J. Kissel, B. Ratto

Now that the installation dust has settled on all HXDSs and we're beginning to design better damping loops for them, Brad and I revisited my Dec 2021 study (LHO:60885) where I systemically compared the best dynamical model against all of the best measurements of various types. 

New this time:
   (1) Several issues with the electronics have been resolved; 
       (a) LHO:61839 -- The pinout of the cable from the M1 OSEM coil driver to the OSEM satamp that carries the drive signal has been corrected for ZM4 / ZM5 / ZM6. Resolving that means that there'll be *much* less measured crosscoupling in the transfer functions of the on-diagonal degrees of freedom, e.g. L to L, P to P, and Y to Y.
       (b) LHO:62107 -- the transimpedance of the OSEM sensor PD has been corrected to be 121k for ZM4 / ZM5 / ZM6. Resolving that means that we can trust our calibration of the data.
   (2) We now have all suspensions in their final state mechanically, and measured in quiet environments with good SNR at all frequencies (and for ZM6 we even have data at vacuum).

Attached is the new comparison: allhxdss_2022-04-25_H1SUSHXDS_alltypecomp_Phase3b_UnDamped_ALL_ZOOMED_TFs.pdf

As I mentioned in the first systemic look (LHO:60885), there're a countably infinite number of questions one can ask of this data, but in this aLOG I'll ask questions and/or make statements that relate to a common damping loop design.

(A) Does the calibration of the data into [m/N] or [rad/(N.m)] agree with the modeled value? Almost, and good enough. 
    We see that we're consistently under-predicting the magnitude by about 10%. Not too shabby, and quite tolerable. Where this becomes important is in our loop design -- we want to make sure the magnitude of our open loop gain transfer function is at least roughly consistent with reality. A 10% consistency is totally fine because 
    (i) We're going to design a loop that has enough phase margin / gain margin that a 10% gain change one way or the other will not drastically impact the loop performance or stability, and 
    (ii) We're going to measure the "after" open loop gain transfer function after its installed and if we don't like what we see, we'll just adjust the gain on the fly to better match the model.

(B) Do the measured resonant dynamical features consistently match the model? For the most part, yes. 
    - Unlike in the first study where we say a lot of cross-coupled resonant features that the model doesn't have, we don't see that any more. I attribute that to the electronics fixes -- *not* to any of the mechanical ideas Rahul and I had in LHO:60927. Nice!  
    - Where the data *doesn't* match the model, it's inconsistent *across* instantiation types, but typically consistent *within* a given instantiation type. 

(C) OK, they're different between instantiations. How mad are you about it? Not so mad.
    Remember there are 3 different types of HXDS under consideration here, and they're different only in their bottom (M2) stage actuator: 
        - (ZM6) HSDS, which has *no* bottom stage actuator
        - (ZM1, ZM3) HDDS, which has a 4 coil dither actuator system where there's no additional contact / interference with the M2 stage, and
        - (ZM2, ZM4, ZM5) HPDS, which a single, large, longitudinal PZT actuator on the radius of curvature of the optic, which requires an additional cable connection that we've chose to *not* lace up through the suspended stages.

    There are two major things that stand out for me:
    (i) One of the first things I see is the the P to P and Y to Y transfer functions show this kind of grouping. The HPDSs (ZM2, ZM4, and ZM5) have consistently the same shift in zeros or resonances, and I can easily believe that this a result of the HPDS PZT actuator cable. 
    (ii) The lowest frequency resonance of the Y to Y transfer function is interestingly low by 0.15 Hz -- the HDDSs (ZM1 / ZM3) match the model quite well, but both the M2 actuator cable influenced HPDSs (ZM2, ZM4, and ZM5) *as well as* the M2 actuator free HSDS (ZM6) show this shift. Recall that the lowest frequency modes' shape is the collection of masses moving in common, so they're influenced by the total suspended mass (or moment of inertia), and the top masses restoring forces. I'm not sure why these would be different between instantiation types. 
    
(D) Should we bother creating a model parameter set that's tailored to the individual instantiation types? No.
    The good thing is that where the suspension types differ in resonant features, they actually *increase* the amount of phase available at the lower frequency edge of the lower resonance (where we would create a low-unity-gain frequency crossing in the future open loop gain transfer function), and upper edge of the upper resonance (where we would create the upper UGF crossing in the OLG TF).

    So that means that if we design a loop around the model, then we're only going to be *more* stable for these suspensions that have more phase wiggle room in the plant design.

    Regardless, in the end, once we have a proposed new design from our modeling work, we're going to measure the open loop gain transfer function to confirm success, so we'll just make sure to do that for all HXDS instantiation types.

In short: We're happy that the model sufficiently represents the physical systems that we'll be designing loops around, so we don't need to adjust the dynamical model parameters.

On to the reproduction of the existing design in modeling land, in order to build up sufficient loop design and noise performance infrastructure for us to comfortably design a new set of filters.