Question $1$: Consider the following second order plant

$G(s)=\frac{1}{(s+2)(s+4)}$

a$)$ Design a controller $C(s)($lead$,$ lag or lead$-$lag$)$ with root locus design which will have a rise time less than $0\mathrm{.}5$ seconds, $M_p$ less than $20\%$ and can track a unit reference signal with a steady state erros less than $0\mathrm{.}01.$

b$)$ Simulate the plant under control with a unit step input in Matlab and Simulink. Check is the design specifications are met or not.

c$)$ Draw a bode diagram of the $C(s)G(s)$ without using Matlab.

d$)$ Draw a bode diagram of the $C(s)G(s)$ with using Matlab.