Closed-loop transfer function

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${\displaystyle Y(s)=Z(s)G(s)\Rightarrow Z(s)={\dfrac {Y(s)}{G(s)}}}$

${\displaystyle X(s)-Y(s)H(s)=Z(s)={\dfrac {Y(s)}{G(s)}}\Rightarrow X(s)=Y(s)\left[{1+G(s)H(s)}\right]/G(s)}$

${\displaystyle \Rightarrow {\dfrac {Y(s)}{X(s)}}={\dfrac {G(s)}{1+G(s)H(s)}}}$

See also

• Federal Standard 1037C
• Open-loop controller

References

•   This article incorporates public ___domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.