- #1

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## Homework Statement

The block diagram of a PM DC servo motor with current loop feedback is shown below:

If K

_{i}is adjusted such that J(K

_{i}+R)

^{2}>> 4K

_{T}K

_{b}L, show that the transfer function may be approximated by

G(s) = (1/K

_{b}) / (τ

_{m}s+1)(τ

_{e}s+1),

where

τ

_{m}= J(R+K

_{i}) / K

_{T}K

_{b}

τ

_{e}= L / (R+K

_{i})

## The Attempt at a Solution

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I simplified the block diagram and got the transfer function:

G(s) = K

_{t}/ (JLs

^{2}+ J(R + K

_{i})s + K

_{t}K

_{b})

Then I tried to factor the denominator. When using the quadratic formula, I found:

(-JR - JK

_{i}) +/- sqrt( J[ J(R+K

_{i})

^{2}- 4K

_{t}K

_{b}L]) / 2JL

Assuming the conditions presented for K

_{i}, I canceled out the 4K

_{t}K

_{b}L.

Am I on the right path? In the end, I still couldn't get the transfer function presented in the homework.