$[40$ pts$]$ Given the following system:

$D(s)=\frac{s+z}{s+p},G(s)=\frac{1}{(s+0\mathrm{.}1)(s+0\mathrm{.}5)}$

a$)$ Design a lag compensator so that the resulting system has a phase margin of around $65$ degrees and steady state error of at most $1\%$ for unit$-$step input.

b$)$ Draw the bode plot $($magnitude and phase$)$ for the resulting system. $($You will need to visualize your design for refinement$).$