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University of Stuttgart
Institute for System Dynamics
Disturbance Feedforward Control for Vibration Suppression in Adaptive Optics of Large Telescopes
Martin Glück, Jörg-Uwe Pott, Oliver Sawodny
University of StuttgartInstitute for System Dynamics
Reaching the Diffraction Limit of Large Telescopes using Adaptive Optics
Martin Glück 2
WavefrontSensor
Camera
Light from Primary Mirror
Tip/TiltMirror
DeformableMirror
Beamsplitter
Adaptive Optics
Disturbances affecting the Telescope Resolution Atmospheric Turbulences Structural Vibrations
Accelerometer-basedDisturbance Feedforward
Observations with Faint Guide Stars Long exposure for better Signal-to-Noise-
Ratio Adaptive Optics (AO) loop speed is reduced High frequency Vibrations are seen at the
Telescope Mirror (> 5 Hz) Classical AO loop is to slow
Adaptive Optics
University of StuttgartInstitute for System Dynamics
Accelerometer-based Disturbance Feedforward Control
Martin Glück 3
Control unit
accelerometer
TTM- control
DM - control
Compensation of the Telescope Vibrations
Measuring vibrations at relevant telescope mirrors
with additional accelerometers
Reconstruction of the Optical Modes influenced
by Vibrations (Piston, Tip, Tilt Zernike Modes)
Compensating by the Tip-Tilt mirror and
Deformable Mirror
Independent of the WavefrontExposure Time
Suppression ofhigh frequency Vibrations
University of StuttgartInstitute for System Dynamics
Agenda
Martin Glück 4
1. Methods for Vibration Suppression
2. Simulation Results
3. Conclusion and Outlook
University of StuttgartInstitute for System Dynamics
1. Classical Integration
2. Observer-basedDisturbance Suppression
𝜙turb
𝜙res𝜙cor𝜙res,d = 0
Overview Adaptive Optics
Martin Glück 5
𝜙vib
-
WavefrontSensor (WFS)
Deformable Mirror (DM)
Controller(R)
Atmospheric Turbulences
(turb)
Vibrations(vib)
u
-
University of StuttgartInstitute for System Dynamics
Observer-Based Disturbance Compensation (LQG) for the Tip/Tilt Modes
Martin Glück 6
𝜙res
𝜙turb𝜙vib
R DM
WFSBEO
0
Assumptions DM ≈ 1 (fast position control) 2 sample delay of the WFS
Disturbance Modelling Atmosphere
Approximation of the temporal power spectral density by a second order AR model
Vibrations Modal representation of the mechanical system (considering dominant natural
frequencies) 𝑥 + 2𝑑𝜔0 𝑥 + 𝜔02𝑥 = 𝑢
𝑋𝑡 = 𝑎1𝑋𝑡−1 + 𝑎2𝑋𝑡−2 + 𝜖𝑡
u-
University of StuttgartInstitute for System Dynamics
Accelerometer-based Disturbance Feedforward Control
Martin Glück 7
Concept Measuring Vibrations with
Accelerometers at Telescope structure
Reconstructing Optical Modes(Piston, Tip, Tilt, Defocus) Different Tip-Tilt Sensitivity
of each Mirror
Adding to the Control Input of the Adaptive Mirrors (M4, M5) Considering time delay
University of StuttgartInstitute for System Dynamics
Reconstruction Algorithms for the Optical Modes
Martin Glück 8
Challenges
Online Double Integration of Accelerometer Signals Unstable
Time Delay
Reconstruction Methods
Approximation of a Double Integrator by a Bandpass Filter, Böhm[2]
Disturbance Observer Modal Model of the Mechanics Luenberger Observer Design
𝑥 = 𝐴 𝑥 + 𝐿 𝑦 − 𝑦 , 𝑦 = 𝐶 𝑥 Adaptive Resonator , Keck[1]
Using Online Fourier Analysis
𝜑𝐴𝑅,𝑖 = 𝐴 𝑐𝑜𝑠 𝜔1t + B sin(𝜔1𝑡)
𝜑𝐴𝑅,𝑖 = −1
𝜔12 𝜑𝐴𝑅,𝑖
𝐴 = 0
𝑡
𝑔( 𝑧𝑖 − 𝑧𝐴𝑅,𝑖) cos 𝜔1𝜏 𝑑𝜏
𝐵 = 0
𝑡
𝑔( 𝑧𝑖 − 𝑧𝐴𝑅,𝑖) sin 𝜔1𝜏 𝑑𝜏
𝑥 =0 1
−𝜔02 0
𝑥 +01𝑢 𝑦 = −𝜔0
2 0 𝑥
University of StuttgartInstitute for System Dynamics
Comparison of the Reconstruction Methods
Martin Glück 9
University of StuttgartInstitute for System Dynamics
𝜙turb
uFF 𝜙res𝜙cor𝜙res,d = 0 uFB
Schematic View of an Adaptive Optics with an additional DFF
Martin Glück 10
𝜙vib
-
WavefrontSensor (WFS)
Deformable Mirror (DM)
Controller(R)
Accelerometers(ACC)
AtmosphericTurbulences
(turb)
ReconstructionFilter(RF)
Vibrations(vib)
u
-
DFF
University of StuttgartInstitute for System Dynamics
Comparison of the Disturbance Compensation Methods
Martin Glück 11
Simulation Parameters Wind velocity 10 m/s
Natural frequeniesat 10 Hz and 13Hz
Sample Rate Accelerometers 1 kHz
Disturbance Feedforward Control with a Kalman Reconstructor
1 10 100
Frequency / Hz
0
-20
-60
-40
-80
0
-20
-60
-40
-80
Error - Transfer Function 𝐺𝑑 𝑠 =𝜙𝑟𝑒𝑠
𝜑𝑣𝑖𝑏
𝐺𝑑𝑠
/ d
B𝐺𝑑𝑠
/ d
B
Exposure Time 1 ms
Exposure Time 10 ms
Integral Control
Disturbance Feedforward
Observer-basedDisturbance Compensation
University of StuttgartInstitute for System Dynamics
Agenda
Martin Glück 12
1. Methods for Vibration Suppression
2. Simulation Results
3. Conclusion and Outlook
University of StuttgartInstitute for System Dynamics
Simulation Results for a bright Guide Star
Martin Glück 14
Stre
hl
0
0,1
0,2
0,3
0,4
0 10 20 30 40 50
frequency / Hz
0,5
0 10 20 30 40 50
frequency / Hz
0 10 20 30 40 50
frequency / Hz
Integral Control Observer-basedDisturbance Compensation
Disturbance Feedforward
Bright guide star 10 mag und exposure time 800 Hz
Typical atmospheric condition 0.8 arcsec
Exciting the system by varying the natural frequency 0 Hz … 50 Hz
25 mas
150 mas
50 mas
Exication Amplitude
University of StuttgartInstitute for System Dynamics
Simulation Results for a faint Guide Star
Martin Glück 15
0 10 20 30 40 50
frequency / Hz
0 10 20 30 40 50
frequency / Hz
0 10 20 30 40 50
frequency / Hz
Stre
hl
0
0,05
0,2
0
0,25
0,1
0,15
Integral ContolObserver-based
Disturbance CompensationDisturbance Feedforward
Faint guide star with 14.6 mag and exposure rate 200 Hz
Exciting the system by varying the natural frequency 0 Hz … 50 Hz
25 mas
150 mas
50 mas
Exication Amplitude
University of StuttgartInstitute for System Dynamics
Agenda
Martin Glück 16
1. Methods for Vibration Suppression
2. Simulation Results
3. Conclusion and Outlook
University of StuttgartInstitute for System Dynamics
Outlook
Martin Glück 17
Conclusion High frequency vibrations worsen the performance for
observations with faint guide stars
Improving the performance with an Accelerometer-based Disturbance Feedforward control
Outlook Considering the influence of the actuator dynamics
(M4, M5)
Testing Disturbance Feedforward at the LBTBild:ESO
Institute for System Dynamics
University of Stuttgart
Thank You! Questions ?
Disturbance Feedforward Control for Vibration Suppression in Adaptive Optics of Large Telescopes
Martin Glück, Jörg-Uwe Pott, Oliver Sawodny