In parallel to some other efforts, I've been lookin at what kind of subtraction we could get with the scheme Arnaud used at LLO using the L4Cs we have installed on the HAM1 passive stack. At least for a band around the RM 6hz bounce mode, it looks like we can get a good reduction in chard pitch.
The only things needed for this scheme are the tabletop L4Cs (which Hugh installed in ~2019), shared through IPC from the HAM1 HEPI model, and a path and filter banks in the ASC model. Jeff has been working on the model changes, adding the filter bankss to the h1seiproc model and routing paths in the h1asc model. There's a lot more to that part, which Jeff is detailing else where, but we hope to give ourselves the flexibility to try a number of other possible solutions.
The filter design is straightforward in Arnaud's scheme, it's just a fit to the transfer function from the L4C to the chard pitch input. My first attached plot shows this transfer function, calculated by using mccs2 in Matlab. Top two subplots are the magnitude and phase for the transfer functions and the filter fit that I've come up with. The bottom subplot shows the coherences between the the tabletop l4c x,ry ,z to chard pitch. We also have the rx signal, but I haven't really looked at that yet.
The second attached plot is an estimate of the subtraction my filter should get. I did this by using lsim in Matlab to calculate my fit filter output for the z L4C and adding that timeseries to the chard pitch timeseries, then using asd2 get the specta of that timeseries. The blue trace is the "current" chard pitch spectra, red is the chard pitch residual from the mccs2 coherent subtraction (so should be an estimate of the best we can get) and yellow is the subtraction I calculate from my filter fit. At 7 hz, this should get about a factor of 5 reduction in chard pitch, but less than a factor of 2 at the 6 hz RM mode. From this point, I've started looking at using the x and ry L4C, but those have less coherence, and don't seem like good candidates for more subtraction.
I've also looked at other signals and it seems like the coupling is consistent in a lot of places. Third attached plot shows the tfs for chard pitch and inp1 pitch. The magnitudes are different, but, the shapes and phases are very almost identical. Maybe it would make more sense to do feedforward to something more common to all these signals like the RMs in pitch.
Small improvement could be got in the tabletop L4C motion by looking at the blends on HAM1, as well. This afternoon, I was able to try pushing the RY blend down from .8hz to .5hz, and this reduced the motion seen by the tabletop L4Cs, by kind of factor of 2 at 1hz. First attached plot shows pier Z and RY L4Cs, red and blue are with the lower RY blend (no other changes), green and dark green are with the nominal configuration. Z looks the same in both case, RY shows improvement from .5 to 2.5 hz, maybe an average factor of 5 improvement.
Second plot are the table top L4Cs, it's not as clear an improvement. Again, red and blue are with the new blend, the greens are the older config. It's maybe a factor of 2 around 1 hz, but both Z and RY show improvement.
I tripped the HEPI and broke the lock just turning off the RY loop to change the blend (HEPI can't switch blends on the fly like the ISIs can), both of which suprised me, so I'm not going to mess with this more today. Turning off the loop at least, should have been relatively safe. The lower blend filter is stable though, and makes things better somewhat, so I'm going to leave it running.
