Stability of a System: Bode Diagram Analysis

[Davidak]

Hi,
Is this Bode diagram tells that the system is stable? As I see it is, because of the φ>0. What doest it mean that the upper diagram has two zero-crossing?

 

[BvU]

Hi dave

I see $\phi < 0$ up to very high frequencies

What's the stability criterion in your context ? The amplitude never runs off to infinity, so you may well be right ...

 

[Davidak]

Thank you for your respons!
As you see in the picture, the second zero crossing defines a phase, which is -90 and according to the stabilty criteria it is stable because -90>-180. Is it correct?

 

[Davidak]

This is the step-respons diagram of the same system. Its stabel. So the Bode should be also stable, but i m not sure.

 

[BvU]

I think you are right. This looks like a second order system with a $\zeta$ of about 0.3.

Apparently your criterion is $\ \phi > 180^\circ\$ when |response/input| = 1 which I don't really recognize. Your call.

 

[FactChecker]

View attachment 91856
Thank you for your respons!
As you see in the picture, the second zero crossing defines a phase, which is -90 and according to the stabilty criteria it is stable because -90>-180. Is it correct?

Yes. It has what is called 90 degrees of "phase margin" at that frequency because 180-90 = 90. All lower frequencies have more phase margin. The higher frequencies have what is called "gain margin" because the gain for those frequencies is less than 1. So it is well within the stable region at all frequencies, as you can see by the damping of the step input signal.
PS. Usually the gain margin of a system is defined as the margin at the frequency where the phase shift is -180. In this system, there is no frequency like that.