disturbance feedforward control for vibration … of stuttgart institutefor system dynamics...

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


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


Agenda

Martin Glück 4

1. Methods for Vibration Suppression

2. Simulation Results

3. Conclusion and Outlook


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

-


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-


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


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


Comparison of the Reconstruction Methods

Martin Glück 9


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


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


Agenda

Martin Glück 12





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


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


Agenda

Martin Glück 16





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

disturbance feedforward control for vibration … of stuttgart institutefor system dynamics...

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