Question

Construct the bode plot on a semilog Graph-paper for a unity feedback system whose open loop

transfer function is given by \(G(S)=\frac{100}{S(S+1)(2+S)} .\) From the bode plot determine

a) Gain and phase crossover frequencies.

b) Gain and Phase margin, and

c) Stability of the closed loop system

Answer 1

gain phare cross over frequency - 180° a 90°- tant a- tantw/a ° +90 = tante + w/ 1-w% wt wie l-w2% 2 to 31 2 Juge= V2 rad's

for phare cross over cross over trequeney Phan cross. Тоо tar тас) - 1 Iww²y i Jatua 1 2 ( loo У w-t 402- +7) Си--+ч) ) det wery | 2 оооо орталы - брита : Я+ 1) 9+2) 100 00 (*+38 28- ** *** 40ooo so Яr= 2 -200 S59 =11078t 18•6чук 8-82 ген 83 w”. * Шр 20°C wp-4053.3 rodis ра 3

@ gain margin, Cim - - po dogoo lat. logio GM= 20 watt J2+4 lat w = wpe = -2ologio 1oo V2v3 vo am = -2404386 phare margin = 180° + Lacgood Hlyws = 180°-90-tante-tantw Jatwounge 90° - tant wtw/ con in wel 90°- tant zo at uz Jat wauge oli mwa 90^-(-36•241") 2 pm =1265241 9