solve the problem

Let the transfor function of the system be given as follows:

$P(s)=\frac{c.}{s[(as+b)(es+f)+C^2]}$

If the last $3($three$)$ digits of your class number are $xyz,C=0.xyz,a=0\mathrm{.}0yxz,b=0.zyx,e=xy\frac{z}{500}$ and $f=1.($for example your class number $($xyz$=013$ and xyz$=036)$

If the last $3$ digits are $123,C=0\mathrm{.}123,a=0\mathrm{.}0213,b=0\mathrm{.}321,e=\frac{123}{500},f=1.)$

Determine whether the system is stable by looking at both the Routh$-$llurwitz and root values?

Justify your answer analytically. Draw the step response of the system.

First, evaluate the performance of the system by considering the feedback architecture in which there

is no disruptive effect on the system. Design P$,$ PI and PID controllers for such a system using the Ziegler$-$Nichols

Method