Hey, guys.

I'm studying the Automatic Control Systems and struggling with characteristic fn.

I'm given a system diagram as an attachment and I got my answer, but it's different from the solution.

My answer is

Transfer function : K/(JS^2 + aS + K*Kf*s +K)

But the answer from the solution is

Transfer function : (K*Kf) / [JS^2 + (aS + K*Kf)s +K*Kf]

As you noticed, there're Kf added on each.

Am I wrong or is solution wrong. I've been struggling with this for 3 hours and can't see

any problem from mine.

(The way I solved this is, I considered the system as two separate closed-loop. Firstly, calculated the first closed-loop in the middle then multiplied by 1/s. Then calculated as a closed-loop again with it. )

And another question is, I need to draw Nyquist plot with transfer function above.
Normally the transfer function is given as a form of 'G(s)/[1 + G(s)H(s)], so I can draw the Nyquist plot with open-loop function G(s)H(s). But with the function above, I can't seem to seperate G(s)H(s). How can I do this?

Could somebody help me with this matter?
Thanks a lot for your time.

 

I believe your answer is the correct one. At least that's the answer I derived.

 

I got the same answer from others. Thanks.