A very long time ago, Brian Lantz wrote a technical document describing how to design filters to compensate BSC stage 1 drives for the forces applied by the stage 2 actuators ( T1600138 ). Over the last month+ I finally got around to figuring out how to actually make and install the filters. I've now installed these filters on every chamber, but it took me a while to figure out if they were doing any good. Today, I just took some transfer functions driving stage 2 and looking at the stage 1 sensors. After I figured out the sign, it looks like stage 2 drive compensation on stage 1 works.

First attached plot shows ITMX X dof for both stages, and it's hard to look at just the asds and say that the compensation is doing anything. I've taken a number of spectra on different chambers and it looks during normal operations we wouldn't see much of a difference. But when I put extra drive on stage 2, it looks like the coupling from stage 2 drive to stage 1 motion is reduced by about an order of magnitude, up to 100 hz. Second plot shows the transfer function from stage 2 drive to stage 1 l4cs and stage 2 gs13s. The 3 configurations I tried were compensation off (blue traces), compensation on with +1 gain (green traces), compensation on with -1 gain (red traces). I also tried a gain of -1.5, but this made this worse, so I think the magnitude is right, I just need to fix the sign in the matlab script I used. The dashed lines show that the stage 2 drive to stage 2 motion transfer function doesn't really change, which is good to know. My drive was mostly over 10-30hz range, so that's why the tf gets ratty below 10 hz.

I wrote a barebones function to do the filter design, so if LLO wants to do this, its pretty simple. The function takes one of the calculated damped plant frd's from the ISI commissioning data, a vector of zpks, and some other plot flags and makes plots like the third attached image. After doing the fits for the first chamber, I basically didn't have to do tweak the filters at all. There are features around 9hz that I'll probably remove on a second round when I fix the signs, because I don't think they help. I haven't checked, but I suspect there might be small gain differences between chambers, but the script does that gain matching on it's own. 

I'm curious as to what effect this will have on the BS during mich locking. I worry that I'll have to turn the compensation off on that chamber, but maybe this will allow the stronger stage 1 actuators to back up stage 2?