phase margin and gain margin

[biolycans]

Hi all !!

I have the transfer function a(s)= 5 / (0.00833333 *s^3 + 0.1333333 * s^2 + 0.65833333 * s + 1), and the feedback is f=1

I simulated in Matlab the open loop system (a(s) *f) and the phase margin and gain margin I obtained are: MF= 23.6 degrees and a GM=5.61 dB so the close loop system is stable.

Then if I increase the gain in the close loop system with a value of 5.61 dB, then the Phase margin and gain margin of this open loop system are PM=0 and GM=0 approximately. In the limit of instability.

I understand the concepts of the PM and GM but I still have a question. For the MG, is the amount of gain I can increase to put the close loop system in the limit of instability. and the same with the PM.

In the simulations I can see a relation between PM and GM. Am I correct ? What make me confuse is that for a change in GAIN (constant), it produced changes in gain (GM) and phase (PM) too. so for a gain of 5.61 dB it correspond a change in phase to 23.6. Am I correct ? Because in many books, the phase margin and gain margin are explained like different item but for me the are really related.

Another thing is how can I produce only a change in phase in the system keeping the gain margin ? and the same for the PM keeping the GM ? is this possible ?

Can you help me, please ?

Regards,

Joaquin

 

[LvW]

In the simulations I can see a relation between PM and GM. Am I correct ? What make me confuse is that for a change in GAIN (constant), it produced changes in gain (GM) and phase (PM) too. so for a gain of 5.61 dB it correspond a change in phase to 23.6. Am I correct ? Because in many books, the phase margin and gain margin are explained like different item but for me the are really related.

For a given system there is - indeed - a certain relation between gain and phase margin. However, only for THIS system!
Of course, increasing the gain factor there will be a decrease in both PM and GM. Increasing the gain will move the 0-dB cross-over frequency to larger values with more phase shift at this frequency.

Another thing is how can I produce only a change in phase in the system keeping the gain margin ? and the same for the PM keeping the GM ? is this possible ?

No - I don`t think so. If you are modifying the phase response only (allpass or another delay element) the PM will be, of course, influenced. However, since the 180 deg-cross-over frequency changes there will be a corresponding change in GM.