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Performance Analysis of the NGST “Yardstick”
Concept via Integrated Modeling
Gary Mosier, Keith Parrish, Michael Femiano
NASA Goddard Space Flight Center
David Redding, Andrew Kissil, Miltiadis Papalexandris
Jet Propulsion Laboratory
Larry Craig, Tim Page, Richard Shunk
NASA Marshall Space Flight Center
August 2000
1
NGST “Yardstick” Concept
Large (200m2) deployable
sunshield protects from sun,
earth and moon
Deployable
Space support module
secondary
(attitude control,
mirror
communications, power,
data handling) is on warm
side
“Open” telescope (no
external baffling)
allows passive Science
cooling to 50K Instruments
Beryllium Isolation truss
primary mirror
2
Observatory FEM
Model
contains
~5400 DOF OTA
Integrated Science
Instrument Module
isolation truss
sunshield short booms
X
Y
spacecraft module
Z
sunshield long booms
3
IMOS Environment
DESIGN Structure Control Optics
PARAMETERS Design Design Design
ENVIRONMENT MODELING IMOS FEM
TOOLS NASTRAN MATLAB MACOS
THERMAL TRASYS /
DISTURBANCES SINDA
STRUCTURE OPTICS
MECHANICAL
DISTURBANCES MATLAB
SYSTEM MODEL
OPTICAL CONTROLS
ERRORS SYSTEM PERFORMANCE
SCIENCE
METRICS
Integrated model was applied to investigate three “focus”
problems during concept development phase:
• thermal-elastic deformation of OTA
• line-of-sight stability (jitter)
• wavefront sensing and control (not really addressed here)
4
System Error Budget Overview
System imaging performance System
Encircled Energy EE , SR budget
Stray Jitter WFS&C Wide-angle Detection
light scatter effects
Post-WFS&C WF C subsystem
WF error optical aberrations WFE budget
OTA actuator OTA figure IM figure Imaging
performance & alignment & alignment performance
OTA mechanical OTA structure OTA optics IM structure IM optics
Non-WF C subsystem s
WFE budget s
5
Thermal-Elastic Analysis
• Linear Systems Model
• Optics Model
• Thermal Model
• OTA FEM
• Results for launch-to-orbit cooldown
• Results for transient (attitude re-orientation)
• Results for transient with active thermal control
6
Linear Error Model for Thermal Analysis
xrb xsegrot Alignment and figure states
xsegtrans
useg x= xIMrot
xIMtrans
w
xfig
udm
xfig w1 Wavefront sampled at
N discrete points in the
w2 exit pupil
w=
wN
Linear optical model
w 0 = C x x + C u u0 Optical controls usegrot
WF sensing usegtrans
u= uSM
west = w0 + dwest
udm
Control
u1 = -G west + du
G = Cu+ = [CuTCu] -1 Cu
7
MACOS Ray Trace Model
8
MACOS Spot Diagram
9
Wavefront Error – Design Residual
10
Wavefront Error – Segment Tilt
11
Wavefront Error – FEM Node Translation
12
OTA FEM
• recover 1044 DOFs (344
nodes on PM, translation
only, plus SM and SI)
• 2.00mm thick face sheet by
4cm deep core orthogrid
beryllium mirror shell
•cells are 14.5 cm on a side
equilateral triangles,cell wall
are 1.00 mm thick
• RBE2s used to attach SI
kinematically to center main
•The petal reaction structure is a beryllium frame- ring instead of CELAS
work of I-beams
• Three OTA to S/C I/F
• The center segment reaction structure is a flat points instead of four
Beryllium frame with a 1.3M dia inner ring. The
frame is composed of a 152 mm deep I-beam
inner ring and 152mm by 100mm wide box
section outer ring and spokes.
13
Observatory Thermal Model – Steady State
14
Steady State Temps Mapped on OTA FEM
Mapping made possible by one-to-one nodalization !!!
15
Computing the Transformation from
Nodal Temperatures to Displacements
Net Force Balance: {rnet} = 0 = -Ku + {rTemp}
Where {rTemp} = BT E {0} dV = Ku
B = standard strain-displacement matrix
{0}= temperature induced strain vector, f (,temp)
We can factor out nodal temperatures, generating a temp to load transformation matrix
– {rTemp} = {rg} = [Agg] {tg}
Where {tg} = nodal temperature (and/or gradient) vector (g-size)
{rg} = nodal force (and/or moment) vector (g-size)
Reduce [Agg] to f-set size and transform to Local (NASTRAN global) system
– [Afg] = [Tfg] [Agg]
Premultipy by the flexibility matrix [Kff]-1 to get the temperature to displacement
transformation matrix G
– [Gfg] = [Kff]-1 [Afg]
Expand to g-set, and transform back to the basic coordinate system
– [Ggg] = [Tfg]T [Gfg] or
– [Ggg] = [Tfg]T [Kff]-1 [Tfg] [Agg]
So we have the temperature to displacement transformation matrix
– {ug} = [Ggg] {tg}
16
Steady State Wavefront Error with Control
On-Orbit Thermal After Segment Control After DM Control Limited DM Control
20 20 20 20
Wavefront
40 40 40 40
60 60 60 60
80 80 80 80
100 100 100 100
20 40 60 80 100 20 40 60 80 100 20 40 60 80 100 20 40 60 80 100
WFE=4.6271e-05 WFE=2.3886e-07 WFE=2.4702e-08 WFE=7.7059e-08
20 20 20 20
40 40 40 40
Image
60 60 60 60
80 80 80 80
100 100 100 100
120 120 120 120
20 40 60 80 100 120 20 40 60 80 100 120 20 40 60 80 100 120 20 40 60 80 100 120
Strehl=0.0061111 Strehl=0.60555 Strehl=1.0117 Strehl=0.96472
17
Thermal Transient following 22.5 degree slew
30.3
• Initial attitude has sun
30.2
Cold Petal
normal to sunshield 30.1
(space-side)
• Final attitude is 22.5 30.0
DT = -0.8 K
degree pitch away from sun
Temperature (K)
• Thermal equilibrium takes 29.9
DAYS to reach 29.8
29.7
29.6
50.2
29.5
0 20 40 60 80 100 120 140 160
50.0
Duration (hrs)
49.8
Hot Petal
(sun-side)
Temperature (K)
49.6
49.4
DT = -1.3 K
49.2
49.0
48.8
0 10 20 30 40 50 60 70 80
Duration (hrs)
18
Thermal Transient Wavefront Error – no Control
-7
x 10 Wavefront Error vs. Time
4
WFE RMS (m)
3
2
1
0
0 5 10 15 20 25 30
StrehlTime (hr) Time
Ratio vs.
1
0.9
Strehl
0.8
0.7
0 5 10 15 20 25 30
Time (hr)
19
Thermal Transient Wavefront Error with Control
20
Jitter Analysis
• Pointing Control Architecture
• Linear Systems Model
• Disturbance Model
• Compensation Model
• Results for parametric studies
21
The CSI Challenge for NGST
frequency
sunshield isolation truss and higher order
modes SM support modes modes
Structure
ACS 0.025 Hz BW
FSM 2 Hz BW
Disturbances >400 Hz
• Lightweight, flexible structure with very low damping limits ACS
bandwidth
• FSM bandwidth limited due to guiding sensor noise
• Thermal environment presents challenges to “smart structures”
solutions for active damping and vibration suppression
22
System Level Block Diagram
External 3
Torque 3 72 74
Wavefront
72 74
6 2
Dynamics
Optics
Centroid
Vibration Isolation ACS uses wheels,
has not been gyros & trackers 2
designed in detail;
model is a LP filter
approximation
LOS Control
72
6 6 4
Image
3
Stabilization
loop uses
NIR & FSM
Vibration ACS ACS
Isolation Commands
23
State-Space Model
W
K11
X AX BU
C
Y CX
X 1 A1 X 1 B1U 1
Y1 C1 X 1
K 21
U1 Y1
K12 GS
Y4
K 22
X 4 A4 X 4 B4U 4
K4
Y4 C 4 X 4
K 3 Y2
X 2 A2 X 2 B2U 2 U2
W TW
U4
Y2 C 2 X 2
W C CT C
Y3
X 3 A3 X 3 B3U 3 U3 KF N rays
Y3 C 3 X 3
RW
A1 B1C 4 X1
0 0
X GS
B K C 0 W
A 2 21 1
A2 B2 K 22 C 2 0 X 2 U KF
Y
B3 K 4 C1 0 X3 C
0 A3
RW
X 4
0 0 B4 C3 A4
0 0 K C K12 C 2 0 0
0 C 11 1
B 0 0 K 21C1 K 22 C 2 0 0
B 2
0 B3 0
0 0 B4
24
Dynamics Model Sensor & Actuator Locations
Model size is
~ 5400 DOF;
only 71 DOF
are required
for jitter model
PM (900-908)
These grid points are located
at the center of the primary and
in a circle with radius 2.8 meters,
connected to mirror grid points
by RBE2 elements
ACS (10291)
ST, IRU, RWA
are co-located
ISIM (825)
FSM, DM, other
optics are co-located
SM (829)
25
Optomechanical Analysis
Structural dynamics
(mode shapes) and
Deformed FEM the associated
optical distortions
are displayed as
animations for
qualitative analysis
Image (log stretch) Wavefront Error
26
Reaction Wheels are Dominant Disturbances
Static Imbalance Dynamic Imbalance
X F
Us = mr Ud = mrd X
F = U s 2 T = U d 2
m
Z Z
Y r r
Y
m m
d
F F
27
Wheel Disturbances - Discrete Speed vs Swept Speed
6000
1
4000
Speed, RPM
0.5
Force, N
2000
0
0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
-0.5 Time, sec
20
-1
0 1 2 3 4 5 6 7 8 9 10 10
Force, N
sec
0
0.03
-10
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Force PSD, N2/Hz
-3 Time, sec
0.02 x 10
4
Force PSD, N2/Hz
0.01
2
0
0 50 100 150 200 250 0
0 100 200 300 400 500 600 700 800 900 1000
Freq, Hz
Freq, Hz
28
Reaction Wheel Isolation
Magnitude Response
50
0
-50 1 Hz Hybrid Device
dB
10 Hz Passive Device
-100
-150
-200
-2 -1 0 1 2
10 10 10 10 10
Hz
29
FSM Response Functions
10
0
-10
Acts as a low-pass
-20 filter to guide star noise
dB
-30
-40
-50 Acts as a high-pass
filter to base-motion
-60
-4 -2 0 2 4
10 10 10 10 10
Hz
30
Linear Analysis - Nominal Response, Effect of Isolation,
Effect of Wheel Imbalance Amplitude
LOS Pointing Error vs. Wheel Speed
4
10
Nominal
1/10th scale wheels
1 Hz isolation
2 3s requirement
10 3s GS noise floor
Pointing Error (mas)
0
10
-2
10
-4
10
-6
10
-1 0 1 2
10 10 10 10
Wheel Speed (Hz)
31
How Much Isolation Is Required?
3
LOS Pointing Error vs. Isolation Corner Frequency
10
2
10
3- requirement
1
10
RMS Pointing Error (mas)
GS noise floor
0
10 O - linear analysis
-1
X - simulation
10
-2
10
-3
nominal FEM, 0.001 damping,
10 nominal wheel disturbances
-4
10
-2 -1 0 1 2
10 10 10 10 10
Isolation Corner Frequency (Hz)
32
Conclusions
• Development of end-to-end models using the IMOS
environment was relatively painless, owing to the
following factors:
• translation from NASTRAN and SINDA was
possible for FEM and TMM, as was output to
FEMAP neutral format
• geometric and material properties were easily
parameterized, as were all other significant entities
in the models
• ray-trace code (MACOS) was open-source, so it
could be integrated via Mex-function API
• Matlab™ is a matrix-oriented language/tool, with
integrated graphics and visualization
• Questions remain about the ability to handle
realistically-sized models within Matlab™ (eigenvalues,
matrix inversion)
• None of these models have been validated, of
course…
33
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