BLACK   - raw ground motion measured by the Guralp
MAGENTA - motion after passive STACIS (20 Hz harmonic oscillator with a Q~2)
GREEN   - difference between ground and top of STACIS
YELLOW  - EUCLID noise in air
BLUE    - STACIS top motion with loop on (60 Hz UGF, 1/f^2 below 30 Hz)
CYAN    - same as BLUE, w/ 10x lower noise sensor

1) Gravity has to be included because the inverted pendulum effect changes the resonant frequencies. The deflection from gravity is tiny but the change in the dynamics is not. The results are not accurate without it. The z-direction probably is unaffected by gravity, but the tilt modes really feel it.

2) You should try a better meshing. Right now COMSOL is calculating a lot of strain/stress in the steel plates. For our purposes, we can imagine that the steel is infinitely stiff. There are options in COMSOL to change the meshing density in the different materials - as we can see from your previous plots, all the action is in the rubber.

3) I don't think the mesh density directly limits the upper measurement frequency. When you redo the swept-sine using the matlab scripting, use a logarithmic frequency grid like we usually do for the Bode plots. The measurement axis should go from 0.1 - 30 Hz and have ~100 points.

In any case, the whole thing looks promising: we've got real solid models and we're on the merge of being able to duplicate numerically the Dugolini-Vass-Weinstein measurements.

I made some progress on a couple issues:

1) I figured out how to create log-transfer function plots directly in COMSOL, which eliminates the hassle of toggling between programs.

2) Instead of plotting maximum displacement, which could lead to inconsistencies, I've started using point displacement, standardizing to the center of the top surface.

3) I discovered that the displacement can be measured as a field vector, so the minor couplings between each translational direction (due to the asymmetry in the original designs) can be easily ignored. 

This plot shows the trend of the OL during the past several hours of roughing pumping.

The big steps at the start of the pump down is NOT due to the pumping, but is instead the "recentering" that Yuta did. Looks like he was unable to find zero on the ETMY.

Some of the rest of the drift is probably just the usual diurnal variation, but there does seem to be some relation to the pumping trend. I guess that the shift of ~0.3 in the ITMX and ITMY pitch is real and pressure related.

We need to figure out how to put the OL calibration factor into the SUS-OL screens.

 Kate & Jenne

About 2:30 this afternoon, we briefly powered off the Guralp (C1:PEM-SEIS_GUR1_{X,Y,Z}) in order to better align it with the other seismometers along its marked N/S direction. It had been visibly off by a few degrees. 

I checked out the cable that I took from you, and all of the connections looked right.  The only thing I did notice was that some of the soldered wires on the 37-pin connector had gotten hot enough to melt their insulation, and potentially short together.  I cut off that connector, and left it on your desk to check out.  I put on a new connector, and checked the pinout.  If the Guralps still doesn't work, we'll have to check out other possibilities.

After some cable swapping, we now have both Guralp seismometers running and the times series and spectra look similar to each other and motley healthy.

Bean and I took a look at the whole situation today. Ben had nicely fixed the Dsub end of the EX cable (the EY one is still just a sad joke), After installing this newly fixed cable, we still saw no signals. There was some confusion in the control room about using the MED displays to diagnose seismometers: flickering MEDM values cannot be used for this. It would be like checking a pizza box temperature to determine if the pizza is any good.

1. Although the +/- 12V LEDs on the front panel are dim, we confirmed that the produce 11.94V even when loaded with a seismometer. So its a LED circuit problem not a power problem.
2. We were able to inject signals into the front panel with a breakout board and see them in DV for Input 1, but not Input 2.
3. After Ben left, I kept poking around and found that the Guralp chassis output gets broken out into 3x3 BNC cables before going to the PEM BNC panel (and then on to the PEM ADC). This is where the problem was.
4. The Input #3 BNC cables were connected to the long cables going to the 'GUR2' channels of the PEM. The Input#2 BNC cables were connected to some short BNC cables that were just hanging from the rack. So, somewhere during the debugging of the past N months, someone plugged this in wrong and didn't notice or forgot to switch it back. So all of the tests using DV or DTT or MEDM since that time have been invalid.

Tomorrow, Lydia is going to change all of the labels and channel names. The new names will be EX & EY to prevent this kind of huge waste of time with channel name swapping. That means no more illegal names with the label maker, Steve.

From the spectrum you can see that the EX seismometer (GUR2) is still not centered or at least its oscillating at 245 Hz for some reason. This should go away after some power cycling or recentering using the magic wand.

I noticed some anomalies in the mechanical setups at the ends:

1. Some junk has been stored on top of the EX seismometer. Please never, even temporarily, store your power supplies, tools, or donuts on top of the vibration sensitive sensors. Just put it on the floor and improve your carma.
2. The EY seismometer has some fishy wires being fished between the can and the rubber seal. This is verboten. That seal must be flush to prevent pressure fluctuations and wires in there will ruin the smooth contact permanently. Temperature sensor wires must go through the grantie block feed-through or else its pointless.
3. The flimsy insulation on the EY seismo is waay toooo mickey mouse. Real thermal insulation should be done using the yellow foam that Jenne used for the seismo huddle test. This flimsy silvery stuff is OK for making hats and mittens and beer cozy's, but its not research grade foam.

The saga has started here  We have to give credit to the Boss who fixed it. The seismometers themself are not labeled yet.

Atm6  added on 8-12-2016   EX needed to be centered

Thanks to Max for the nice plost at summery pages

2.1 mag earth quake in Norhten Ca

Our seimometers need professorial centering. Related electronics must be checked too.

I've been suggesting that there may be something wonky with the Seismic Rainbow Striptool on the wall for the last couple of weeks. Here are a few things that were verified today.

1. If you want to restore the StripTools in the control room, just run /opt/rtcds/caltech/c1/scripts/general/startStrip.sh. I have verified as of today that this works, and in future, any changes to channels/limits/colors of traces etc should be reflected in this script.
2. Though some of the BLRMS bands have looked anomalous over the last few weeks, in particular the 0.3-1Hz band. The attached 120 day trend plot suggests that there hasn't been any dramatic change recently. In fact, looking on the summary pages, Rana noticed that today was an unusually low 0.3-1Hz activity day..

I tried to get some minute trend data today, but was unable to get it from inside or outside the control room using our matlab or python tools.

It seems the NDS2 interface will not work anywhere since it needs our minute trends to be written as frames; in the last version that Jamie left us, our minute trend frame files are not being written since they lead to periodic daqd crashes.

From inside the control room, we can get the minute trend (only with DataViewer). I've attached 30 days of BS_X just to show its real.

We can get the numerical data from the Grace plot window using the menu option Data->Export->ASCII.

You must select all of the 'Write Sets' to get all of the traces in the plot window. The resulting ascii file is not in a great format, but its not terrible.

We've been thinking about putting in a blade spring / wire based aluminum breadboard on top of the ETM & ITM stacks to get an extra factor of 10 in seismic attenuation.

Today Koji and I wondered about whether we could instead put something on the outside of the chambers. We have frozen the STACIS system because it produces a lot of excess noise below 1 Hz while isolating in the 5-50 Hz band.

But there is a small gap between the STACIS and the blue crossbeams that attache to the beams that go into the vacuum to support the stack. One possibility is to put in a small compliant piece in there to gives us some isolation in the 10-30 Hz band where we are using up a lot of the control range. The SLM series mounts from Barry Controls seems to do the trick. Depending on the load, we can get a 3-4 Hz resonant frequency.

Steve, can you please figure out how to measure what the vertical load is on each of the STACIS?

We could use similar load cells   to make the actual weight measurement on the Stacis legs. This seems practical in our case.

I have had bad experience with pneumatic Barry isolators.

Our approximate max compression loads are 1500 lbs on 2 feet and 2500 lbs on the 3rd one.

1500 and 2000 lbs load cells arrived from MIT to measure the vertical loads on each leg.

Gautam and Steve,

The "called 225 lbs" steel crane load measured right on 102 kg

The trick to the measurment to maintain 1 mm gap to the central cilynder of the load cell.

The lead plate stabilized the large load.

gautam: some additional notes:

1. the wiring on the Omega controller unit as given to us was wrong - I had to fix this on the D-sub connector in order to get the load cell to work. something to check for the other units.
2. the main difficulty in doing this calibration run was that the readback is very sensitive to tilts of the load relative to the sensor.
3. the problem is complicated by the fact that the load cell itself does not have a flat surface - it has a ring that protrudes above the flat face of the cylindrical load cell by a few mm as Steve mentioned.
4. so in order to measure the weight of our stacks, we have to mitigate this problem and ensure that the full load of the stack is normally incident on the load cell - if the load cell itself is somehow torqued during the measurement because of the distribution of the load on it being uneven, we get an inaccurate measurement.
5. In this calibration measurement, we think the error is <1% (true mass is 102kg, we measure 104kg on the meter which seems reasonable as the sum of the donut + lead plate)

Gautam and Steve,

We have calibrated the load  cells. The support beams height monitoring is almost ready.

The danger of this measurment that  the beams height changes can put shear and torsional forces on this formed (thin walled) bellow

They are designed for mainly axial motion.

The plan is to limit height change to 0.020" max

0, center oplev at X arm locked

1, check that  jack screws are carrying full loads and set height indicator dials to zero ( meaning: Stacis is bypassed )

2, raise beam height with aux leveling wedge  by 0.010"  on all 3 support point and than raise it an other 0.005"

3, replace levelling wedge with load cell that is centered and shimmed.     Dennis   Coyne pointed out that the Stacis foot has to be loaded at the center of the foot and formed bellow can shear at their limits.

4, lower the support beam by 0.005" ......now full load on the cells

Note: jack screw heights will not be adjusted or  touched.......so the present condition will be recovered

[ Dennis Coyne'  precision answer ]

Differential Height between Isolators

According to a note on the bellows drawing (D990577-x0/A), the design life of the bellows at ± 20 minutes rotational stroke is 10,000 cycles. A 20 minute angular (torsional) rotation of the bellows corresponds to 0.186" differential height change across the 32" span between the chamber support beams (see isolator bracket, D000187-x0/B).

Another consideration regarding the bellows is the lateral shear stress introduced by the vertical translation. The notes on the bellows drawing do not give lateral shear limits. According to MDC's web page for formed bellows in this size range the lateral deflection limit is approximately 10% of the "live length" (aka "active length", or length of the convoluted section). According to the bellows drawing the active length is 3.5", so the maximum allowable lateral deflection should be ~0.35".

Of course when imposing a differential height change both torsional and lateral shear is introduced at the same time. Considering both limits together, the maximum differential height change should be < 0.12".

One final consideration is the initial stress to which the bellows are currently subjected due to a non-centered support beam from tolerances in the assembly and initial installation. Although we do not know this de-centering, we can guess that it may be of the order of ~ 0.04". So the final allowable differential height adjustment from the perspective of bellows stress is < 0.08".   Steve:  accumulated initial stress is unknown.  We used to adjust the original jack screws for IFO aligment in the early days of ~1999. This kind of adjustment was stopped when we realized how dangereous it can be. The fact is that there must be unknown amount of accumulated initial stress. This is my main worry but I'm confident that 0.020" change is safe.

So, with regard to bellows stress alone, your procedure to limit the differential height change to <0.020" is safe and prudent.

However, a more stringent consideration is the coplanarity requirement (TMC Stacis 2000 User's Manual, Doc. No. SERV 04-98-1, May 6, 1991, Rev. 1), section 2, "Installation",which stipulates < 0.010"/ft, or < 0.027" differential height across the 32" span between the chamber support beams. Again, your procedure to limit the differential height change to < 0.02" is safe.

Centered Load on the STACIS Isolators

According to the TMC Stacis 2000 User's Manual (Document No. SERV 04-98-1, May 6, 1991, Rev. 1), section 2, "Installation", typical installations (Figure 2-3) are with one payload interface plate which spans the entire set of 3 or 4 STACIS actuators. Our payload interface is unique.

Section 2.3.1, "Installation Steps": "5. Verify that the top of each isolator is fully under the payload/interface plate; this is essential to ensure proper support and leveling. The payload or interface plate should cover the entire top surface of the Isolator or the entire contact area of the optional jack."

section 2.3.2, "Payload/STACIS Interface": "... or if the supporting points do not completely cover the top surface of each Isolator, an interface plate will be needed."

The sketch in Figure 2-2 indicates an optional leveling jack which appears to have a larger contact surface area than the jacks currently installed in the 40m Lab. Of course this is just a non-dimensioned sketch. Are the jacks used by the 40m Lab provided by TMC, or did we (LIGO) choose them? I beleive Larry Jones purchased them.

A load centering requirement is not explicitly stated, but I think the stipulation to cover the entire top surface of each actuator is not so much to reduce the contact stress but to entire a centered load so that the PZT stack does not have a reaction moment.

From one of the photos in the 40m elog entry (specifically jack_screw.jpg), it appears that at least some isolators have the load off center. You should use this measurement of the load as an opportunity to re-center the loads on the Isolators.

In section 2.3.3, "Earthquake Restraints" restraints are suggested to prevent damage from earth tremors. Does the 40m Lab have EQ restraints? Yes, it has

Screw Jack Location

I could not tell where all of the screw jacks will be placed from the sketch included in the 40m elog entry which outlines the proposed procedure.

Load Cell Locations

The sketch indicates that the load cells will be placed on the center of the tops of the Isolators. This is good. However while discussing the procedure with Gautam he said that he was under the impression that the load cell woudl be placed next to the leveling jack, off-center. This condition may damage the PZT stack. I suggest that the leveling jack be removed and replaced (temporarily) with the load cell, plus any spacer required to make up the height difference. Yes

If you have any further question, just let me know.

    Dennis

Dennis Coyne
Chief Engineer, LIGO Laboratory
California Institute of Technology
MC 100-36, 1200 E. California Blvd.

follow up email from Dennis 5-13-2018. The last line agrees with the numbers in elog13821.

[Ian, JC]

I want to take measurements of seismic noise at different places on Caltech's campus and in different buildings. I will try to use the accelerometer in my phone for this but first I must calibrate it (Against the 40m accelerometers). 

I placed my iPhone 11 pro next to the seismometers at the 40m MC as seen in Attachment 1.

The calibration from the instrument was done using cts/rthz * 1V/16384cts * 1/ampgain * g/10V * 10m/s^2/g. The ampgain for all was 100.

Next, I took 100 seconds of data on both the iPhone and the three orthogonal Wilcoxon accelerometers.

The ASD for both of the total acceleration is shown in Attachment 2

The ASD for the individual directions acceleration is shown in Attachment 3

The coherence between the individual directions acceleration and the 40m's individual directions is shown in Attachment 4. For this calculation, the 40m data were downsampled to roughly match the phone's sample rate. This coherence is not very good. It should be higher. Because the phone and 40m sensors were picking up the same data as the phone. Because of this I also looked at the coherence between the individual 40m sensors.

In Attachment 5 I look at the coherence between the individual 40m sensors. This should give me a good idea of whether this is some other issue giving me mow coherence. This plot shows that the coherence between the individual 40m sensors is much better than between the phone and the 40m sensors.

Now I wanted to see what kind of data the iPhone could get from real-world tests. I placed it in a number of locations described below and plotted their ASDs in Attachment 6. The locations are thus:

Notice how at the low end the amplitudes follow the relative amplitudes I would expect. QIL and WBSH are the lowest then WB1H is noisier and 40m desk is the noisiest. However, this is only true up until about 0.5 Hz then they all overlap. Since I would expect the 40m desk should be much noisier at all frequencies I suspect that the phone accelerometer is not suitable for measurements higher than 0.5 Hz.

Possible Problems:

One possible problem with my measurement is that my phone was in a leather case. this may have damped out higher frequencies. Also, my phone was not weighed down or bolted to the floor. this stronger connection would make it better at detecting higher frequencies. I could repeat the experiment with no case and a weight on top of my phone.

What's next:

Since I don't think the phone can give me accurate data above 0.5Hz for quiet environments. It may not be suitable for this task. It would seem that the right instrument is the Wilcoxon 731A but it requires an amplifier that I can't track down.

I included all the data and code in the zip file in attachment 7

[Rana, Ian]

We built a power supply for the accelerometer shown in Attachment 1 based on the diagram shown in the Wilcoxon manual and shown in attachment 2. We used a 9V power supply and a capacitor value of 680uF. We did not use a constant current diode. 

When hooked up to an oscilloscope we saw vibrations from hitting our hands on the table but we did not see the same amplitude in the negative and positive directions. For example, when I held the accelerometer and moved it down you would see a dip then a peak as the accelerometer accelerated down then accelerated up when I stopped the down word movement. But weirdly when I did the opposite (moved the accelerometer up the same dip then a peak appeared. This is a little concerning because it should be the opposite. it should be a peak then a dip. This in addition to the seemingly decreased sensitivity in one direction make me think that the accelerometer is broken.

I labeled the box with "might be broken" before I returned it to the cryo lab.

[Yuta, Paco, JC]

This eq  potentially tripped ETMY, PR2, PR3, AS1, AS4, SR2, LO1, LO2 suspensions during today's WB meeting. We restored them into normal local damping.

We aligned the arm cavities just to verify things were ok and then moved on to BHD comissioning. No problems spotted so far.

[Mayank, JC]

STACIS Vibration Cancellation Isolators contain a PCB board called the Compensator board. These are boards that "allow you to control the feedback to the PZT stacks." The board is essentially held up by the 2 rear plugs and 3 screws on the front rim (Highlighted in Yellow). You don't need to disassemble the entire islotar to remove this, you just need to loosen the tension screws and pull out softly. Attachment #4 shows the seat made for the board to be placed, highlighted in Green. When placing the board back into its original position make sure in slips into this slit nicely. The extender/compensator board is part of the STACIS Isolator and each Isolator should have this. Each board seems to haver it's own serial # but not an actual part #. On this board, the S/N is 033509.

[Ian, Torrey Cullen, Sander Vermeulen]

We are trying to calibrate one of the Wilcoxon accelerometers from the cryo lab to do a seismic study of campus. To calibrate it, we took data on Friday afternoon until about 6 pm for the Wilcoxon in the X, Y, and Z orientations and took cross-spectra with the seismometer down the end of the X arm from the channels C1:PEM-SEIS_EX_X_IN1, C1:PEM-SEIS_EX_Y_IN1, C1:PEM-SEIS_EX_Z_IN1. For the Wilcoxon, we used the channel from [17717] that was not being used. In the image of the panel in [17717] we tried channel 5, with the channel name C1:X01-MADC0_EPICS_CH28 but it was a slow channel. We asked Koji if there was a fast channel we could use, and he lent us channel 4 on that board with the channel name C1:ALS-X_SLOW_SERVO1_IN1. We took data from this channel to do our measurements. nothing was plugged into this channel when we started using it so we left it that way when we were done. 

I have attached our data.

NOTE: As it turns out the seismometer down the x end is not calibrated. We will recalibrate using the seismometer at the vertex

There is a version of this on the McCuller Logbook. It includes some plots. More non-40m related posts will continue there.

There is a small wood cabinet under the south end flow bench, labeled STACIS.

Unit is complete with extension cards and cables.

The beginning of my first week was spent at various orientations and safety meetings, some for general SURF and some more specific to LIGO and the lab. In between these I started  work.

Jenne and I took out the spare STACIS and took it apart, taking out the circuit boards. I've spent some time looking through the boards and sketching various parts of the board in trying to understand the exact function without any useful technical diagrams (STACIS supplied us only with a picture of the board without components, not all that helpful). I think I now at least understand the basic block diagram of the circuitry: the STACIS geophone signal goes through a preamplifier and filters (the semi-circular board), and converts it into a signal for the PZT stacks. This signal then goes through a high voltage amplifer, and then goes to the five PZTs (3 in the z, one each in the x and y direction). The unit I am looking at has an extension board, which allows us to tap into the signal going into the preamp and the one leaving it. This should allow us to input our own signal instead of the geophone signal, and thereby drive the PZTs ourselves.

My next step, once I get a resistor to replace a burnt one on the high voltage amplifier, is to take a transfer function of the STACIS and see if it is possible to drive the PZT stacks with the cables from the extension board. If that does not work, I'll have to keep tracing the circuit to determine where to input our own signal.

This past Friday I swapped out a burnt resistor on the spare STACIS unit I'm working with and powered it up. Here's the setup:

And here's what happened:

X an Y directions: When I switched from open to closed loop (making the internal geophones provide feedback), the STACIS started making a loud noise- it seemed like it was oscillating uncontrollably.

Z direction: The same thing happened in z until I added some weight to the top of the STACIS- then it quieted down, and seemed to work okay. The geophone signal dropped considerably compared to the open loop signal, which is expected if the feedback is working.

Then I tried driving the PZTs with a signal from the SR785 network analyzer. With an amplitude of tens of mV and frequencies from around .1 to 200 Hz, I could see the accelerometers I mounted on top of the STACIS definitely register motion, which means I was successfully driving the PZTs.

Below are transfer functions of the STACIS as I drove the PZTs from .1 to 100 Hz at 10 mV. The top graph is open loop, the second is closed loop. These were measured with the internal geophones.

In the bottom graph, "A" is closed loop and "B" is open loop, where the transfer functions were taken with the accelerometers instead of the geophones.

I'm still having issues with the STACIS oscillating uncontrollably with the slightest extra vibration, but with some more added weight both x and z direction are stable if you don't disturb the setup.

I took more transfer functions of the STACIS. In the last data I took Jenne pointed out that the geophone signals were not correlated well with the driving signal, so I increased the amplitude of the driving signal and am looking in x and y too instead of just z. 

Details of the driving signal: 25 mV, swept sine from 0.1 to 100 Hz from the SR785. 

NOTE: The data below was all transferred from the SR785 using netGPIB, which works fine, if anyone was interested in using it.

Open loop in the y direction, taken with the y geophone (magnitude on top, phase on bottom):

Open loop in the x direction, taken with the x geophone (with some extra weight to try to make the closed loop more stable):

Open loop in the x direction, taken with accelerometer instead of geophone:

The X and Y directions in the STACIS still both oscillate uncontrollably in closed loop, so I'll be doing my testing in Z for now. If I need to use the other axes I'll lower their gain with the pots and add weight to the STACIS platform to try to make it more stable.

Measurements I've taken for Z:

--Open loop gain, taken by driving the PZTs with a swept sine signal and measuring with both internal geophones and external accelerometers. These measurements look a lot like the plots supplied by the STACIS manufacturer, with a resonance at 15-16 Hz (X and Y also look good). Figure below was taken with geophones:

--Open loop gain, where the input is ambient seismic noise measured by one set of accelerometers on the floor and one set on top of the STACIS:

--Closed loop gain, where the input is ambient seismic noise, and feedback is supplied by the geophones (like normal STACIS operation). There's a definite drop in the transfer function, as expected:

--Open and closed loop transfer functions superimposed (the higher one is open):

I am currently working on using the less-noisy accelerometers to provide feedback instead of the geophones. I have found the right point before the extension board to input the accelerometer signal which is NOT the same as the Signal IN/OUT cables- those are at the end of the board, after amplifying and filtering. I want the accelerometer signal to go through the same circuitry as the geophone signal so that the noise of the sensors themselves can be compared.

Problem: Coherence isn't great between the accelerometer sets at low frequencies, which leads to a not very smooth transfer function. I might try using the shaker, because the larger motion may lead to better coherence between the accelerometers on top of the STACIS and at its base.

 Here's a picture of where I am now inputting signals into the STACIS with the accelerometers (the orange and blue wires): 

I know this is the right point because I could see the geophone signal from these points . By inputting a swept sine signal into this point, I was able to take a transfer function of this first amplifier/filtering circuit board, which will be useful if I need to make my own filter for the STACIS:

I have unplugged the geophones and am inputting a signal from an accelerometer into this point. The accelerometers output a different signal than the geophones, so I am trying to modify the accelerometer signal to be closer to the geophone one. I've lowered the gain on all the pots for the z axis and put in several BNC attenuators to lower the accelerometer signal amplitude.

At the moment, using the accelerometers as feedback makes the platform vibration worse, which will hopefully be solved by some more attenuation or filtering of the accelerometer signal.

I have been working on substituting the internal geophones in the STACIS with accelerometers, and this week specifically I have been trying to modify the accelerometer signal so the STACIS PZTs respond properly.

The major problem was that the high signal amplitude caused the STACIS to oscillate uncontrollably, so I lowered all of the pots (for the z direction) and placed several BNC attenuators before the accelerometer signal enters the first amplifier board. The accelerometers now successfully provide feedback without making the STACIS unstable, as shown by this transfer function (the higher and flatter line is open loop, the lower is closed loop with accelerometers providing feedback):

The next step is to optimize the accelerometer feedback so it provides good isolation from 0.1 to 3 Hz, a span that the geophones introduced a lot of noise into. The accelerometers definitely don't introduce as much noise in that region, but don't seem to be doing much isolation either. I will also make some more quantitative plots of the platform motion (using the calibration value for the Wilcoxon accelerometers in the velocity setting with a gain of 1).

Some random discoveries I made this week which are relevant for STACIS testing:

1) Placing weight on the STACIS platform improves stability, but NOT if several blocks are placed on top of each other (they rub against each other, causing lots of vibrations).

2) The accelerometer that is providing feedback must be VERY securely fastened to the STACIS platform; even with three clamps there was extra motion that caused instability. Luckily, there's a convenient steel flange Steve showed me which has a hole that perfectly accommodates the accelerometer and doubles as a weight for the platform. Here is said flange, clamped to the STACIS platform with the accelerometer sitting in the center:

 3) Using the shaker next to the STACIS (all on one platform) improves coherence between the base and platform accelerometers above around 10 Hz, but does nothing lower than that, which unfortunately is the region I'm most concerned with.

The past few days I've been working on making a noise budget for the STACIS that incorporates all the different noises that might be contributing.

The noises I am concentrating on are accelerometer noise, geophone noise, electrical noise, and ground noise. Noise from the PZT stacks themselves should be tiny according to various PZT spec sheets, but I haven't actually found a value for it (they all just say it's negligible), so I'll keep it in mind as a potential contributor.

Here's how I am determining accelerometer noise: I take two vertical accelerometers side by side, sitting on a granite block and covered in a foam box, and take the time series of both. Then I take the difference of the time series and calculate the PSD of that, which with the calibration factor of the accelerometers (the V/m/s sensitivity) I am able to find the noise in m/s/rtHz. The noise agreed with the accelerometer specs I found at low frequencies but was higher than expected at high frequencies, so I'm still investigating. If I can't find an obvious problem with my measurements I'll try the three-corner hat method (as per Jenne's recommendation), which would allow me to determine the noises of the independent accelereometers.

I tried a similar method for the geophone noise, but the value I came up with was actually higher than the accelerometer noise, which seems very fishy. I realized that the geophones were still connected to the STACIS circuitry when I took the measurements ,which was probably part of the problem. So this morning I disconnected the STACIS entirely and am looking at just the geophone signals which should give a more accurate noise estimate.

Once I have all the noises characterized, the next step is seeing how those noises affect the closed loop performance of the STACIS. I've been working on a block model that incorporates the different noises and transfer functions involved, and when I have the noises characterized I can test a prediction about how a certain noise affects the platform motion.

I have a tentative noise plot for the STACIS that includes accelerometer noise, geophone noise, and platform motion with the STACIS off. (Accelerometer noise was measured for the VEL and NONE setting, which are settings on the accelerometer box which make the accelerometer signal correspond to velocity and acceleration, respectively. ) I'm focusing on sensor noise because this is the variable I am looking at changing, and knowing how the sensor noise translates into STACIS platform motion is therefore important.

The accelerometer and geophone noise I determined as described in my last eLog (http://nodus.ligo.caltech.edu:8080/40m/7027) Along the way I found out several things of importance:

1) Horizontal geophones are ONLY horizontal geophones. This is obvious in retrospect, because the springs supporting the magnet inside must be oriented based on vertical/horizontal operation.

2) The geophones in the STACIS are GS-11D (geospace), with a sensitivity of 32 V/m/s (compared to about 3.9 V/m/s for the accelerometers in VEL setting).

3) The accelerometers have different V/m/s sensitivities. I noticed the voltage output of one was consistently higher than the other, leading to very high noise estimates, but then Jenne showed me the actual calibration factors of the individual accelerometers which differed by as much as 0.4 V/m/s (a few percent difference). Taking this into account made the noise plots much more reasonable, but variations in calibration could still create some error.

The accelerometer noise agrees fairly well with the specs on the Wilcoxon page (http://www.wilcoxon.com/prodpdf/731A-P31%2098079a1.pdf). The geophone noise seems surprisingly low; it is even better than the geophone below about 4 Hz. 

To see how this noise translates into actual platform motion, I took PSDs of the STACIS while it was off, on with accelerometer feedback, and on with geophone feedback (the "off" PSD is in the above noise plot). Using this data I'm working on estimating a transfer function that shows how the sensor noise translates to motion so I can come up with a sensor noise budget.

This shows that the geophones are actually doing a better job of isolating than the accelerometers, which is not surprising if the noise plot is accurate and the geophones are actually lower noise. It must be noted, though, that the noise plot was for the horizontal geophones whereas the plot above is for the vertical axis which may have a different noise level. Also, the vertical have some extra isolation by being enclosed in a metal stack with rubber padding at its base.

The problem with the STACIS in the past was the differential motion it introduced. I think this might be because the horizontal isolation was not uniform for each chamber. This means that even what would be symmetric motion (no differential length change) would be translated to differential motion because one end is more fixed than the other. Having accelerometers or better-padded geophones (maybe like the vertical geophones) in the STACIS ought to help with this by making the horizontal isolation more consistent and thus reducing differential motion. So the key may not be the geophone noise as much as varying geophone sensitivities or variation in how well they're mounted in the STACIS. I can test this by swapping out the horizontal geophones with other spares, changing the tightness of the mount, and seeing if either of these changes the horizontal isolation significantly, since these are factors that may differ from unit to unit.

I will also compare horizontal closed loop response with geophone vs. accelerometer feedback to see if the geophones are only doing a good job in the above plot because of their extra padding (the vertical stack).

The geophone noise in my last eLog was taken before any amplification of the signal, but what really matters is the noise after amplification, since it is this signal that the PZTs are driven by. The noise goes on to be amplified about 1000x before the geophone signal gets to the PZTs.

To obtain a more relevant noise plot, I multiplied the geophone noise by 1,000, the approximate gain of the amplification stage for the geophones (called the "compensator board", the semicircular board that sits toward the top of the STACIS). Below is a plot () that shows the noise for the geophones after amplification and the accelerometer noise (with accelerometers set with a gain of 100x, their highest).

The actual signal from both these sensors has the right magnitude to drive the PZTs (whereas it was much too small in my last plot, where I looked at the sensors before any gain)- this means that for these sensors, both of which are outputting signals that are ready to provide feedback to the STACIS, the accelerometer noise is significantly lower than the geophone noise. This is good news, because it means that there could be a real advantage to using the accelerometers instead of the geophones.

In the process of investigating further advantages of the accelerometers, I believe I killed one of the horizontal PZTs in the spare STACIS (the eBay one). The story: I had that axis in closed loop, and I saw the STACIS shudder, heard a noise, and there was a faint acrid smell. I shut the STACIS off and took out the high voltage card at the base but couldn't find any visible signs of damage (like the current-limiting resistors which burn when a PZT shorts, acc. to old STACIS records). I then tried driving the PZTs with a sine wave, and there was no response in that axis (the other axes looked fine), which leads me to believe I either did unseen damage to the high voltage amplifier (for the y-axis) or killed the PZT itself.

Tonight I looked at the signal from a geophone and accelerometer side by side, in order to see if they show the same ground motion and if the sensitivity factor I am using to convert from V to m/s is right. This is plotted below, along with the current estimates for accelerometer and geophone noise:

From this it is pretty clear that at least one of the sensitivity factors (V/m/s) I am using is wrong (the noise levels are much lower than the ground motion, so they can't account for the difference). I suspect it is the geophone one, because Wilcoxon provided these sensitivities for each individual accelerometer, but I was just using the number I found in online specs for the geophones.

The reason the online value is wrong is probably because of the value of the shunt resistor, a resistor that just goes across the top of the geophone (its purpose is to provide damping, by Lenz's Law). The specs assume a value of 380 Ohm, but I measured the one in the STACIS to be about 1.85 kOhm.

Assuming the accelerometer signal is correct, I multiplied the geophone signal by different factors to try to get an idea of what the true calibration factor is, and found that a value of 0.25 (m/s)/V gives decent agreement at higher frequencies (below 10 Hz the sensitivity drops off, according to the online specs). This is shown below:

Above, the geophone noise was recalculated with the new sensitivity and assuming that both geophones in the noise measurement had the same sensitivity. I took the transfer function of two geophones side by side to see if their gains were dramatically different; this plot is shown below. The coherence is only good for a small band, but looking at that band the gain is approximately unity, implying very roughly that the sensitivity of each is approximately the same. The lack of coherence is strange, and I'm not sure what the cause is. Even using the shaker near the geophones only improved the coherence slightly.

First, a quick note on the PZT I thought I killed- it was most likely something in the high voltage amplifier that broke, since I put the amplifier in another STACIS with a working y-axis PZT and it still didn't work properly. Conclusion: something in the y-axis amplifier circuitry is broken, not the PZT itself.

Today I retook the open loop gains in the X and Z axes (Y axis out of commission for now, see above). With the loop open, I input a swept sine signal from 0.1 to 100 Hz, and measure the output of the geophones. This way all the transfer function that are present in the closed loop are present here as well: the transfer functions of the physical STACIS, the geophone pre-amplifier circuit, the high-voltage amplifier, and the PZT actuators.

Here is a block diagram showing what I am measuring, with the various transfer functions in blue boxes (the measurement is their product):

These open loop gains show there is gain of at least 10x from 2 to 80 Hz in the z-axis and 2 to 60 Hz in the x-axis. This is the region I was seeing isolation in when I switched to closed loop, which is consistent. These measurements were with all the pots in the geophone preamplifier set very low, so more gain (and thus isolation) is hypothetically possible if I find a way to stop the horizontal axes from becoming unstable at higher gains. There is unity gain at around 0.5 Hz and 100 Hz for the z-axis, but the phase is nowhere near 180 deg. at these points so there shouldn't be instability due to this. The peak at around 15 Hz is consistent with old records of the STACIS open loop gain.

With your definition of the open loop gain, G=+1 is the condition to have singularity in a closed loop transfer function 1/(1-G).

But this is not the sole criteria of the loop stability.
Basically, the closed loop transfer function should not have "unphysical" pole.
For more about loop instability, you should refer stability criteria in literature such as Nyquist's stability criterion.

Both of the X and Z loops look unstable with the current gain.

This week I've looked into finding an accurate sensitivity for the geophones in the STACIS. I found that when placing a geophone and accelerometer side by side, and using the sensitivity values I had from spec sheets, the readings were very different (see eLog 7054: http://nodus.ligo.caltech.edu:8080/40m/7054).

I cut the shunt resistor off one of the STACIS geos and found it to be 4000 Ohm, which is one of the standard values for this geophone model. When it is connected to the geophone the net resistance is 2000 Ohm (I took a more careful measurement, I took the geophone out). Then the internal coil resistance should be 4000 Ohm, if they are connected in parallel. However, the geophone spec sheet does not have a sensitivity value for this exact scenario, so I'll have to find a different way to determine the calibration (maybe by putting it next to a seismometer with a known sensitivity). So I know for sure that the sensitivity value I was originally using is wrong, because it assumed an internal coil resistance of 380 Ohm, but I have to check if the value I found by forcing the geophones to agree with the accelerometers (eLog 7054 --> 0.25 (m/s)/V) is correct.

I've also been looking again at the open loop gains of the STACIS (see eLog 7058: http://nodus.ligo.caltech.edu:8080/40m/7058). Attached is what TMC, which makes the STACIS, says it should look like (with a 4000 lb load on the STACIS). Today I am taking the open loop gains into higher frequencies to get a better comparison, but the plots look quite similar to what I have so far. So if it is an unstable open loop gain, then it's at least not new.

Yesterday I plugged the geophone and accelerometer output into the ADC, rather than the SR785, so I could collect for longer and take more data at once.

As per Rana's suggestion, I am also now taking the geophone output after the first op-amp in the circuitry following the geophone (a low-noise op-amp, OPA227). It acts as a buffer so I'm not just measuring other local noise sources (which explains why the geophone noise curve sort of matched the SR785 noise curve in my old plots).

With these changes, I remeasured the accelerometer and geophone noises as well as collected an ASD of a geophone sitting on the STACIS in open loop operation. I also looked up the noise specs for the various op-amps in the geophone pre-amp and high voltage board; everything I found, I added in quadrature to come up with an approximate op-amp noise value for the STACIS. All of this is plotted below:

I left the y-axis in V/rtHz instead of converting it to m/s/rtHz so that the op-amp noise could be compared to the other noises. All sensor data was taken with the sensors horizontal (noise data taken in granite and foam).

The accelerometer and geophone noise still appear to be similar, and the op-amp noise, at least according to specs, is low compared to the other noises. This implies there's not much to gain from switching the geophones with accelerometers nor with swapping out the op-amps for lower-noise components (unless the ones I couldn't find specs for were high-noise, though it seems like mainly low-noise components were used). 

Looks like you're just measuring the ADC noise. You should add ADC noise to your plot. To compare the geophones with the accelerometers, you have to correct for the preamp gain and plot them both in the same units.

To get above the ADC noise you can use an SR560 preamp. (AC Coupled, G = 100)

As Rana pointed out (http://nodus.ligo.caltech.edu:8080/40m/7112), the geophone/accelerometer noise lines from my last eLog (http://nodus.ligo.caltech.edu:8080/40m/7109) were dominated by ADC noise. I checked this today by terminating the ADC channels with 50 Ohm terminators and measuring the noise. The ADC noise line is included on the plot below, and it is clearly dominating the sensor noise data.

I set the accelerometer gain to 100, and will hook up the geophones to the SR560 pre-amp today- this should put both signals above the ADC noise, and I can calculate the sensor noises without the ADC noise being significant.

I have also begun to make some progress in understanding the pre-amp circuitry, and I will post a schematic when I've sketched it all.

Another issue that seems increasingly relevant to me is the power supply to the high voltage amplifier. It appears to go into the high voltage board from the power supply, then into the geophone pre-amp, then back into the high voltage board (see block diagram below). I tested this by inputting a signal after the pre-amp, with the geophones disconnected- the signal only drives the PZT if the pre-amp is plugged in, so the power that returns from the pre-amp must be powering some chips on the high voltage amplifier.

Power flow through the STACIS :

This is somewhat inconvenient, because it means if I want to provide external feedback (with accelerometers, for example) or actuation (such as feedforward), which I want to input after the geophone pre-amp, the pre-amp still needs to be plugged in for the high voltage amplifier to work and drive the PZTs.  I am cataloging all of the pins on the high voltage amplifier and pre-amp so I can figure out how to reroute the power and cut out the geophone pre-amp entirely if necessary. I'll include a pin diagram with the pre-amp circuit sketch.

I hope you're not all tired of the STACIs noise budgets, because I have another one! Here, the main difference is my modeling of the geophone sensitivity according to a predicted physical model for the system (just a damped oscillator) instead of trying to fit it to the accelerometer motion signal with more arbitrary functions.

The result of this calibration is shown below (accel and geo signals taken for 5 minutes at the same time, in granite and foam):

The m/s/V sensitivity function I am using is g*[(w^2-2idww(0)-w(0)^2)/w^2], where g (the high freq. m/s/V sensitivity) was 2.5*10^-5 and d (damping) was set to 2.

Now, the recalculated noise plot looks like this:

The accel. specs I took from the Wilcoxon spec sheet, and the geo specs I found in https://dcc.ligo.org/public/0028/T950046/000/T950046-00.pdf, a LIGO document about the STACIS. The geo noise was measured for the STACIS geo and their pre-amp, while I was using the SR560 as the pre-amp. If anything, my noise should be lower, since the SR560 noise spec is lower than what I estimated for the STACIS geophone pre-amp, so I'm not sure about that order of magnitude difference between the experimental and expected geo noise. A sign that my noise values are at least reasonable is that the geophone noise flattens out above the geophone's resonant frequency (4.5 Hz), as Jan pointed out it should.

The sensor noise (either accel. or geo.) is the dominating signal below 1 Hz in the STACIS platform measurement, which then limits the closed loop performance at those frequencies. Since the noises I am finding are looking reasonable, I think it's fair to definitively state that accelerometers will not significantly help at low frequencies (there may be at most a factor of 2 lower noise below 1 Hz for the accel., but I need more data to say for sure).

The plan right now is to concentrate on using the STACIS as actuators, perhaps with seismometers on the ground and a feedforward signal sent into the high voltage amplifier.

I took the transfer function of the high voltage board itself (no pre-amp included) by driving the PZTs with a swept sine and measuring the accelerometer response (which I am now fairly confident is calibrated correctly). The input point was the signal IN on the extender board, but with the geophones disconnected from the pre-amp.

I took the coherence at just a few single frequencies (you can't do coherence measurements in swept sine mode on the SR785) to make sure I was really driving the PZTs, and it was near 1 (998, 999.9, etc) at the frequencies at which I drove. Without the extra notches at 1 Hz (which may be real, it's coherent there too), it looks like a 2-pole high pass filter (goes from -180 to 180 deg, approx. an f^2 dependence). This transfer function should be taken into account by the feedforward algorithm.

The current plan is to make a box with a switch that allows geophone feedback and/or external signals into the high voltage amplifier. It would act sort of like the extender card, except more compact so it could fit into the STACIS. It also would have the advantage of not having to reroute the power, since those lines from the pre-amp could all still be connected (see eLog 7118: http://nodus.ligo.caltech.edu:8080/40m/7118).

In eLog 7148 (http://nodus.ligo.caltech.edu:8080/40m/7148), Koji pointed out that the op-amp and SR560 noise values (which I took from specs and then multiplied by the geophone calibration factor to get m/s/rtHz) were waaay too low. My error was an extra multiplication factor in the plotting script.

The other change was recalculating the ADC noise by splitting a signal into two ADC channels and subtracting the time series (then taking the PSD and converting to m/s/rtHz). It compares well to the value I got by terminating the ADC channels, which was the ADC noise line in my last eLog.

Both these changes are included in the below plot:

This week I've been focusing mainly on two things: 1) Designing a port for the STACIS that will allow external actuation and/or local feedback and 2) Investigating the seismic differential motion along the interferometer arms.

The circuit for the port is just a signal summing junction (in case we want to do feedforward and feedback at the same time) with BNC inputs for the external signal and switches that allow you to turn the external signal or feedback signal on/off. I'll test this on a breadboard and post the schematic if it works. I looked at the noise of the geophone pre-amp and DAC, which would be the feedback and external signal sources, respectively. According to Rolf Bork, the DAC noise is 700 nV/rtHz, and I measured the pre-amp board's minimum noise level at 20*10^-6 V/rtHz (which seems quite high). Both these noises are higher than the op-amp noise for my circuit (I'm considering the op-amp LT1012), which according to the specs is 30 nV/rtHz. This confirms that my circuit will not be the limiting noise source. 

Along with Den, I calibrated the seismometers in the lab and measured the displacement differential arm motion (see eLog 7186: http://nodus.ligo.caltech.edu:8080/40m/7186). I'm trying to find a transfer function for the seismic stacks (and pendulum, but that's simpler) so I can calculate the differential motion in the chamber. After doing this offline, I'll make new channels in the PEM to look at the ground and chamber differential motion along the arms online.

I also am looking at the noise of the geophones with their shunt resistor (4k resistor across the coil) removed, to see if it improves the noise at low frequencies. My motivation for this was that the geophone specs show a better V/m/s sensitivity at low frequencies when the shunt resistor is removed, so the actual signal may become larger than the internal noise at these frequencies.

Below is the bottom view of the geophone preamplifier and controller for the STACIS. It slides into the upper part of the STACIS, under the blue platform. The geophone signal goes in the bottom left, gets amplified, filtered, and otherwise pampered, and goes out from the bottom right. From there it goes on to the high voltage amplifier, and finally to the PZT stacks. Below right is a closer view of the output port for the preamplifier, top and bottom.

I suggest de-soldering and bending up the pins that carry the geophone signal (so the signals don't go directly to the high voltage amplifier), and adding the circuit below between the preamp and amplifier. The preamp connector is still attached to the high voltage amplifier connector in this setup, only the geophone signal pins are disconnected.

More on the circuit and its placement:

The first op-amp is a summing junction, and the second is just a unity gain inverter so that signal doesn't go into the high voltage amplifier inverted. I tested this with the breadboard, and it seems to work fine (amplitudes of two signals add, no obvious distortion). The switches allow you to choose local feedback, external feedforward, or both.

The geo input will be wires from the preamp (soldered to where the pins used to go), and the external input will be BNC cables, with the source probably a DAC. The output will go to the bent up pins that used to be connected to the preamp (they go into the high voltage amplifier). This circuit can sit outside of the STACIS- there is a place to feed wires in and out right near where the preamplifier sits. For power, it can use the STACIS preamp supply, which is +/- 15V. The resistors I used in the breadboard test were 10 kOhm, and the op-amp I used was LT1012 (whose noise should be less than either input, see eLog 7190).

This is visually represented below, with the preamp pin diagram corresponding to the soldering points with the preamp upside down (top right picture):

I made the signal box as described in eLog 7210. It adds the geophone signal and an external signal.

It has six switches, for x, y, and z signals from both an external and local (geophone) source. The x signals add if both x switches are flipped down (and the same for the other directions). For example, if you want to feed in only an external signal in the x direction, flip down the external x direction switch (it's labeled on the box), leaving all others flipped up.

The x, y, and z outputs are wired to the pins from the preamplifier that go to the high voltage board. These I disconnected from the preamplifier by cutting at their base (there are spare connectors if this wants to be undone, or, a wire can just be soldered from the pin to its old spot on the board). The power (plus/minus) and ground are wired to the respective pins from the geophone preamplifier (naturally, the STACIS must be turned on for the box to work since the box shares its power source). Below, the front (switches and geophone/external inputs) and back (power, ground, outputs) of the box are shown:

The preamplifier can plug into its regular connectors- the x,y,and z signals will all be redirected to the signal box with these modifications. The box sits outside the STACIS, there is room to feed the wires out from underneath the STACIS platform.

NOTE: The geophone z switch is a little different than the others, just make sure it's flipped all the way down if you want that signal to be seen in the z output.

 I found this entry in the old 40m ilog which describes the STACIS performance. It shows that even though the STACIS is bad for the differential arm motion below 3 Hz. It has quite a big and positive effect at 10-30 Hz. The OSEMs show a bigger effect than what the single arm does. I think this is because the single arm is limited by the MC frequency noise above 10 Hz.

We should figure out how to turn on the STACIS but set the lower UGF to be ~5 Hz.