# Relationship between offset in electrical angle and BLDC motor performance

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?

• 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. Commented Dec 6, 2017 at 8:33
• Should be multiplying by the number of pole pairs Commented Dec 6, 2017 at 14:30
• @user28910 you are right, I corrected it Commented Dec 6, 2017 at 14:35

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.