Draw Bode plot for the system with following loop transfer functions:

(a) \(\mathrm{G}_{1}(s) \mathrm{H}_{1}(s)=\frac{3(s+1)(s+6)}{s^{2}\left(s^{2}+18 s+400ight)}\)

(b) \(\mathrm{G}_{2}(s) \mathrm{H}_{2}(s)=\frac{20(s+1)}{s(s+5)\left(s^{2}+2 s+100ight)}\)

and determine each of the following therefrom (as best read)

(i) gain cross over frequency \(\left(\omega_{\mathrm{gc}}ight)\)

(ii) phase cross over frequency \(\left(\omega_{p c}ight)\)

(iii) Gain margin (GM)

(iv) Phase margin (PM)

Comment on stability