# Unity negative feedback controller, why does Gain K go on the numerator of the transfer function

I have a system G(s). It has no zeroes, but some poles.

When applying unity negative feedback, with a static gain K, why does K remain on the numerator of my transfer function T(s) which describes the whole closed loop system?

If I have no zeroes, Z(s), then surely K multiplied by Z(s) is 0? But it is K.

In addition, in the denominator, there is another term that is again, K multiplied by Z(s). No zeroes, but this term simplifies to K, and not 0.

I understand that Z(s) is a function, and normally takes the form (s+3)(s+1) or something, but if there are no zeroes, can someone explain why K remains on the numerator?

Thanks

• en.wikibooks.org/wiki/Control_Systems/…, i'm unsure of your question May 31 '17 at 14:06
• K doesn't have any zeroes.
– Chu
May 31 '17 at 14:52
• No zeros means $Z(s)=1$, hence $K Z(s)=K$ May 31 '17 at 15:00