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From Bode Plot to Root Locus

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sky2020

sky2020

Electrical
May 21, 2019
39
I have software that generates the bode plot of a system. How can I get the poles and zeros of this system using the bode plot?
 
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Maybe it's a real system and it actually measures the frequency response.
 
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Presumably, by exciting it with a swept-frequency signal and seeing what it does - granted, that's something I think I've only ever seen done in a teaching lab.

A.
 
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It's done very often in vibration testing, and can be done in electrical circuits, but it's uncommon, I think. My prof in college was very into that sort of thing, but I've not seen anyone else doing it.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! faq731-376 forum1529 Entire Forum list
 
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The problem I had with the OP is that he didn't say what format his Bode plot data was in or how the Bode plot is generated. I agree with IRStuff that trying to look a plot and estimate where there are poles and zeros is not accurate. It is easier to compare input and output data.

Presumably, by exciting it with a swept-frequency signal and seeing what it does - granted, that's something I think I've only ever seen done in a teaching lab.
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But what data do you measure? You don't measure a Bode plot directly. We can and have done it to evaluate valves and perform system identification.

It's done very often in vibration testing, and can be done in electrical circuits, but it's uncommon, I think. My prof in college was very into that sort of thing, but I've not seen anyone else doing it.
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I bet your college professor never did it for a system in the wild.
We can do it but it is hard to do right. I have examples of using swept sine waves and other wave forms. Swept sine waves are difficult because in our case we run out of oil pretty quickly. We usually help test valves. We sell motion controllers, we are not a testing lab but we do help others.

1. get the data. It will be either position or velocity data as a function of time. A Bode plot
2. fit a transfer function to it. I use differential equations because they can handle non-linear systems.
3. If the differential equation for the transfer function is linear it is easy to find the eigenvalues ( poles ). Most systems don't have zeros.
4. if the system is non-linear the poles will move as function of amplitude. It is probably easiest just to compare amplitudes and phase between the input and the output but at least one has data instead of trying to read points off a plot with little resolution.

The motion controller can generate swept sine waves or any other pattern. In this case we were testing a Parker non-linear valve. The problem is that we run out of oil when doing swept sine waves so we can't test to high frequencies. The first .svg ( scalable vector graphics ) file shows how our system identification can find the transfer function for a non linear valve. The model matches the data very well.

This plot shows the non-linearity of the gain, flow, as a function of the valve opening and what the motion controller must do to compensate.

I use .svg files because .svg files are easier for the magazine editors to work with and they work well with browsers.











Peter Nachtwey
Delta Computer Systems
IFPE Hall of Fame Member
 
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sky,
your question requires supporting data, as it make no sense by it self.
 
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