Question

The block diagram of a system is illustrated inthe figure shown, where $X\left(s\right)$ is the input and $Y\left(s\right)$ is the output. the transfer function $H\left(s\right)=\frac{Y\left(s\right)}{X\left(s\right)}is$

• A. $H\left(s\right)=\frac{s^2+1}{2s^2+1}$
• B. $H\left(s\right)=\frac{s^2+1}{s^3+2s^2+s+1}$
• C. $H\left(s\right)=\frac{s+1}{s^2+s+1}$
• D. $H\left(s\right)=\frac{s^2+1}{s^3+s^2+s+1}$

Answer 1

The correct option is B $H\left(s\right)=\frac{s^2+1}{s^3+2s^2+s+1}$

Using block diagram reduction , we get,

$\frac{Y\left(s\right)}{X\left(s\right)}=H\left(s\right)=\frac{s^2+1}{s^3+2s^2+s+1}$