Method of finding natural frequency

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Discussion Overview

The discussion revolves around methods for finding the natural frequency of a closed-loop system, particularly focusing on the significance of the phase at -90 degrees and the interpretation of Bode plots. Participants explore the relationship between phase and frequency, as well as the implications for system stability and identification.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant mentions that the natural frequency can be found at a phase of -90 degrees and asks for clarification on why this specific phase is significant.
  • Another participant questions the implications of different phases and seeks further understanding of their relevance.
  • Discussion on Bode plots includes a participant stating that they illustrate the difference between asymptotic behavior and actual data, linking this to system identification and transfer functions.
  • Participants express confusion about the meaning of specific phase values, such as -60 degrees, and inquire about their origins and significance in the context of the system.
  • There is a mention that transfer functions and parameters serve to describe the system rather than represent the system itself.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the significance of phase in relation to natural frequency and Bode plots. There is no consensus on the interpretation of phase values or their implications for system behavior.

Contextual Notes

Participants highlight the need for clarity on the definitions and implications of phase in the context of closed-loop systems, indicating potential limitations in understanding the mathematical and physical relationships involved.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in control systems, particularly those seeking to understand the relationship between phase and natural frequency in closed-loop systems.

MissP.25_5
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This is a closed loop system. My teacher showed me that one of the methods to find the natural frequency of this system is by finding the frequency at phase -90 degrees. Why must it be -90 degrees? Please explain. From the phase graph, the frequency at -90 degrees is 32 [rad/s], so that's the natural frequency.
 

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What does the bode plot tell you?
 
Simon Bridge said:
What does the bode plot tell you?

The bode plot tells us the difference between the asymptote and the real data. Actually, these graphs are plotted for system identification by finding the transfer function G.
 
The bode plot tells us the difference between the asymptote and the real data.
Yes, but what does that mean?

i.e. in the bottom graph you plot a phase against frequency - which phase is this?
The point of these questions is to focus your mind on the physics of the situation that is relevant to your question.
So far you appear to have been concentrating on the math.
 
Simon Bridge said:
Yes, but what does that mean?

i.e. in the bottom graph you plot a phase against frequency - which phase is this?
The point of these questions is to focus your mind on the physics of the situation that is relevant to your question.
So far you appear to have been concentrating on the math.

That means we can see how sensitive the closed-loop transfer function is to the changes in the parameters of the plant transfer function, and also whether the closed-loop system is stable or not.
I am sorry, I don't understand what you mean by "which phase is this".
 
MissP.25_5 said:
I am sorry, I don't understand what you mean by "which phase is this".
What does "-60 degrees" mean, for example? The phase is a numerical value, but where does it come from?
 
What mfb said :)

The transfer functions and parameters are ways to describe and model the system of interest - they are not the system.
 

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