mod11lec65

[@rd-tk6js]

how to locate wg and wp in nyquist plot of OL tx func 5:00 Def : 8.30 a) gain margin Kg : is reciprocal of | G(jw) H(jw) | at w=wp i.e. Kg = 1/ [ | G(jw) H(jw) | ] = --20 log | G(jw) H(jw) | in dB b) phase margin ( lambda) : it is additional amount pf phase lag that needs to be added to ph of the syst at w = wg to bring syst on the verge of instability i.e. lambda = ang [ G(jw) H(jw) ] -- ( --180 deg ) = 180 deg + ang [ G(jw) H(jw) ] note : gain margin involves scaling and ph margin involves rotaion 15:30 mote : given a syst whose OL tx func doesn't have poles/ zeros in RHP, both gain and ph margin should be positive to ensure stability of CL syst. estimating gain and ph margin by locating wg and wp in bode plots of OL tx func 18:00 example 23:45

[@aakashdewangan7313]

relative stability part2

[@vattevineeth4567]

why should GM be positive?

[@chaitanyaprasad6924]

yes sir why cant it be negative..

[@kaizoku_oni9071]

It arises from the Nyquist stability criteria. I think its not mentioned by the Prof. but probably the system that he has under observation has open loop poles in the LHP(stable open loop system), therefore the Nyquist diagram must not encircle -1 . There is a sub-section of Nyquist criteria: stability via mapping only +jw axis and according to that gain margin must be positive. You can also think of it in the form of root locus plot. Root locus plot starts at open loop poles, so if the open loop system is stable then the closed loop system is at least stable for low values of gain and if the gain is small ,the Nyquist Plot will pass to the right of -1 therefore |G(jw)H(jw)| < 1 and consequentially gain margin Kg > 1.

[@lateral2182]

it is pretty obvious that the Nyquist plot at phase cross over frequency is in the negative real axis so to scale it enlarge it or to minimize it we just have to multiply it with positive scalar.If we use the negative scalar then the phase turns around and it reaches the 1 point in real axis rather than -1 in negative real axis..