$($a$)$ Simulate the process transfer function with a unit step change in

input in Figure$-4.$ Choose values for your process parameters using

your date of birth:

K$=11$

T$\_(1)=2$

$($b$)$ Take required measurements from the response in $($a$)$ for use in the

Ziegler$-$Nichols open loop PID tuning method. $[5$ marks$]$

$($c$)$ Design a PI controller $($ K$\_($c$)$ and T$\_($i$))$ for the process using your results

in part $($b$)$ and Ziegler$-$Nichols open loop method. Simulate the closed

loop PI control response to a unit step input. $[10$ marks$]$

$($d$)$ Adjust K$\_($c$)$ if required to achieve a percent overshoot $(\%$OS$)$ of

between $10\%$ to $20\%.$ With this value of K$\_("$c $"),$ choose two other values

for T$\_($i$)$ to show the effect of changing the integral action time $($T$\_($i$))$ on

the controlled response. Include:

$($i$)$ plots of the step responses,

$($ii$)$ a table comparing the percent overshoot $(\%$OS$),$ settling time and

steady state error for the three values of T$\_($i$)$ used.