Note
This technote is a work-in-progress.
1 Abstract¶
Data analysis of the LVV-T1829 M2 Rigid Body Position - Stability and Repeatability - Position Sensor Verification - Data Analysis.
The test is designed to check the repeatability in the measured position for all the 6 DoF. related to the IMS measurements The requirements verified by the test are:
Linear repeatability within 1 \(\mu\mathrm{m}\)
Rotation repeatability within \(1\cdot10^{-5} deg\)
2 Test Case¶
The test case is the data collection of the test case M2 Rigid Body Motion - TMA https://jira.lsstcorp.org/secure/Tests.jspa#/testCase/LVV-T1791
In this test M2 is moved sequentially along each DoF for most of the travel range in a positive and a negative.
Excursion ranges retrieved by the test are \(\pm 250 \mu\mathrm{m}\) for the linear movements and \(\pm 15 \mathrm{arcsec}\) for rotations. For each DoF are perfomed 5 sequence of 8 steps holded for 37 sec.
3 Data analysis¶
3.1 Walking of the DoF¶
The values are retrieved from the IMS. In the code are stored the start times for each sequence and it filter the datatset accordingly. Then the first result is a summary plot showing the DoF walks with all the sequence. The X-axis are the relative time from the beggining of each sequence, so that they are overlapped to each other.
Figure 1 DoF walking subplots.¶
3.2 Reserach of the Plateau¶
In order to understand if the requirements are met or not, we need to claculate the statistic (i.e. mean, RMS and PtV) of the plateaus in each sequences of the DoF s. The code exploits the proximity difference of the points to each other in order to indentify the flat regions. More precisely the function np.ediff1d is used. Doing so, a new columns in the data frame is created with the difference of each element wrt the next one. Using this information the code identifies the flat region if the difference fall below a certain threshold defined empirically. This method is more robust against high frequency noise. Because of noise is present in the plateau (see fig. Figure 2) the simple difference has been applied. Moreover, to avoid contamination from the outer part, when the M2 cell is still moving, the code rejects data found at the border of the plateau region.
Figure 2 Example of a plateaus found in a single sequence.¶
3.3 Retrieving the plateaus statistic¶
For each IMS axis statistics have been reduced for the plateau of each of the 8 step in which the path has been fractionated. The Peak to Valley values (P_V) between the commanded position and the measured one is plotted to check if the requirement LVV-18727 LTS-146-REQ-0111-V-04 3.4.4 MIRROR POSITION SENSORS - M2 LSST Re-verification is verified.
Figure 3 Repeatability along X axis.¶
Figure 4 Repeatability along Y axis.¶
Figure 5 Repeatability along Z axis.¶
Figure 6 Repeatability along DRX angle.¶
Figure 7 Repeatability along DRY angle.¶
Figure 8 Repeatability along DRY angle.¶
As cleary indentified by the plots repeatibility is well inside specifications and the requirement is so verified.
4 Conclusions¶
Data analysis for Rigid Body Position its stability and repeatability and position sensor verification has bee carry out. Results show that requirements are verified and the IMS works as by design.