Question

2.) You are given the Bode magnitude and phase plots. a.) You have to approximate the ain and phase margin and determine if stable. b.) How much do have to change the gain to make the system marginally stable. You

Answer 1

Magnitude plot & phase plots are given Consided an example Magnitude plot wgcow ea frequency odB d WPC Wge Gain Cross over "The frequency at which the Magnitude = OdB or -188 y w phase plot frequency wpc-phase Cross over The frequency at which the phase angle is - 180° Now Gain Margin is given by the the Magnitude of the given System at w pc Inverse of

ie G.ME 1 G(JWHCjw)) \w.wpc GM(dB): -2010g (Golju) H1300)) w-wpc phase margin is given by P.M= 180+ <bljw. Hljw) (wwge Phose margin is defined at gain Cross over frequency & G. Mat phase Cross over foequency. tve s if Gain margin is tve (dB) & phase Morgin is also then System is ottable if Gain Margin is odB El Phare Hargin= 0° then Systemis Marginal Itable sif Gain Margin is -ve (dB) & phoebe laugos is also love) then System is unstable. If we have to make the System Marginal Stable then we have to shift the Magnitude plot by a certain EBS This shift has to be Equated to 20logk 20log k= k= shift in dB Now get the value of k from this . This is the change in gain Required