Hello Haribabu!

Q:My question is, how do you account for the influence of the two loops closed at the same time in your analysis?

A: Stability margins (e.g. phase margin) can be defined only for an open loop. It is defined as the amount of additional (parasitic) phase shift which must be introduced into this loop in order to make the system instable if the loop is closed again. Therefore, when both loops of a two-loop system are closed you cannot perform any additional stability analysis (hopefully I did understand your question correctly).

**Eugene wrote on Jan 14**^{th}, 2008, 10:41pm:I thought there was already a discussion of this somewhere in the Forum but I could not find it. ................................................................................

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If you insist on using more classical frequency domain methods, there is a little known procedure called sequential loop closures, or sequential return differences. The procedure is as follows:

1. Open all loops such that the resulting system is stable.

2. Assess the loop gain of one loop with all other loops open. Keep track of the number of clockwise encirclements of the Nyquist point.

3. Close that loop and assess the loop gain of the next loop. Keep track of the net number of encirlcements of the Nyquist point.

4. Close that loop and do the same for the next loop. And so on.

5. If the net number of encirclements (clockwise - counter clockwise) equals zero, the system is stable. If the net is greater than zero, the system is unstable.

The only problem with this method is that it is hard to identify a single phase margin or gain margin. You could select the minimum phase margin and minimum gain margin as you assessed each loop but you may get different numbers if you select a different sequence. Despite this shortcoming, the procedure is mathematically rigorous........................................................................

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Of course, I completely agree with the procedure as quoted above.

One short comment to the "problem" as mentioned above: If one system has three different feedback loops it certainly will exhibit three different stability margins. Therefore. to ask for a single system margin is - for my opinion - a more or less philosophical question, because in reality additional parasitic phase shifts will occur not only in one of these loops.

I think the whole subject seems to be a very interesting one and I appreciate the discussion about it.

Lutz

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