brett.shapiro@LIGO.ORG - posted 00:29, Monday 29 July 2013 - last comment - 17:01, Monday 29 July 2013(7261)
Damping MC2 with cavity feedback
Over the weekend I tested recruiting the IMC cavity feedback to simultaneously damp the MC2 longitudinal DOF. It is possible to make a cavity controller damp a the longitudinal modes of a suspension of 3 or more stages if three rules of thumb are met: 1. Cavity feedback exists below the top mass for at least 2 of the stages. Those are M2 and M3 here. 2. The feedback on the stages below the top mass have unity gain frequencies (UGFs) greater than the longitudinal resonances. The highest mode in this case is 2.75 Hz. 3. The damping increases as the UGF of the highest stage below the top mass decreases towards the highest frequency longitudinal mode. Here the M2 UGF decreases towards the 2.75 Hz longitudinal mode. This is part of the more general global damping scheme described in G1200774. Global damping is intended to both isolate OSEM sensor noise from the cavity degrees of freedom and decouple the damping design from the control of the optics. Parameters for this test: 1. The IMC was locked with feedback to MC2 M2 and M3. 2. There was also ~10 kHz feedback to the laser frequency, but this was unimportant for this test. 3. The MC2 M1 longitudinal (MC2_M1_DAMP_L) damping was off. 4. The varying parameter is the gain on the M2 feedback loop (MC2_M2_LOCK_L). The gain was set to 4 different values [0.03, 0.06, 0.12, 0.3], corresponding to M2 UGFs at [3.3, 4.0, 6.0, 14.7] Hz respectively. 0.03 is the default gain. The M3 loop was not adjusted. Its gain was left at -1000. Fortunately, the existing IMC cavity control was designed with oodles of phase margin, making it relatively easy to adjust the M2 gain by an order of magnitude without redesigning any filters (except for the addition of a 41 Hz notch filter for stability as described in 7257). See the three attached figures. 1. IMCCavityRingdown.pdf shows the impulse response of the cavity at these different M2 UGFs. The impulse was applied to the M1 stage. Note that the Q of the top mass is a strong function of the M2 UGF, and is positively correlated with it. The magnitudes of the curves in this plot were normalized because they are naturally different since the cavity has differing loop gains with the differing UGFs. 2. MC2M1Ringdown.pdf is structured exactly like IMCCavityRingdown.pdf except the M1 response is shown rather than the cavity response. The results here are the same, the M1 Q drops with the M2 UGF. The curves here are not normalized, since we are not looking at a stage with cavity feedback (no changing loop gains at this stage to effect our scaling). 3. MC2M1toM1TFs.pdf shows longitudinal transfer function measurements on M1 (MC2_M1_TEST_L_EXC to MC2_M1_DAMP_L_IN1). Like the previous two plots, a curve is shown for each UGF case. Here we see again, but in the frequency domain, that the Qs of M1 decrease with M2 UGF. For reference, the transfer function without cavity control or L and P damping (other damping on) is plotted in green. This reference shows clearly how much the cavity control influences the top mass dynamics. More general comments: 1. In general, if cavity feedback is applied to the two stages below the top mass in a 3 or more stage pendulum, and that feedback has UGFs beyond the longitudinal modes, some longitudinal damping will be observed. However, by carefully placing the UGF of the stage right below the top mass near that mode, one can maximize the damping provided by the cavity. In this way, no noisy top mass longitudinal damping is required for the pendulum that receives this cavity feedback. The loss in loop gain by dropping this UGF can be compensated for by increasing the UGF at a lower stage. 2. Note, if the cavity feedback is sent to each pendulum in the cavity equally, all longitudinal modes seen by that cavity are damped by the cavity feedback. There are then undamped longitudinal modes not seen by the cavity (or more precisely seen weakly). However, this can be overcome by damping these modes by recombining the OSEM sensors into a global coordinate system orthogonal to the cavity as discussed by G1200774. Some more nitty gritty measurement details: 1. The impulse is applied at the M1 L stage with MC2_M1_TEST_L_EXC. DTT was used for this by filtering its native impulse excitation through a filter with two poles at 10 Hz. The 10 Hz roll-off is greater than the longitudinal modes, so the ringing response should be true to an impulse. However, it is also smoothed out enough that the otherwise extremely tall and short excitation will excite the suspension and not saturate the DAC. 2. I left the cavity pretty much as I found it when I was done. i.e. the MC2 M1 L damping was turned back on, and the MC2_M2_LOCK_L gain was set back to 0.03. The one exception is that I left a 41 Hz notch filter in place in MC2_M2_LOCK_L at filter module 5 since the cavity seems to be more robust with it there. aLog 7259 describes the notch more fully. The IMC cavity was still locked when I left. 3. The MATLAB code that generates these plots is found at .../sus/trunk/HSTS/Common/FilterDesign/H1MC2_CavityControlTest_27July2013.m
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Here are some additional plots of the measurements. The data is the same, but shows the M1 to M1 transfer functions and the cavity impulse responses against model predicted results. The first 4 pages show the M1 to M1 TFs, where each following page represents a UGF of the M2 cavity control in descending order. The next, and final, 4 pages show the ringdown of the cavity to an impulse at M1. The model agrees well with the results. Details on the HSTS model: In order to make the model agree as well as it does I had to tweak the HSTS model a bit. The final long mode at 2.7ish Hz was off by 1.7 %, and some of the zeros in the various L to L transfer functions did not agree so well either. This may not sound like much, but the impulse response ringdowns were out of phase by more than 180 degrees at 10 seconds before adjusting the model. Also, the single damped mode in the M1 to M1 TFs was noticeably off. The agreement is much better now. To make the model agree, I ran the triple model through a Gauss-Newton least squares algorithm (like the ones used for the quad pendulums). I only had good longitudinal mode frequencies off hand to give it, so some pitch mode information was missing. Nonetheless, the algorithm spit out a good match on resonances and zeros when I floated the mass values of the M2 and M3 stages. It decreased M2 by 0.189 kg and M3 by 0.140 kg. Proportionally this is a lot for a nominally 3 kg stage. However, the model claims to be metal and MC2's optic (M3) is I believe glass. Note, this fit does not necessarily reflect the true as-built state (though it could potentially). The adjusted model is on the svn at /ligo/svncommon/SusSVN/sus/trunk/Common/MatlabTools/TripleModel_Production/H1MC2_L_GuassNewtonFit_29July2013.mat The state space variable of the model is called pen_mod. The MATLAB code that produced this model is not yet on the svn, but I plan to put it there (some effort to get it working from the svn directory structure).
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