Consider the following open loop transfer function

$L(s)=\frac{1}{(s+1{)}^3}$

a$)$ Draw the Nyquist plot

b$)$ Identify on the Nyquist plot where the phase and geain margins are

c$)$ Catculate the gain and phase margins

d$)$ Draw the straight$-$line approximation Bode plots

e$)$ Identify on the Bode plot where the phase and gain margins are

f$)$ Calculate the gain and phase margins from the Bode plot

Consider the following open loop transfer function

$L(s)=\frac{5s+1}{s(s+1{)}^3}$

a$)$ Compute and plot the phase and gain Bode plots $(=0\mathrm{.}01,0\mathrm{.}1,1,$ and $10)$

b$)$ What are the phase and gain margins? How stable is this system?

c$)$ How could you change the transfer function to improve the stability of the system?