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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

Example

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  • \$\begingroup\$ en.wikibooks.org/wiki/Control_Systems/…, i'm unsure of your question \$\endgroup\$ – sstobbe May 31 '17 at 14:06
  • \$\begingroup\$ K doesn't have any zeroes. \$\endgroup\$ – Chu May 31 '17 at 14:52
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    \$\begingroup\$ No zeros means \$Z(s)=1\$, hence \$K Z(s)=K\$ \$\endgroup\$ – Suba Thomas May 31 '17 at 15:00
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The order of the Tf goes from its highest power down to s^0 which is one ie theres always a one there

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