multidisciplinary analysis of the nexus precursor space telescope · • for new generation of...

MIT Space Systems LaboratoryChart: 1August 23, 2002

de Weck, Miller and Mosier

Multidisciplinary Analysis of theMultidisciplinary Analysis of theNEXUS Precursor Space TelescopeNEXUS Precursor Space Telescope

Olivier L. de Weck David W. Miller Gary E. MosierOlivier L. de Weck David W. Miller Gary E. [email protected] [email protected] millerdmillerd@@mitmit.edu .edu [email protected]@gsfcgsfc..nasanasa..govgov

SPIESPIE--48484848--3939Highly Innovative Space TelescopesHighly Innovative Space Telescopes

Session 6: Detectors, Modeling and TestbedsSession 6: Detectors, Modeling and Testbeds

SPIE Astronomical Telescopes and InstrumentationSPIE Astronomical Telescopes and Instrumentation2222--28 August 2002, Waikoloa, Hawaii, USA28 August 2002, Waikoloa, Hawaii, USA



Problem SettingProblem Setting

Disturbances

Opto-Structural Plant

White Noise Input

Control

Performances

Phasing

Pointing

Appended LTI System Dynamics

(ACS, FSM)

(RWA, Cryo)

d

w

u y

z

Σ ΣActuator Noise Sensor

Noise

Jz,1=RMMS WFE

[Ad,Bd,Cd,Dd]

[Ap,Bp,Cp,Dp]

[Ac,Bc,Cc,Dc]

[Azd, Bzd, Czd, Dzd]

z=Czd qzd

“Science Target Observation Mode”

Parameters: pj Jz,2 = RSS LOS

Traditionally: Define System Parameters pj = po Predict H2 performances Jz,iIsoperformance: Find Locus of Solutions pLB < pj < pUB Constrain performances Jz,i = Jz,req



Nexus Case StudyNexus Case Study

on-orbitconfiguration

OTA

0 1 2meters

InstrumentModule

Sunshield

launchconfiguration

NexusSpacecraftConcept

Pro/E models© NASA GSFCPurpose of this case study:

Demonstrate the usefulnessof Isoperformance on a realistic

conceptual design model ofa high-performance spacecraft

The following results are shown:

• Integrated Modeling• Nexus Block Diagram• Baseline Performance Assessment• Sensitivity Analysis• Isoperformance Analysis (2)• Multiobjective Optimization• Error Budgeting

NGST Precursor Mission2.8 m diameter apertureMass: 752.5 kgCost: 105.88 M$ (FY00)Target Orbit: L2 Sun/EarthProjected Launch: 2004

DeployablePM petal

Delta IIFairing



Nexus Integrated ModelNexus Integrated Model

XY

Z

8 m2 solar panel

RWA and hexisolator (79-83)sunshield

2 fixed PMpetals

deployablePM petal (129)

SM spider

(I/O Nodes)Design Parameters

Instrument

Spacecraft bus(84)

t_sp

I_ss

Legend:

m_SMK_zpet

m_bus

K_rISO

K_yPMCassegrainTelescope:

PM (2.8 m)PM f/# 1.25SM (0.27 m)f/24 OTA

(149,169)(207)

,Ω Φ

SM (202)

Structural Model (FEM)(Nastran, IMOS)



Nexus Block DiagramNexus Block Diagram

24

3

30

30

2

2

3 3

2

2

gimbal angles

36

ControlTorques

physicaldofs

rates3

3

2

8

desaturation signal

[rad]

[m,rad]

[Nm]

[rad/sec]

[rad] [rad]

[m]

[m]

[N,Nm]

[N]

[nm][m]

[microns]

[m]

2

-K- m2mic

K

WFESensitivity

WFE

Out1

RWA Noise

In1 Out1

RMMS

LOS

Performance 2

WFE

Performance 1Demux

Outputs

x' = Ax+Buy = Cx+Du

NEXUS Plant Dynamics

MeasuredCentroid

Mux

Inputs

Out1

GS Noise

K

FSM Plant

x' = Ax+Buy = Cx+Du

FSM Controller

K FSMCoupling

Demux

Out1

Cryo Noise

K CentroidSensitivity

Centroid

Mux

Attitude

Angles

Out1

ACS Noise

x' = Ax+Buy = Cx+Du

ACS Controller

3

Number of performances: nz=2Number of design parameters: np=25

Number of states ns= 320Number of disturbance sources: nd=4



Initial Performance Assessment JInitial Performance Assessment Jzz(p(poo))

-60

-40

-20

0

20

40

60

Cen

troid

Y [µ

m]

T=5 sec

14.97 µm

1 pixel

Requirement: Jz,2=5 µm

Time [sec]5 6 7 8 9 10

-50

0

50

Cen

t x S

igna

l [ µm

]

10-1 100 101 102

10-5

100

PSD

[ µm

2 /Hz]

Frequency [Hz]

Freq DomainTime Domain

10-1 100 101 1020

10

20

Frequency [Hz]

RSS

[µm

]

Cumulative RSS for LOS

requirement

Jz,1 (RMMS WFE)Jz,2 (RSS LOS)

Lyap/Freq Time

25.61 19.5115.51 14.97

[nm][µm]

Results

Video Clip

Critical Mode23.1 Hz

Centroid Jitter on Focal Plane [RSS LOS]

-60 -40 -20 0 20 40 60Centroid X [µm]



Nexus Sensitivity AnalysisNexus Sensitivity Analysis

Graphical Representation ofJacobian evaluated at designpo, normalized for comparison.

-0.5 0 0.5 1 1.5Kcf Kc fca

Mgs QE Ro

lambda zeta I_proptI_ss t_sp

K_zpet m_bus K_rISO K_yPM m_SM

Tgs Sst Srg Tst Qc fc

Ud Us Ru

Norm Sensitivities: RMMS WFE

Des

ign

Para

met

ers

o z,1,o∂

z,1∂p /J * J / p

analytical finite difference

-0.5 0 0.5 1 1.5Kcf Kc fca

Mgs QE Ro

lambda zeta

I_proptI_ss t_sp

K_zpet m_bus K_rISO K_yPM m_SM

Tgs Sst Srg Tst Qc fc

Ud Us Ru

Norm Sensitivities: RSS LOS

∂ ∂po /Jz,2,o * Jz,2 / p

dist

urba

nce

para

met

ers

plan

tpa

ram

eter

sco

ntro

lpa

ram

sop

tics

para

ms

,1 ,2

,,1 ,2

z z

u uo

zz o

z z

cf cf

J JR R

pJJ

J JK K

∂ ∂ ∂ ∂ ∇ = ∂ ∂ ∂ ∂

L L

RMMS WFE most sensitive to:Ru - upper op wheel speed [RPM]Sst - star track noise 1σ [asec]K_rISO - isolator joint stiffness [Nm/rad]K_zpet - deploy petal stiffness [N/m]

RSS LOS most sensitive to:Ud - dynamic wheel imbalance [gcm2]K_rISO - isolator joint stiffness [Nm/rad]zeta - proportional damping ratio [-]Mgs - guide star magnitude [mag]Kcf - FSM controller gain [-]



2D2D--Isoperformance AnalysisIsoperformance Analysis

Ud=mrd [gcm2]

CADModel

K_rISO[Nm/rad]

isolatorstrut

ω

r

mmd

joint

0 10 20 30 40 50 60 70 80 90

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Ud dynamic wheel imbalance [gcm2]

K_rIS

O R

WA

isol

ator

join

t stif

fnes

s [

Nm

/rad]

Isoperformance contour for RSS LOS : Jz,req = 5 µm

10

20

20

20

60

60

60

120

120

160

po

Parameter Bounding Box

testspec

HST

Initialdesign

5

5

E-wheel



Nexus Multivariable IsoperformanceNexus Multivariable Isoperformance nnpp=10=10

Design A

Design B

Design C

3850 [RPM]

K

5000 [Nm/rad]

Ru

Us 2.7 [gcm]

Ud 90 [gcm2]

Qc 0.025 [-]

Tgs 0.4 [sec]

rISO

Kzpet 18E+08 [N/m]

tsp 0.005 [m]

Mgs 20 [mag]

Kcf 1E+06 [-]

10

10-5

100

PSD

[ µm

2 /Hz]

100

2

4

6

RM

S [ µ

m]

Cum

Best “mid-range”compromise

Smallest FSMcontrol gain

Smallest performanceuncertainty

Pareto-Optimal Designs p*iso

Performance Cost and Risk Objectives

0 102

Frequency [Hz]

0 102

Frequency [Hz]

ulative RSS for LOS

Jz,1 Jz,2 Jc,1 Jc,2 Jr,1Design A 20.0000 5.2013 0.6324 0.4668 +/- 14.3218 % Design B 20.0012 5.0253 0.8960 0.0017 +/- 8.7883 %Design C 20.0001 4.8559 1.5627 1.0000 +/- 5.3067 %

A: min(Jc1)B: min(Jc2)C: min(Jr1)



Nexus Error BudgetingNexus Error Budgeting

Error SourceContributions

Allo

cate

d Bu

dget

LOS BudgetCapability

**Ψ

2, , ,

1

dn

i i j z req ij

J=

Ψ = Ψ =∑

Error Source VAR % Allocation VAR% CapabilityRWA 50.00 3.535534 0.01 0.4988912Cryocooler 25.00 2.500000 0.00 0.2439626Attitude Noise 5.00 1.118034 0.00 7.564E-06GStar Noise 20.00 2.236068 0.99 5.1715676Total 100 5.000000 5.2013

0.20.4

0.60.8

0.20.4

0.60.8

0.2

0.4

RWA Cryo

FGS

A

Budget

B

C

LTI System , Jz,req, p_bounds, p_nom (Design A)

Isoperformance Toolbox

piso

Capability Budget

0.8

Note: ACSsensor noisecontributionsnot shown

var_contr 0.6

Plot Error Contribution Sphere

00



Nexus Nexus Initial pInitial poo vs. Final Design p**vs. Final Design p**isoiso

+X+Z

+Ysecondaryhub

SM

Deployablesegment

SM Spider SupporttspSpider wall

thickness

Dsp

Kzpet

Initial FinalRu 3000 3845 [RPM]Us 1.8 1.45 [gcm]Ud 60 47.2 [gcm2]Qc 0.005 0.014 [-]Tgs 0.040 0.196 [sec]KrISO 3000 2546 [Nm/rad]Kzpet 0.9E+8 8.9E+8 [N/m]tsp 0.003 0.003 [m]Mgs 15 18.6 [Mag]Kcf 2E+3 4.7E+5 [-]

-50 0 50-50-40-30-20-100

1020304050

Cen

troid

Y

Centroid Jitter on Focal Plane[RSS LOS]

T=5 sec

Initial: 14.97 µm

Final: 5.155 µm

Parameters

Improvements are achieved by a well balanced mix of changes in thedisturbance parameters, structural

redesign and increase in control gainof the FSM fine pointing loop. Centroid X



Paper ConclusionsPaper Conclusions

• For new generation of lightweight, deployable telescopes such asNGST and NEXUS the disciplines of structures, optics and controls are coupled and must be considered together during early design stages

• Performance predictions can be made for “engineering” metrics such as WFE, LOS jitter etc that flow down from science requirements. These predictions are based on integrated models, but are uncertain and depend on many assumptions.

• Nevertheless one can gain valuable insights from sensitivity analysis to identify key driving system parameters.

• Isoperformance seeks not the best achievable performance, but acceptable performance, while balancing the burden among subsystems.

• Error budgeting and Integrated Modeling can be linked.

multidisciplinary analysis of the nexus precursor space telescope · • for new generation of...

Documents