zero and +/- max torque. Sep 25, 2019 at 21:26

For a simple motor with a two-pole armature, if $$\\theta_A\$$ is the armature angle, and $$\\theta_S\$$ is the stator's electrical angle, and a motor with a sinusoidal back-EMF, then the torque is going to be $$\k_T I \sin \theta_A - \theta_S\$$, where $$\k_T\$$ is the motor torque constant and $$\I\$$ is the armature current intensity.