# Presentation: 116791

## 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

## NGST “Yardstick” Concept

## Observatory FEM

**Observatory FEM**

**Model contains ~5400 DOF**

## IMOS Environment

**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)**

## System Error Budget Overview

**System Error Budget Overview**

**Post-WFS&C**
**optical aberrations**

**OTA figure**
**& alignment**

**IM figure**
**& alignment**

**OTA actuator**
**performance**

**Imaging**
**performance**

**OTA structure**

**OTA optics**

**IM structure**

**IM optics**

**OTA mechanical**

- Encircled Energy

- WF error

**WFS&C**

*WF C  subsystem*
*WFE  budget *

*System*
*EE , SR budget *

*Non-WF C  subsystem s *
*WFE  budget s*

## 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**

## Linear  Error Model for Thermal Analysis

**Linear optical model**
**w****0**** = C****x**** x + C****u**** u****0**
**WF sensing**
**w****est**** = w****0**** + ****dw****est**
**Control**
**u****1**** = -G w****est**** + ****du**
**G = C****u****+**** = [C****u****T****C****u****] ****-1 ****C****u**

- w

- xrb

- xfig

- udm

- useg

- Alignment and figure states

- Wavefront sampled at
- N discrete points in the
- exit pupil

- Optical controls

## MACOS Ray Trace Model

## MACOS Spot Diagram

## Wavefront Error – Design Residual

## Wavefront Error – Segment Tilt

## Wavefront Error – FEM Node Translation

## OTA FEM

**OTA FEM**

** ****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 ring instead of CELAS**
** ****Three OTA to S/C I/F points instead of four**

**The petal reaction structure is a beryllium frame-work of I-beams**
** ****The center segment reaction structure is a flat 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.**

** ****recover 1044 DOFs (344 nodes on PM, translation only, plus SM and SI)**

## Observatory Thermal Model – Steady State

## Steady State Temps Mapped on OTA FEM

**Mapping made possible by one-to-one nodalization !!!**

## Computing the Transformation from Nodal Temperatures to Displacements

**Net Force Balance: {r****net****} = 0 =  -Ku  + {r****Temp****} **
**Where         {r****Temp****} =  ******** B****T**** 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 **
**{r****Temp****} =      {r****g****} =  [A****gg****] {t****g****} **
**Where     {t****g****} =  nodal temperature (and/or gradient) vector (g-size)**
-       {rg} = nodal force (and/or moment) vector (g-size)
**Reduce [A****gg****] to f-set size and transform to Local (NASTRAN global) system**
**[A****fg****] = [T****fg****]  [A****gg****]**
**Premultipy by the flexibility matrix [K****ff****]****-1**** to get the temperature to displacement transformation matrix G**
**[G****fg****] = [K****ff****]****-1****  [A****fg****]**
**Expand to g-set, and transform back to the basic coordinate system**
**[G****gg****] = [T****fg****]****T****  [G****fg****]     or**** **
**[G****gg****] = [T****fg****]****T****  [K****ff****]****-1****  [T****fg****]  [A****gg****]**
**So we have the temperature to displacement transformation matrix**
**{u****g****} = [G****gg****]  {t****g****} **

## Steady State Wavefront Error with Control

## Thermal Transient following 22.5 degree slew

**Cold Petal**
**(space-side)**

**Hot Petal**
**(sun-side)**

******T = -0.8 K**

******T = -1.3 K**

** ****Initial attitude has sun normal to sunshield**
** ****Final attitude is 22.5 degree pitch away from sun**
** ****Thermal equilibrium takes **_**DAYS**_** to reach**

## Thermal Transient Wavefront Error – no Control

## Thermal Transient Wavefront Error with Control

## Jitter Analysis

** ****Pointing Control Architecture**
** ****Linear Systems Model**
** ****Disturbance Model**
** ****Compensation Model**
** ****Results for parametric studies**

## The CSI Challenge for NGST

** ****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**

## System Level Block Diagram

## State-Space Model

## Dynamics Model Sensor & Actuator Locations

## Optomechanical Analysis

## Reaction Wheels are Dominant Disturbances

## Wheel Disturbances - Discrete Speed vs Swept Speed

## Reaction Wheel Isolation

## FSM Response Functions

## Linear Analysis - Nominal Response, Effect of Isolation, Effect of Wheel Imbalance Amplitude

## How Much Isolation Is Required?

## 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****TM**** is a matrix-oriented language/tool, with integrated graphics and visualization**
** ****Questions remain about the ability to handle realistically-sized models within Matlab****TM (eigenvalues, matrix inversion)**
** ****None of these models have been validated, of course...**