- #1
Stability of a System: Bode Diagram Analysis
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Discussion Overview
The discussion centers around the stability of a system as analyzed through its Bode diagram. Participants explore the implications of phase margins and zero crossings in relation to stability criteria, including references to step response diagrams.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant suggests that the system is stable based on the observation that φ > 0, questioning the significance of two zero-crossings in the Bode diagram.
- Another participant notes that φ < 0 at high frequencies and asks for clarification on the stability criterion being used, indicating that the amplitude does not diverge.
- A participant argues that the second zero crossing indicates a phase of -90 degrees, asserting that this meets stability criteria since -90 > -180.
- One participant presents a step-response diagram, suggesting it indicates stability, but expresses uncertainty about the Bode diagram's implications.
- Another participant interprets the system as a second-order system with a damping ratio of approximately 0.3, questioning the stability criterion of φ > 180° at |response/input| = 1.
- A later reply confirms the previous claim about the phase margin, explaining that the system has 90 degrees of phase margin at the frequency of -90 degrees and that lower frequencies have more phase margin, while higher frequencies exhibit gain margin.
Areas of Agreement / Disagreement
Participants express differing views on the stability criteria and the interpretation of the Bode diagram, indicating that multiple competing views remain and the discussion is unresolved.
Contextual Notes
Participants reference specific phase margins and stability criteria without fully resolving the definitions or assumptions underlying these concepts. The discussion includes varying interpretations of the Bode diagram and its implications for system stability.
- #2
BvU
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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 ...
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 ...
- #3
Davidak
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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?
- #4
- #5
BvU
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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.
Apparently your criterion is ##\ \phi > 180^\circ\ ## when |response/input| = 1 which I don't really recognize. Your call.
- #6
FactChecker
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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.Davidak said:
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.
Last edited:
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