How do I reduce a block diagram with just a line as a feedback loop, I dont get how it adds K to the denominator. The bottom equation is supposed to be the answer.
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- $\begingroup$ Write $W(s) = R(s)-C(s)$, then $C(s)/W(s)$ equals the transfer function in the block. Now do the algebra to find $C(s)/R(s)$ eliminating the intermediate $W(s)$. $\endgroup$Andy Walls– Andy Walls2023-08-22 10:29:24 +00:00Commented Aug 22, 2023 at 10:29
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1 Answer
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Let's call the transfer function of the filter $H(s)$:
$$H(s)=\frac{K}{s(Js+B+KK_h)}=\frac{K}{D(s)}\tag{1}$$
From the diagram we have
$$C(s)=\big[R(s)-C(s)\big]H(s)\tag{2}$$
from which you get
$$\frac{C(s)}{R(s)}=\frac{H(s)}{1+H(s)}=\frac{K}{D(s)+K}\tag{3}$$
I'm sure you can fill in the details yourself.