Suppress noise to below the white noise level?

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.

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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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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snipped-for-privacy@gmail.com wrote:

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.
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Tim Wescott
Wescott Design Services
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