Question

The signal flow graph representation of a control system is shown below:
The transfer fucntion $\frac{Y\left(s\right)}{R\left(s\right)}$ is computed as

• A. $\frac{1}{s}$
• B. $\frac{s^2+1}{s(s^2+2)}$
• C. $\frac{s(s^2+1)}{s^2+2}$
• D. $1-\frac{1}{s}$

Answer 1

The correct option is A $\frac{1}{s}$

Forward path gain,
$P_1=\frac{1}{s}$
$P_2=\frac{1}{s^3}$
${\Delta }_1={\Delta }_2=1$
Loop gain,
$P_{11}=-\frac{1}{s^2}$
$P_{21}=-\frac{1}{s^2}$
$P_{31}=\frac{1}{s^2}$
$TransferfunctionT\left(s\right)=\frac{P_1{\Delta }_1+P_2\Delta 2}{1-P_{11}-P_{21}-P_{31}}$

$=\frac{\frac{1}{s}+\frac{1}{s^3}}{1+\frac{1}{s^2}+\frac{1}{s^2}-\frac{1}{s^2}}=\frac{(s^2+1)}{s(s^2+1)}=\frac{1}{s}$