While attempting to develop a somewhat accurate noise budget for the 40m, I reasoned that while the shape of the transfer function for the ISS is important, the degree to which we can 'tune' it to a particular experiment/application is limited.
Beyond that, we're sort of limited by the desired high and low frequency behavior as well as the general principle that more electronics = more noise so we probably don't want more than 3 or 4 filter stages, if that. Additionally, the ISS can be over-engineered so that it suppresses the laser noise to levels well below other fundamental noise sources over the important regime ~10 - 10^3 Hz without particular regard to a noise budget.
The design I propose is very similar to a previous design, with a few adjustments. It consists of 3 filter stages that easily be modified to increase gain for higher frequencies if it is known/determined that the laser being stabilized has a lot of high frequency noise.
Stage 1: Basic LP Filter + Establish UGF (each stage 'turning on' will not change the UGF), Stage 2: Integrator with zero @ 10 kHz, Stage 3: Optional extra gain if necessary
With the full TF given by,
As usual we consider the noise caused by the servo itself. Noise analysis in LISO is done with a 1 V input excitation.
This servo should function sufficiently for the 40m.