# Method of finding natural frequency

1. Nov 24, 2013

### MissP.25_5

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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2. Nov 24, 2013

### Simon Bridge

3. Nov 24, 2013

### MissP.25_5

4. Nov 24, 2013

### Simon Bridge

What does the bode plot tell you?

5. Nov 24, 2013

### MissP.25_5

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.

6. Nov 24, 2013

### Simon Bridge

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.

7. Nov 24, 2013

### MissP.25_5

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".

8. Nov 25, 2013

### Staff: Mentor

What does "-60 degrees" mean, for example? The phase is a numerical value, but where does it come from?

9. Nov 25, 2013

### Simon Bridge

What mfb said :)

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