George Angeli 11 September, 2001

Current Concepts and Statusof GSMT Control Systems

Introduction

Feasibility of GSMT depends on its controllability

Segment alignment maintenance

Wind effect compensation (structure correction)

Whatever is designed, it must be observable and CONTROLLABLE!

How does the boot get on the dinner table?

Why do we care about the control system in this early phase of design?

Frequency Band Separation of Subsystems

0.001 0.01 0.1 1 10100 Bandwidth [Hz]

Ze

rnik

e m

od

e s

~100

~50

~20

~10

2

aO (M1)

AO (M2)

Main Axes

LGS MCAO

Secondary rigid body

temporal avg

spatial & temporal avg

spatial & temporal avg

spatial & temporal avg

spatial avg

spatial avg

MCAO

MCAO can be separated from telescope control First MCAO sensor is behind the last

telescope control actuator in the light path

MCAO is fed with a wavefront corrected up to 30-50 Zernike @ 20 Hz BW on tracking guide star

Active Optics

Initial phasing in open loop

Low spatial frequencies barely observable by edge sensors

Phasing maintenance in closed loop with edge sensors

Assumption: wind buffeting has negligible high spatial frequency effects on primary mirror

Continuity maintenance system is static (no interference with structural resonances)

Phasing Maintenance

Static influence function

actuatoredge

actuatoredge

BACG

Guy1

Edge detector / actuator modes by SVD

actuatoractuator

edgeedge

actuatoredge

uVu

yUy

uGy

VUGG

~

~

~~

T

Control Configuration for Phasing Maintenance

TUVGG

From phasing

Edge sensors

GK(s)

<1 Hz

n(s)

r(s) y(s)u(s)R=G†

d(s)

estimator controller

Actuator space

Pseudo-inverse:

Adaptive Optics Adaptive (deformable) secondary

Atmospheric correction

r0 0.5 m @ 1.2 ~7000 actuators for 30 m

MMT 1200 actuator/m2 on secondary@ 0.6 m

GSMT 2200 actuator/m2 on secondary@ 2 m

Telescope deformation correction

max. 1800 actuators for 600 segments

570 actuators/m2 on secondary

In the close future atmospheric correction is not feasible in the NIR (maybe in midIR)

Deformable Secondary

Face-sheet mass is negligible

No interaction with telescope structure

Face-sheet motion is over-damped No local dynamics

Secondary AO system is static

Wavefront correction with deformable secondary

Temporal average (0.1 Hz) off-loaded on primary

Frequency Band Separation of Wavefront Correction and Tracking

2

3

20

50

0.1 10 1001

Bandwidth [Hz]

Zer

nik

e m

odes

0.01

AO (M2)

Secondaryrigid body

Main Axes

temp.avg.

temp.avg.

temp.avg.

temp.avg.

aO (M1)

Control Configuration for Wavefront Correction and Tracking

Measurement noise Wind, Gravity, Heat Atmosphere

Offset due to:• telescope aberration• off-axis guide star

A

C

D1B1

B2

d(s) a(s)n(s)

r(s) y(s)xu(s)

G(s)

Ksec(s)<10 Hz

{Z1... Z2}

{Z1... Z3}

{Z1... Z50}

Kmain(s)<0.5 Hz

KAO(s)<20 Hz

D2

KaO(s)<0.1 Hz

D3

{Z3... Z50}

Physical Configuration

Segmented PrimaryMirror

Actuators

EdgeSensors

ActiveOptics

AdaptiveOptics

SecondaryControl

Main Axes

TelescopeStructure

Secondary Mirror

DeformableFacesheet

MainAxes

WFS

WindGravityHeat

Atmosphere

1 Hz .1 Hz 20 Hz 10 Hz .5 Hz

Z3... Z50 Z1... Z50Z1... Z3 Z1... Z2

Computational Load Static active optics

Deformable secondary

1 Hz bandwidth 10 Hz sampling rate Reconstructor matrix [1800 x 3600]

2 sensors on each edge 230 GFLOP/s

20 Hz bandwidth 200 Hz sampling rate Reconstructor matrix [1800 x 1000] 360 GFLOP/s

Texas TMS320C64x 4.8 GFLOP/s

Intel P4 1.4GHz 5.6 GFLOP/s

System Modeling and Simulation

Investigate telescope behavior

Validate design assumptions

Observability (sensor choices, placement) Controllability (actuator choices,

placement)

Allows modal-based feedback design (Linear Quadratic Gaussian, H, etc.)

Performance

Validate model reduction for simulation and control

Current Model Modal based state space representation of

the structure, based on FEA (20 modes)

Primary mirror as a surface fit on raft support nodes

Line-of-sight equation for rigid body motion of primary and secondary

Force actuators at weakened or completely opened degrees of freedom

Zernike representation of wavefront quality

Integrated structure FEA

Redefined base for OPD as a linear combination of Zernikes linked to structural modes

Primary Mirror Truss Structure

Structural Mode Shapes on the Primary Mirror

Zernike Content of the Structural Modes

0 1 2 3 4 5 6 7 8 9-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1Z

ern

ike

coef

fici

ents

[ar

bit

rary

un

it]

Zernike modes

#1 2.169Hz#2 2.248Hz#3 2.754Hz#4 3.207Hz#5 3.259Hz#6 3.908Hz#7 4.376Hz#8 4.559Hz#9 4.777Hz#10 4.783Hz

Zernike Content of the Structural Modes

0 1 2 3 4 5 6 7 8 9-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

Zernike modes

Zer

nik

e co

effi

cien

ts [

arb

itra

ry u

nit

]

#11 4.792Hz#12 5.396Hz#13 5.404Hz#14 5.952Hz#15 6.000Hz#16 6.091Hz#17 6.208Hz#18 6.274Hz#19 6.553Hz#20 7.635Hz

Zernike Content of Secondary Rigid Body Motion

0 2 4 6 8-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Zernike modes

Zer

nik

e co

effi

cien

ts [

arb

itra

ry u

nit

]

TxTyTzRxRy

Wind Load (X Direction)Bode Magnitude Diagram

Frequency (Hz)

Mag

nit

ud

e (d

B)

100

101

102

-350

-300

-250

-200

-150

-100From: Wind (x)

piston (0)

y tilt (2)

y astig (5) x coma (6)

x tilt (1)

x astig (4)

y coma (7)

focus (3)

spherical (8)

Wind Load (Y Direction)Bode Magnitude Diagram

Frequency (Hz)

Mag

nit

ud

e (d

B)

100

101

102

-350

-300

-250

-200

-150

-100From: Wind (y)

y tilt (2)

piston (0)

x astig (4) y coma (7) focus (3)

spherical (8)

y astig (5)

x tilt (1) x coma (6)

Wind Load (Z Direction)Bode Magnitude Diagram

Frequency (Hz)

Mag

nit

ud

e (d

B)

100

101

102

-350

-300

-250

-200

-150

-100From: Wind (z)

piston (0)

x tilt (1)

y tilt (2)

focus (3)

x astig (4)

y astig (5)

x coma (6)

y coma (7)

spherical (8)

Future Path

Wavefront control (wind buffeting)

Segmented primary model (edge detectors, detector and actuator mode spaces)

Verification of ‘static phasing maintenance’ hypothesis

Primary control

Feedback design and simulation

Deformable secondary ‘surface fit’ model Primary ‘surface fit’ model on actuator nodes Wind load definition (on structure and primary) Feedback design and simulation

Future Path (cont’d)

Tracking Actuator definition Nonlinear (large signal) and linearized (small signal)

models Gravitational load definition Feedback design and simulation

Integration Structural model integration Optical model integration Feedback integration and simulation

Modeling Issues Structural model

Integrated structure versus interfaced subsystems Boundary value problems

Optical model Refined ‘fitted surface’ model with ray tracing and

fitting each structural modes, i.e. building a new orthogonal basis for OPD which is characteristic to the telescope

Segmented mirror optical response

Load model Wind power spectral density and spatial distribution Wind-to-force conversion