This logpost is a follow up to the executive summary on PR3 OSEM estimator Filter and Blend design [LHO: 86563]

Oli took the measurements needed to commission the PR3 OSEM estimator in P and Y [see LHO: 86459]. The P measurements were taken with all M1_DAMP gains at -1, except for M1_DAMP_P, which was set to -0.2. Similarly, Y, All M1_DAMP gains were -1, except for M1_DAMP_Y, which was set to -0.2.

Ivey and I used her vectfit3 scripts to fit the transfer functions. The fits were committed to the SUS SVN under revision 12616. They live in 'sus/trunk/HLTS/Common/FilterDesign/Estimator/'

We made a few minimal changes to the original output from vectfit to match our expectation of the plants:

• Vectfit3 does a fantastic job at fitting the M1 drive to M1 transfer functions [see for example the first attached image]. However, to do so, it often adds a pair of high-frequency right-half-plane zeroes to match the phase delay that comes from the anti-aliasing filter that's a part of the TF measurement process. We often remove these zeroes entirely from the fit. This results in fits that look like the yellow trace in the first attached figure.
• We ensured that all zeroes on the fitted M1 drive to M1 transfer functions are in the left half of the complex plane. This is because we don't want to risk creating right-half-plane poles if we increase the gain of the damping through the estimator path.
• The Suspoint P and Suspoint L to M1 P transfer functions are expected to have 1 or 2 pairs of right-half-plane zeroes. In this case, we worry much less about the risk of creating unstable poles because these transfer functions are relevan in feedfordward-type paths only. Therefore, we tend to leave the zeros where vectfit3 places them.

The images of the resulting filters, together with the data that Oli took are summarized in the attached pdfs.

In order of appearance, the zpk of the fits are:

Suspoint Y to M1_DAMP_Y fit

    'zpk([-0.012+20.621i,0,0,-0.012-20.621i,-0.012+11.426i,-0.012-11.426i],[-0.218+6.292i,-0.218-6.292i,-0.382+14.697i,-0.382-14.697i,-0.226+21.579i,-0.226-21.579i],-0.001)'

M1 drive Y to M1_DAMP_Y fit

    'zpk([-0.024-8.341i,-0.024+8.341i,-0.011+19.405i,-0.011-19.405i],[-0.088+6.403i,-0.088-6.403i,-0.115+14.485i,-0.115-14.485i,-0.069+21.379i,-0.069-21.379i],13.34)'

Suspoint P to M1_DAMP_P fit

    'zpk([-2.428-2.295i,-2.428+2.295i,-0.795-9.324i,-0.795+9.324i,-0.011-22.26i,-0.011+22.26i,0.034-5.811i,0.034+5.811i,0.382-13.672i,0.382+13.672i,1.168-1.459i,1.168+1.459i],[-0.507-1.499i,-0.507+1.499i,-0.395-10.253i,-0.395+10.253i,-0.204-4.167i,-0.204+4.167i,-0.141-4.759i,-0.141+4.759i,-0.13-13.137i,-0.13+13.137i,-0.066-22.16i,-0.066+22.16i],-0.001)'

Suspoint L to M1_DAMP_P fit

    'zpk([-0.773-7.242i,-0.773+7.242i,-0.635-18.11i,-0.635+18.11i,0.301-20.227i,0.301+20.227i,1.062-6.916i,1.062+6.916i,-99.035,-0.197,0.331,45.41],[-1.293-19.638i,-1.293+19.638i,-0.33-10.141i,-0.33+10.141i,-0.289-13.191i,-0.289+13.191i,-0.162-4.1i,-0.162+4.1i,-0.122-4.732i,-0.122+4.732i,-0.087-22.103i,-0.087+22.103i],0)'

M1 drive P to M1_DAMP_P fit

    'zpk([-0.339-4.576i,-0.339+4.576i,-0.031-21.157i,-0.031+21.157i,-0.009-5.455i,-0.009+5.455i],[-0.298-13.183i,-0.298+13.183i,-0.205-4.126i,-0.205+4.126i,-0.138-4.803i,-0.138+4.803i,-0.092-22.128i,-0.092+22.128i],80.907)'