[SOLVED] System stability questions.

[E-design]

Can a negative-feedback system ever have large positive phase shifts that causes instability?

All the examples in my old textbooks deal with instances where the overall phase shift approaches -180°.

How do we deal with instances of positive phase shifts near and beyond +180°?

I found this reference on the web that mentioned phase angles larger than +180°
It says that above +180° can be seen as above -180° (less negative i.e > -180°), and +180° is basically the same as -180°, if I read it correctly.
It appears that it takes the positive angle, say +200° and subtract -360° to get above -180° (-160° in this instance).

So, what about below 180°? Will say +150° be evaluated as it is? Surely it can't be seen as (+150 - 360° = -210°) because then it will suggest instability for all positive phase shifts with a gain more than 0dB, since the resulting angle will be more negative than -180°.

 

[erikl]

A 2^nd order Zero at the origin generates a +180° phase shift, see here (scroll down to A Zero at the Origin).

 

[E-design]

Yes, I know, but is that possible when we have a negative-feedback system?
To go beyond +180 we need 3 zeros in our transfer function.
Such uncontrollable increase in gain and phase will make it inherently unstable correct?

Also can you explain why my document suggests that above +180 can be seen as above -180 when looking at stability?
Does that suggest that when the phase increase beyond +180 we regain stability with gains larger than 0dB?

 

[FvM]

You should remember previous discussions you took part, e.g. https://www.edaboard.com/threads/245138/

It gives a much clearer picture of the stability criterion.

The question in the original post can be answered quite easily. -180° is the same as +180° and can't be distinguished for a single frequency point. But if you refer to the example in post #3, you should consider "what goes up must come down". Means there will be deadly sure multiple crossings of the critical phase line, and you have to refer to the complete Nyquist stability criterion rather than the simplified Bode diagram phase margin criterion. Just this point has been discussed in detail in the said thread.

 

[E-design]

FvM, I remember that discussion. Thanks for your explanation.