Question

The steady state error due to a unit-step disturbance input D(s) in figure is

• A. 0
• B. 0.012
• C. 0.021
• D. 0.025

Answer 1

The correct option is D 0.025


Now we have to find $e_{ss}$due to D(s) input so, R(s)=0. The reduced block diagram will be



C(s) = CLTF x D(s)

$CLTF=\frac{1/s(1+5s)}{1+\frac{40}{s(1+5s)}}$

$=\frac{1}{5s^2+s+40}$

$=\underset{t\to \infty }{lim}c\left(t\right)={lim}_{s\to 0}sC\left(s\right)$

$=\underset{s\to 0}{lim}s\times CLTF\times D\left(s\right)$

$=\underset{s\to 0}{lim}s\times CLTF\times \frac{1}{s}$

$=\underset{s\to 0}{lim}CLTF$

$=\underset{s\to 0}{lim}\frac{1}{5s^2+s+40}$

$=\frac{1}{40}$

$=0.025$