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wegwerp@gmail.com
science forum beginner
Joined: 07 Nov 2005
Posts: 2
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 Posted: Tue Apr 04, 2006 10:01 am Post subject:
Suppress noise to below the white noise level?
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Hi group,
I am controlling a process that has a certain white noise level
combined with some pink noise (1 over f in the power spectral density)
at low frequencies. I am able to succesfully stabilize the process with
a PID like controller. The resulting power spectral density with the
feedback on is very close to the white noise level I already had, with
all the 1 over f noise almost eliminated.
| Quote: | From my (limited) understanding of control theory, this is worse than I
expected: If I did the math correctly the free running power spectral |
density should be multiplied with K=1/(1+Gloop)^2 to obtain the power
spectral density in the locked case, with Gloop the total loop gain.
Gloop is essentially an integrator at low frequencies (1/f), so K
should be proportional to f^2 at low frequencies. Multiplied with the 1
over f noise, I expect the resulting PSD to scale with f at low
frequencies.. Instead, it is constant.
Is this some fundamental limit of controlling a process, maybe because
some of the high frequency white noise is aliasing back to low
frequencies? Or is my theory wrong? Or could this be something specific
to my process only?
Background: the process is a tunable laser which can be locked to a
very stable Fabry-Perot cavity. The 1 over f noise is probably caused
by the current source and things like temperature drift. The white
noise level is probably something fundamental to the physics of the
laser.
Cheers,
Bas |
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RRogers
science forum beginner
Joined: 09 Jun 2005
Posts: 10
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| Posted: Thu Apr 06, 2006 4:54 pm Post subject:
Re: Suppress noise to below the white noise level?
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Did you actually measure the low frequency noise slope? If it should
happen to be 1/f^2 then you would get the result mentioned. Your
theory is correct, but your facts or implementation might be wrong.
For instance, like you said, lack of anti-aliasing before a sampler can
introduce high->low signals that the low frequency correction can not
take out.
I am afraid I can't be of much more help without knowing how you took
your measurements and some kind of diagram of; your system and test
setup. |
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Tim Wescott
science forum Guru Wannabe
Joined: 03 May 2005
Posts: 292
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| Posted: Fri Apr 07, 2006 5:37 am Post subject:
Re: Suppress noise to below the white noise level?
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wegwerp@gmail.com wrote:
| Quote: | Hi group,
I am controlling a process that has a certain white noise level
combined with some pink noise (1 over f in the power spectral density)
at low frequencies. I am able to succesfully stabilize the process with
a PID like controller. The resulting power spectral density with the
feedback on is very close to the white noise level I already had, with
all the 1 over f noise almost eliminated.
From my (limited) understanding of control theory, this is worse than I
expected: If I did the math correctly the free running power spectral
density should be multiplied with K=1/(1+Gloop)^2 to obtain the power
spectral density in the locked case, with Gloop the total loop gain.
Gloop is essentially an integrator at low frequencies (1/f), so K
should be proportional to f^2 at low frequencies. Multiplied with the 1
over f noise, I expect the resulting PSD to scale with f at low
frequencies.. Instead, it is constant.
Is this some fundamental limit of controlling a process, maybe because
some of the high frequency white noise is aliasing back to low
frequencies? Or is my theory wrong? Or could this be something specific
to my process only?
Background: the process is a tunable laser which can be locked to a
very stable Fabry-Perot cavity. The 1 over f noise is probably caused
by the current source and things like temperature drift. The white
noise level is probably something fundamental to the physics of the
laser.
Cheers,
Bas
This isn't something fundamental, you have your theory right. It is |
either something in the way that you're setting up your system or your test.
Where and how are you measuring this noise? The easiest explanation
that I can think of is that the 1/f noise was from the laser, and the
white noise is in your measurement. If it's measurement noise and
you're taking the measurement from the output of the same sensor that
you're using for closed-loop control then you would expect to see the
white noise go down (unfortunately this would be due to there being
_more_ noise in the laser output). If it's measurement noise and you're
using two distinct but separate sensors then you may see a fairly level
noise spectrum, with maybe 3dB of bumpiness.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Posting from Google? See http://cfaj.freeshell.org/google/ |
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