I am controlling a BLDC motor using Field Oriented Control (FOC). I use a 14-bit absolute encoder to read the rotor's position \$\theta_{m} \$, and use it to reconstruct the electrical angle \$\theta_{e}\$, which is given by:

\$\theta_{e}=\theta_{m}\cdot N_{p} + \theta_{offset}\$

This angle is used in Park's transformations to reconstruct current readings, and to produce, with inverse transform, PWM voltage references.

Given knowledge of the number of pole pairs \$N_{p}\$, and a perfectly homogeneous distribution of the pole pairs, how sensitive is motor's performance to the accuracy with which we experimentally define \$\theta_{offset}\$?

How accurately is it usually defined for high-accuracy torque control application field such as robotics?

Edit: with some more research, I found \$\theta_{offset}\$ accuracy is mostly sought for torque efficiency. What I am surprised not to find yet is people discussing its induced disturbances on the closed-loop current control systems. How does it affect, for instance: bandwidth, vibrations, audible noise, and energy consumption?

  • \$\begingroup\$ The accuracy of angle to determine the PWM phasors generally affect the smoothness of operation in case of sinusoidal back emf machines. If your machine has trapezoidal back emf, the effect would be less. \$\endgroup\$ Dec 6, 2017 at 8:33
  • \$\begingroup\$ Should be multiplying by the number of pole pairs \$\endgroup\$
    – user28910
    Dec 6, 2017 at 14:30
  • \$\begingroup\$ @user28910 you are right, I corrected it \$\endgroup\$
    – raggot
    Dec 6, 2017 at 14:35

1 Answer 1


In my experience (with my own FOC design) \$ \theta_{offset}\$ errors primarily affect torque efficiency and bandwidth, and have a lesser or insignificant effect on vibration and audible noise. Small valued errors will result in 'lopsided' performance, where your motor spins faster in one direction than the other.

  • \$\begingroup\$ Thanks for answering this so long after I asked it. I just saw it and +1'd it. I can't accept the answer purely based on your experience though. If you add some more theoretical backing or source I'll be happy to do it. I'm especially interested in your last statement. Does the lopsided effect follow from Park math? \$\endgroup\$
    – raggot
    Feb 11, 2020 at 9:48
  • \$\begingroup\$ Sure. Inverse Park transfom gives you the phase voltages which will optimally advance your rotor at a given rotor angle. If you have an error, you'll either lead or lag that angle depending on the sign of the error and the direction you're trying to spin. Think of a donkey following a carrot on a stick; if you try and maintain a longer distance (positive torque, small positive error and negative torque small negative error) he will walk faster to catch up to you. If you maintain a smaller distance (positive torque, small negative error and negative torque, small positive error) he will walk a \$\endgroup\$
    – Ocanath
    Feb 11, 2020 at 22:38
  • \$\begingroup\$ – little slower. This effect is called 'phase advance control', and can be applied to control techniques other than FOC as well (such as trapezoidal or sinusoidal) to, in some cases, spin the motor faster than its rated maximum speed. It also happens to be a convenient way to converge on the correct motor phase angle because of its effect on speed. \$\endgroup\$
    – Ocanath
    Feb 11, 2020 at 22:43
  • \$\begingroup\$ After two years, the answer to the riddle has come. Cheers! \$\endgroup\$
    – raggot
    Feb 13, 2020 at 22:20

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