Question $2$: The transfer function of a plant is $G(s)=\frac{10}{(s+1)(s+5)}.$

a$)$ Our task is to design a controller $C(s)$ to meet the following specifications in closed

loop with unit feedback: $M_{p}16\%,{}_n=5,$ and steady state error for unit step input

$0\mathrm{.}1.$ Use the root locus approach and a lag compensator.

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.