$5.$ Consider a plant given by $\backslash ($ P$($s$)=\backslash$frac$\{100\}\{($s$+1)($s$+10)\}\backslash ).$ The goal is to achieve steady state tracking error less than $\backslash (1\backslash \%\backslash )$ without affecting the phase margin.

$($a$)$ Design a lag compensator to achieve the above.

$($b$)$ Plot the step response of the closed loop system before and after compensation $($on the same figure$),$ as well as the open loop Bode plot before and after compensation $($on the same figure$).$ Verify that the above specification has been met, and report the change in phase margin, if any.