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

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)

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