# Vector Control Q & D axis Current Loop Gain Calculation

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#### jnnewton

##### Member
I am trying to understand how motor parameters can be used to calculate (or at least estimate) the gains in the current PI loops (for d-axis and q-axis). The closest I have come to finding a resource on how this actually works is this AN from Freescale: http://cache.freescale.com/files/microcontrollers/doc/app_note/AN4680.pdf

They have two equations:
Kp = 2 *ζ*ω*L - R (Equation 1)
Ki = ω^2 * L (Equation 2)

Where:
Kp - Proportional Gain
Ki - Integral Gain
L - inductance (for whichever axis the loop is being applied, distinction made in Table 1)
R - Single Phase Resistance
ζ - current loop attenuation
ω - natural frequency of the current closed-loop system

1. how can I calculate or estimate the inductances Ld & Lq so i can use the proper value for Kp&Ki(d-axis) as well as Kp&Ki(q-axis)?
1a. Can I assume that Lq = Ld = L for estimation purposes?
1b. Is there a more accurate way of calculating those values without measuring them as shown in the AN?
2. How do i estimate current loop attenuation and natural frequency theoretically?
2a. What motor parameters would need to be provided?
2b. Is there an equation for this calculation that is not listed in the AN?
3. Where can I find additional relevant documentation on this matter (not Vector / FOC / motor control in general, but the estimation or calculation of these gains from standard motor nameplate & datasheet values)?

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