The block diagram of a PM DC servo motor with current loop feedback is shown below:
If Ki is adjusted such that J(Ki+R)2 >> 4KTKbL, show that the transfer function may be approximated by
G(s) = (1/Kb) / (τms+1)(τes+1),
τm = J(R+Ki) / KTKb
τe = L / (R+Ki)
The Attempt at a Solution
I simplified the block diagram and got the transfer function:
G(s) = Kt / (JLs2 + J(R + Ki)s + KtKb)
Then I tried to factor the denominator. When using the quadratic formula, I found:
(-JR - JKi) +/- sqrt( J[ J(R+Ki)2 - 4KtKbL]) / 2JL
Assuming the conditions presented for Ki, I canceled out the 4KtKbL.
Am I on the right path? In the end, I still couldn't get the transfer function presented in the homework.