A liquid mixture is heated in a perfectly mixed tank with a heating coil using a

saturated steam at $120C.$ Temperature of the mixture is controlled using a

proportional integral controller. Temperature of feed stream and flow rate of steam

act as disturbance and manipulated variable, respectively.

The open loop transfer functions are

$G_p=\frac{1}{1+s}$ and $G_d=\frac{0\mathrm{.}5}{1+s}$

For proportional$-$integral controller;

$G_c=5(1+\frac{1}{0\mathrm{.}5s})$

The measuring device and control valve have the following transfer functions:

$G_m=1G_f=1$

a$)$ Draw the block diagram of closed loop system

b$)$ Drive the expression for closed loop response.

c$)$ Find the offset for a unit step change in the set point $($servo problem$)$ Is there

a change in the order of the response? Please state what is the reason for the

occurrence or absence of the change.

d$)$ How would response will change if $Kc=10?$ Just make a comment, do not make

any calculations.

Please write your answer step by step and clearly. I'll remember to evaluate your answer.