TPTCSPNT_070410 Half power tracks

Scan 29 (Azimuth half power track)

There are a lot of caveats to place on this result, but when I posed the question:

“Given estimates az rates and accels, and the inclinometers and accelerometers on both elevation bearings, how well can a dynamical model predict/estimate the HP track offset?”. Note that scan29 is an azimuth track.

The result for scan 29 (20 minutes at Ku) is: standard deviation of 0”.8, very Gaussian residual. See attached plots.

This result really represents the best performance, given

1) No thermal effects

2) Correct gravity model

3) Track has not changed

4) Real-time correction (really saying that I don’t believe 3))

Given a this dynamical model, the forward prediction error (how well you can predict forward the beam offset given all inputs to present) is essentially the same as the “batch” performance for a 0.1 sec forward prediction (5 steps at 20 Hz). Prediction forward 0.4 sec shows some degradation.

What does this really mean? That in principle the data from the elevation bearings and az encoder is sufficient (some might not be necessary). To do this in practice is still not assured, but that it’s possible in principle is still nice to know.

How is this different from what I’ve done before? I’m skipping the intermediate step of estimating el axle pose and going directly to the beam offset. Why? Not because the axle pose is insufficient (although it might be) but rather to establish the adequacy of the data and the conceptual correctness of the dynamical model.

An open question is what the equivalent HP track offset noise is, i.e., given the experiment, what is the angle equivalent to the receiver/IF/etc. noise? I suspect that it’s not much below 0”.8- Does someone have a good approximation to this?

The power spectral density plot attached.

1) Some minor structure at 0.27 Hz, around 0.4 Hz and 0.54 Hz.

2) Not any obvious scaling law in log-log (e.g., f^-a)- so it would seem that the noise is not associated 1/f noise, and thus probably not receiver 1/f noise. I must admit that this is just a first impression, and to pin it down would take a bit of work. Any interest?

3) The minor structure could conceivably be removed with a higher order state-space model, but I’m not disposed to pursue it. 0”.8 is quite good enough, if it can be generalized across telescope configurations.

Attached figure shows “clunks” (three of them, two are marked) during scan29. The evidence is an impulse of az acceleration (lower trace) with an associated ringing of the structure (upper trace).

Since this was a HP track this shouldn’t be happening. Note in the previous emails the estimator does an excellent job of removing it (since there aren’t any remnants of the ring in the residual trace). The reason that I bring it up is that it may be an indication of a malformed command set to the servos. And then again, it may be evidence of running over pennies on the track, or such like. It is likely not wind, since the PSD of the impulses isn’t consistent with the spectral content of wind over a 20 minute interval. It could be something pretty massy shifting and banging as elevation changes, but I suspect that it would be pretty loud in order to produce this effect.

Last interesting thought: Remember the “pinging” in the az truck assemblies, which I though to be a hysteretic release of, say, a bearing on a shaft… This could be confirmatory evidence of such a phenomena.

John suggested that dynamic corrections might be the cause- Look at prelimFig9.JPG to see that they don't appear to correlate. It's a plot of dyn_az1 (blue), dyn_az2 (red), and dyn_el (green) above a plot of the ringing in inc Y1, all from scan29. There doesn't seem to be a correlation... Note that the top Y axis is degrees in this case, the lower is inclinometer arcsec, and the X axis is samples @ 20 Hz.

* prelimFig1.JPG:
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• prelimFig2.JPG:
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• prelimFig3.JPG:
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• prelimFig4.JPG:
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• prelimFig6.JPG:
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• prelimFig9.JPG:
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Scan 35 (Elevation track)

Identical processing was applied to Scan35 (elevation) which yielded a standard deviation of 0".81 for the error. Comparison of the PSD of Scan29 and Scan35 indicate that both have about the same power in the 0.45 Hz region and Scan35 does not have the well defined 0.27 and 0.54 Hz components.

• prelimFig7.JPG:
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• prelimFig8.JPG:
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All Scans

Identical processing again. Scans 29 and 41 are az, scans 35 and 47 are el. In the PSD comparison, blue is scan 29, green is 35, red is 41, and cyan is 47. Note:

1) The common broad spectral feature centered around 0.4 Hz,

2) The 0.27 and 0.54 spikes (harmonics?) in scan 29 (az),

3) The 0.26 and 0.51 spikes (harmonics?) in scan 41 (az),

4) The common ~ 0.12 peaks in both scan 35 and 47 (el).

The standard deviation of residuals are all 0".8.

• prelimFig10.JPG:
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• prelimFig11.JPG:
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-- KimConstantikes - 22 Jun 2007