A design study of a Cryogenic High Accurate Derotator.

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A design study of a Cryogenic High Accurate Derotator.

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Assignment

Perform a design study a derotator to prevent the smearing of the image with such a precision that an object falling on one pixel does not shift more then 1/5th (6.2μm) in one hour of observation time.

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• Introduction (E-ELT,METIS)• Problem definition• Concept design• Feasibility test• Conclusion and remarks

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Introduction (E-ELT,METIS)

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• Mid-infrared E-ELT Imager and spectrograph • Imaging/spectroscopy in the mid infrared range (wavelengths of 2.9-14 µm)• Environment cryogenic and vacuum


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• Mid-infrared E-ELT Imager and spectrograph • Imaging/spectroscopy in the mid infrared range (wavelengths of 2.9-14 µm)• Environment cryogenic and vacuum


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Why is derotation necessary• The detector of the metis instrument needs and integration time

of at least 15 minutes to get an high enough signal to noise ratio.• When not derotating smearing on the detector will occur, due to

the rotation of the earth.• Because of the altitude azimuth configuration of the E-ELT the

rotation can not be compensated by the telescope

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Optical configuration

Angle (αmir) ≈28 degrees

Length (Lmir) =109.04 mm

Length science beam (Bmir) =195 mm

Radius of the science beam (Rmir) ≈58.0 mm

Height of the second mirror (Hmir) ≈161.7 mm

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Influence of DOF

Mirror influences• 6 degrees of freedom for each mirror• Only 3 influence the science beam

Derotator• 6 degrees of freedom for the derotator• 4 influence the science beam

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Influence of DOF

Mirror influences• 6 degrees of freedom for each mirror• Only 3 influence the science beam

Derotator• 6 degrees of freedom for the derotator• 4 influence the science beam

Movement in x-direction

Rotation around x-axis(αx)

Movement in y-direction

Rotation around y-axis(βY)

Movement in z-direction

Rotation around z-axis(γZ)

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Influence of DOF

Derotator• Specific property when rotating

around the specific rotation pointRed (1 degree)Blue (2 degrees)

Rotation around y-axis(βY)

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Concluding optical analysis

• When defining the rotation point as shown in the previous slide the problem will reduce to a 3 DOF problem.

• In the x-z plane the axis of the derotator needs to be directed to the rotation point (β)

• The angle of the axis of the derotator in the z-y plane needs to be zero (α).

• The rotation around the axis needs to be controlled to control the rate of derotation (γ)

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Problem definition

The end goal for the derotator is to prevent the smearing of the image with such a precision that an object falling on one pixel does not shift more then 1/5th (6.2μm) in one hour of observation time.

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Requirements mirrors

Requirements mirrors• Rotation: 2,6 arcsecond• Translation: 5 micrometer

Environmental aspects• Working temperature: 25-90 K• Working pressure 10-7-1 bar

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Requirements DerotatorRequirements derotator• rotation α and β: 2,6 arcseconds• rotation γ: 2 arcseconds• Maximum rotation speed: 7,5 degrees/hour• Minimum rotation speed: 0 degrees/hour• Setup speed: 90 degrees/minute• Needs to rotate in both directions• MTBF: 36500 hours• Maximum allowed weight: 30 KgEnvironmental aspects• Working temperature: 25-90 K• Working pressure 10-7-1 bar

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Concept design Derotator

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Feasibility test

Purpose of test setup

• Test the feasibility of the used principles

• Test the accuracy of the capacitive sensors

• Kept as simple as possible

• Modelled as a pendulum

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Feasibility test

I d2θd t 2

+C dθdt

+(k +m ∙g ∙ L) ∙ θ=M

Calculating PID values

Controller variable ValueKp 2000Ki 1000Kd 200

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Feasibility test

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-25

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-15

-10

-5

0

5

Mag

nitu

de (d

B)

10-2

10-1

100

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103

-90

0

90

180

270

360

450

Pha

se (d

eg)

Bode Diagram of closed loop system

Frequency (Hz)

Closed loop bode plot• Phase margin in zero degrees up to 1 hertz

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Feasibility test

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Feasibility test

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Test resultsRequired accuracy: 2,6 arcseconds = 12 micro radiansSignal that needs to be followed is of very low frequency

Applying a sinusoidal reference signal with:• Amplitude 400 micro radians• Frequency 0,02 Hz

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Test results

• Proven that an accuracy of 2,6 arcsecond is feasibly with a low disturbing frequency (up to 0.02 Hz)

• This was done with relative simple building block (capacitive sensor; Voice coil actuator)

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Conclusion and remarks

• With optical analyses the 4 DOF system is reduced to a 2 DOF system

• This 2 DOF can steer the science beam on the detector

• Errors in the mirrors position can be compensated with the derotator reducing the requirements on the mirror

• Relative easy to build a system with a 2,6 arcsecond angular accuracy at low frequencies

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Conclusion and remarks

There is still some work that needs to be done• The test setup can be improved with a discrete

controller such that error at higher frequencies is reduced

• A trade of has to be made between the amount of heat dissipation and the required force to reduce error at higher frequencies

• A thermal analyses of the system needs to be done

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Questions

A design study of a Cryogenic High Accurate Derotator.

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