1   Introduction¶

The Auxiliary Telescope (AT) primary mirror (M1) is supported by 3 hard points plus 21 pneumatic actuators. The actuators are connected to a pneumatic system that regulates pressure on the line, which is uniformly distributed between each element.

When pressure in the pneumatic system is turned off the mirror sits in the 3 hard points. One of the hard points (a.k.a. the load cell) contain a “digital scale” that measures the load (how much weight) it supports. With the mirror supported by the 3 hard points distort the shape of the mirror resulting in considerable image aberration. The pneumatic system can provide additional support to the mirror, spreading the load over its back surface, mitigating the problem.

With different elevation angles, the normal support force on the mirror change, decreasing as elevation decreases. This means that the pressure on the actuators need to be adjusted with elevation to compensate for that effect.

To first order one expects that this will be a simple relation with the normal vector. In a real case scenario, secondary effects in the system can cause the pressure to deviate somewhat for a simple linear relation requiring higher-order terms to account for systematics in the hardware.

There are 3 components that work together to account for this effect in the Auxiliary Telescope (AT); ATPneumatics, AT Active Optics System (ATAOS) and AT Mount Control System (ATMCS).

The ATPneumatics is the component is charge of regulating the pressure for the pneumatics actuators. There are 3 valves involved when it comes to setting the M1 support pressure: master air supply, instrument air supply and M1 air valves. Once all 3 valves are opened there will a small back pressure applied to M1 even if it is commanded to zero. It is important to have that in mind since it will impact the way we measure the optimum pressure.

The ATAOS is the component in charge of storing the look-up table and setting the M1 pressure in the ATPneumatics depending on the elevation. It works by listening to the position of telescope, published by the ATMCS, and the current M1 support pressure, published by the ATPneumatics. The elevation is used to calculate the expected pressure, according to a polynomial equation. If the computed value changes by more than a configurable threshold compared to the current pressure, it will send a command to the ATPneumatics to update the M1 support pressure.

This document describes the procedure to measure the optimum M1 pressure for different telescope elevations and fit the data with a polynomial equation to obtain the coefficients required by the ATAOS component. We also describe how to load the new coefficients into the ATAOS.

2   Measuring optimum M1 support pressure for different elevations¶

As mentioned above, the support system contains 3 hard points and 21 actuators, all have the same contact area with the mirror. The total mirror weight is \(800lb\) (\(\sim 362.9kg\)). Nevertheless, as it is possible to note furthermore, we developed a procedure that does not require knowing the total weight of the mirror, using the load cell to measure the supporting weight.

In principle, to minimize distortion in the mirror shape we must make sure the load is evenly distributed between all the 24 actuators. The first step in the process is determining what it expected “optimum load”, as measured by the hard point load scale mentioned above. When there is no pressure in the pneumatic system all the weight of the mirror will be supported by the 3 hard points. That means the “total load” for a given elevation is 3x the one measured by the load cell. Consequently, the “optimum load” will be the “total load” divided by 24, the number of actuators.

Once the optimum load is defined for a given elevation we need to determine what is the corresponding pressure set point to the ATPneumatics needed. In order to obtain the value for the optimum pressure we then perform a binary search inside a sensible range.

Assuming a lower and upper limit for the pressure of \(P_{min}\) and \(P_{max}\), the binary search for the optimum pressure is as follows:

1. Set pressure to zero (\(P=0\)) and measure load to determine \(\mathrm{optimum\_load}\) using equation (1).
2. Set pressure to \(P=P_{min}\) and measure the load in the load cell.
   • If the load is lower than the optimum load, it means the minimum pressure is larger than the optimum value. The process is terminated.
3. Set pressure to \(P=P_{max}\) and measure the load in the load cell.
   • If the load is larger than the optimum load, it means the maximum pressure is lower than the optimum value, e.g. maximum was not correctly measured. The process is terminated.
4. Compute the mid-pressure point \(P_{set}=(P_{min}+P_{max})/2.\).
5. Set the pressure in the ATPneumatics to the mid-pressure point.
6. Measure the mid-pressure load.
   • If the mid-pressure load is larger than the optimum load, set \(P_{max} = P_{set}\).
   • If the mid-pressure load is lower than the optimum load, set \(P_{min} = P_{set}\).
7. Repeat steps 4, 5 and 6 until the relative difference between the mid-pressure load and the optimum load is smaller then 1%.

Before running this process for a range of elevations we need to define a reliable procedure to determine the initial minimum and maximum pressures. For the minimum pressure \(P_{min} = 0.\) was taken as the starting point.

For the maximum pressure it is key that the procedure gives a higher enough value that guarantees the optimum load will be larger than the load at maximum pressure or the procedure will fail in step 3. It also must not be too high that will cause the mirror to lift from the hard points.

To determine a safe maximum pressure we selected the lowest elevation in the grid as a reference point (\(\mathrm{elevation} = 20^\circ\)). Then, the pressure was manually set until the measured load was lower than the optimum load but still did not caused the mirror to lift. Assuming pressure is zero for an \(\mathrm{elevation} = 0^\circ\), we then compute the linear coefficient with the normal angle.

Then, the maximum pressure for each elevation is computed as;

With this we proceed to measure the optimum pressure for 20 different elevations, linearly spaced between \(20^\circ\) and \(85^\circ\).

The result is shown alongside with the polynomial fit in Figure 1.

Figure 1 Upper panel: Data for the optimum M1 support pressure vs. elevation (blue dots) alongside a linear and a 7th-order polynomial fit with the normal gravity vector. Lower panel: Residuals when using the linear (solid blue line) and the 7th-order (solid orange line) polynomial fit.

In the bottom panel of Figure 1 we show the residue of linear and 7th-order (solid orange line) polynomial fit. It is clear that there are systematic residuals in the linear fit. We increased the order of the fit until the residual was satisfactorily. Since there are no apparent small scale structures we are not particularly worried about overfitting the data.

The output of the fit is shown in Table 1.

3   Loading values into ATAOS¶

The process to load a new configuration into the ATAOS is pretty standard. It starts by cloning the configuration repo <https://github.com/lsst-ts/ts_config_attcs.git> locally.

git clone https://github.com/lsst-ts/ts_config_attcs.git

Create a ticket branch in the repo and create the file hex_m1_hex_202003.yaml to host the configuration in the ATAOS configuration host in ATAOS/v2. Here we choose to add only year and month to the name of the configuration file. In case multiple configurations are generated over the course of a run, one can think about appending a day and even an index to the file name. Add the data in the third column of Table 1 into the m1 session of the file.

It is also important to edit the _labels.yaml file in the package and make sure the new configuration is mapped to the current (or the first entry in the file) tag. This will make sure the high level software will select the configuration by default.

Once these changes are implemented, proceed with commit, push and open a PR to the configuration package.

The final result can be found here, for the configuration file, and here, for the labels.