$(2)$ A servomechanism position control has the plant transfer function

$G(s)=\frac{10}{s(s+1)(s+10)}$

You are to design a series compensation transfer function $D_c(s)$ in the unity feedback configuration to meet the following closed$-$loop specifications.

The response to a reference step input is to have no more than $16\%$ overshoot.

The response to a reference step input is to have a rise time of no more than $0\mathrm{.}4$ sec $.$

The steady$-$state error to a unit ramp at the reference input must be less than $0\mathrm{.}05$

$($a$)$ Design a lead compensation that will cause the system to meet the dynamic response specifications, ignoring the error requirement.

$($b$)$ What is the velocity constant $K_v$ for your design? Does it meet the error specification?

$($c$)$ Give the Matlab plot of the root locus of your final design.

$($d$)$ Give the Matlab response of your final design to a reference step.