Problem #$2$

The forward path transfer function of a unity feedback control system is:

$G(s)=\frac{K(0\mathrm{.}2s+1)(0\mathrm{.}1s+1)}{s^2(0\mathrm{.}01s+1)(s+1)}$

Plot the Bode diagram of $G\frac{j}{K}$ and do the following:

a$)$ Find the phase and gain margin, and check the stability of this system.

b$)$ Suggest the value of K so that the gain margin of the system is $20$ db