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R-1267

FINAL TECHNICAL REPORT ILS3 SIMULATION OVERVIEW AND

PREL .VIINARY USERS GUIDE

by

S. Serben F. Satlow

June 1979

Sponsored oy

Advanced Research Projects Agency

ARPA Order No. 3223

The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily repre- senting the official policies, either expressed or implied, of the Advanced Research Projects Agency of the U.S. Government.

The Charles Stark Draper Laboratory, Inc. Cambridge, Massachusetts 02139

Distribution limited to U.S. Government agencies only. Test and Evaluation (June 1979). Other requests for this document must j\v

be referred to SAMSO/YAD. . f' *' VOX ^1.*? 6 0/ ^or« n

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REPORT DOCUMENTATION PAGE 2. GOVT ACCESSION NO.

J,simulation _gyerview T'felimi - inary CTsers Guide t

c

READ INSTRUCTIONS BEFORE COMPLETING FORM

V* TYBi »I RE

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HWM&ORfl. REPORT NUMBER

R-1267 '^/^ MWIWLI mi'CHHIII UUIIIULIIIIIV

»r «afORMÄO-OROANIZATlOW l*AME AND ADDRESS ' 7 ^

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{U7^1-760)k78a

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11. CONTROLLING OFFICE MAME AND ADDRESS

Advanced Research Projects Agency Arlington, Virginia 22209 m

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17. DISTRIBUTION STATEMENT tot the abstract entered in Block 20, if different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

aberrations modes actuators state-vector deformations sensors data base nodes

disturbance truncation FFT PSF

-V 20. ABSTRACT (Continue on reverse side if necessary and identify by block number)

A system software architecture and accompanying algorithms are developed to aid in the analysis of large flexiDie satellites and their sensors, System features and constraints as well as data base definition are included. A sample problem to il- lustrate the use of the system for a simplified model of a typical large space structure is presented.^^

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R-1267

FINAL TECHNICAL REPORT

ILS3 SIMULATION Overview and

Preliminary Users Guide

Approved ,£L D.G. Head

Hoag^l A »Advanced Sysj

uduJtt. ems Department

ARPA Order No.-3223 Program Code NO.-7E20 Name of Contractor-The Charles Stark Draper Laboratory,Inc Contract No.-F0470 1-76-C-O178 Date of Contract-22 October 1976 » Contract Expiration Date-31 December 1978 Principal Investigator-Dr.Keto Soosaar(6 1 7 ) 258-2575 Short Title of Work-LAS Evaluation

The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the Advanced Research Projects Agency of the U . S.Government.

80 1 14 022

/

ACKNOWLEDGMENT

The uorV. -eported herein was performed by the Charles Stark Draper laboratory, Inc. (CSDL). This research was supported by the advanced Research Projects Agency of the Department of Defense, and was monitored by Deputy for Advanced Space Programs, Space and Missile Systems Organisation, under Contract No. F0470 1-76-C-0178. This report covers the time period from January, 1978 to December 31, 1978 The various technical advisors of the program at DARPA have been Lt. Col. W. Cuneo, Dr. A. Pike, Dr. J. Jenney; and Capt. T. Ernst of SAMSO.

The simulation was developed within the Large Space Structures Division of the CSDL Advanced Systems Department headed by Mr. David Hoag. Dr. Keto Soosaar, Division Leader of the Large Space Structures Division, was the Program Manager. Mr. Saul Serben has been responsible for the architecture and software development.

Key organisers to the simulation Mahajan in optics and the late dynamics and control. Other followingi

formulation were Dr. V. Dr. J. Canavin in the contributors were the

Ms.

Mr.

Mr, Mr. Mr Dr

F. J T L

Satlou

Anagnostis

Ayer Govignon Henderson Matson

Software architecture. Code Generation Structure, ßuasi-Static, Steady State ßuasi-Static Optics Structure, Control, Plotting System Consultant

The authors uould also like to thank Dr. M. Balas, control analyst, Mr. R. Grin, structure analyst, Mr. R. Therrien, project administrator. Dr. R. Wilkinson, attitude control analyst, and Dr. W. Koenigsberg, Fast Fourier Transform consultant

We also gratefully acknowledge the assistance following students: R. Bickford and C. Hogan.

of the

Publication of this report does not constitute approval by ARPA or the U.S Air Force, of the findings and conclusions contained herein. It is published for the exchange and stimulation of ideas.

ii

/ .'.: ~

TABLE OF CONTENTS Section 1. Introduction 2. System Overview... 3. Source Code Editor

Page ... 1 . . .2

6 3.1 Purpose Q

3.2 Input Definitions For Each Subsystem 6 3.2.1 DYNAMICS 6 3.2.2 STEADY STATE .6 3.2.3 ßUASI-STATIC .9 3.2.4 INTERFACE 10 3.2.5 OPTICS ! ! . . 1 1

DYNAMICS ]3 4.1 Purpose .13 4.2 Technical Summary 13

4.2.1 Plant Equations of Motion 15 4.2.2 Structure Control System 17 4.2.3 Attitude Control is Features And Constraints 18 Subsystem Architecture 19 Subroutine Nesting Hierarchy 23

4 4 4 4 4 4 4 . U ,

3 4 5 6 7 8 9 10

Summaries 21 Subroutine User Input Specifications 27 External Stored Data Bases 32 Internal Stored Data Bases 34 Glossary 35

bTEADY STATE . . . 29

5 5 5 5

1 2 3 4 5 6 7 8 9 10

5.1 Purpose .39 5.2 Technical Summary 39 5.3 Features And Constraints 40

Subsystem Architecture 40 Subroutine Nesting Hierarchy 43 Subroutine Summaries 43 User Input Specifications 43 External Stored Data Bases 46 Internal Stored Data Bases 48 Glossary 49

ßUASI-STATIC .......... .5} 6.1 Purpose .51 6.2 Technical Summary 6.3 Features And Constraints 6.4 Subsystem Architecture 6.5 Subroutine Nesting Hierarchy 6.6 Subroutine Summaries 6.7 User Input Specifications... 6.8 External Stored Data Bases.. 6.9 Internal Stored Data Bases.. 6.10 Glossary

111

■

■

TABLE OF CONTENTS - CONT'D Jection Page 7. INTERFACE .TTJI

7 . 1 Purpose .... .62 7.2 Technical Summary .,...$%

7.2.1 Dynamic 62 7.2.2 fiuasi-Static 62 7.2.3 Net Wave Aberrations 63

7.3 Features And Constraints 63 7.4 Subsystem Architecture ..!..64 7.5 Subroutine Nesting Hierarchy 67 7 . 6 Subroutine Summaries 68 7.7 User Input Specifications 69 7.8 External Stored Data Bases ..!.... 70 7.9 Internal Stored Data Bases 72 7.10 Plotting Outputs ..1 ^ 7.11 Glossary 76

8. OPTICS 80 8. 1 Purpose \ z§ 8.2 Technical Summary ^80 8.3 Features And Constraints 82 8.4 Subsystem Architecture .M 8.5 Subroutine Nesting Hierarchy .85 8 . 6 Subroutine Summaries 36 8 . 7 User Input Specifications ! ! ! . ! 87 8.8 Internal Stored Data Bases 89 8 . 9 Plotting Outputs .......!..... 90 8.10 Glossary ! " 91

9. Sample Test Case 93 9.1 Model Description ...93

IV.

. ■ :. . -:!h.... ■ ■ ... .■ .

LIST OF ILLUSTRATIONS

Figure Page 2 . 1 Simulation architecture flow 3 2.2 Simulation data flow .4 4. 1 DYNAMIC technical overview It 4.2 DYNAMIC subsystem architecture 21 5.1 STEADY STATE subsystem architecture 41 6. 1 eUASI-STATIC subsystem architecture 53 7.1 INTERFACE susbsystem architecture 65 8. 1 OPTICS subsystem architecture 83 9.1 Sample structure model 94 9.2 Sample plots 100

LIST OF TABLES Table Page 2.1 Data base index 5 9.1 Sample natural frequencies and mode shapes 95 9.2 Sample DYNAMIC local input 96 9.3 Sample DYNAMIC local input (continued) 97 9.H Sample INTERFACE local input 98 9.5 Sample OPTICS local input 99 9.6 Sample CPU time and storage requirements 101

vi

~ ■: :. - ■ . .: ....-.■. ■ .: ■

I PPPr'- >

1, INTRODUCTION

a preliminary guide to the Integrated Large Emulation (ILS3) computer program. It^?;s

ethodology of the

This manual is Space Sensors S: intended to illustrate the software m« astern as well as to supply information to those persons involved in maintaining and using the system. "5 *« to aid in the analysis of large flexible satellite, their sensors with special emphasis on dynamics, optics and control disciplines associated "*** i'

»uples the appropriate disciplines shown in

tool and

structures,

the system. Defaults are provided for key parameters

. .... ■.-■.. , ■ .. ... .■ ' ■ ;, . .• I-.'-' ...- ■■ I ■.■

/ ■MMHBHBHMV

2. SYSTEM OVERVIEW

The ILS3 system currently consists of five major modules and a source code editor, which may be run either together or decoupled.

One subsystem is called the DYNAMICS module. This module consists of the dynamic formulations, the dynamic disturbances, and the control of both structure and attitude of the satellite. The output of this subsystem is the transient dynamic deformations. Another module, called the STEADY STATE, determines the steady state of the system in response to a sinusoidal input. These two subsystems are mutually exclusive. A third module, known as the ßUASI- STATIC accounts for slowly varying loads, resulting in residual thermal deformations. The data essential to the execution of all of the above mentioned modules comes from a finite element mathematical model of the entire structure. The fourth subsystem, the INTERFACE module is used for merging and interpolating the output of the above modules with optical data from the raytrace program and performing coordinate system transformations. The fifth subsystem, known as the Deformed Optics Evaluator (OPTICS) uses the outputted results from the INTERFACE module to evaluate the optical performance by computing line-of-sight and power on the detector.

The configuration of the system is shown in Figure 2.1, its associated data flow in Figure 2.2, and a description of the data bases in Table 2.1. The configuration may be started and/or stopped at any subsystem along the path.

The source code editor, written in SNOBOL, is used to modify variables having complicated functional source code dimensions prior to compilation time, thereby increasing efficiency and decreasing turnaround time.

, ■v-mmm1 ' wm^mm^w^1

tinuCTU«*!. wood. DIFINITlONt HEAT

•OUKCIi

THf RMAL MOOtL

TfunnATURt DISTKHUtlON

MtCMANlCAL mOftHTIES

STRUCTURAL. MODE L OIONiIlONS

ST«UCTU«Al MOOll

7 INFLUENCE MATRICES

THERMAl OISri>CEMENTS

QUASI STATIC COHAECTION

L.

nisiouAi THE «»Al OEfOAMATtONS

1 OISTURIANCII '

♦ 1 ♦ ^CON,«.L 1

DTNAUICS

" OAWUNC ' ^ PATIO 1

^ SENSORS» | ACTUATORS |

^VSUWORT »OINT . DEtlNITIONANOI GEOMETRY 1 1

-i r" Sl IOAM ir DAMPING t SURtlRl

O »OiNT GIOVtTRT

STEAQV STATE DVANAMICS

TRANSIENT DYNAMIC DEFORMATIONS

I

1-rTp.

J RA-rTMACE |

Figure 2.1 Simulation architecture flou

3

■

,-.,:~J"

__L_

-©

PLOTIEH fioinn IOUTPMI

Figure 2.2 Simulation data flow

4

/

Table 2.1 Data base index

No. Contents Section

Name

1 Dynamic or steady state transient 4 9 IQTAP deformations 5 9 IfiTAP

7 9 FIL3 2 Mode shapes and frequencies 4 8 ITAPE

5 8 ITAPE 3 Initial thermal displacements 6 8 FIL1 4 Actuator influence matrices 6 8 FIL5 5 Local input 4 7 IN

5 7 IN 6 7 IN 7 7 IN 8 7 IN

6 Nodal coordinates on surfaces 6 8 FIL7 7 8 FIL5

7 Normal vectors 6 9 FIL2 8 Figure control matrices 6 9 FIL6 9 Thermal deformations 6 .9 UFIL

7 .9 FIL1 10 7 8 FIL7 1 1 Interpolated quasi-static deformations 7 .9 FIL2 12 Interpolated dynamic or steady-state

deformations 7 .9 FIL4

13 Nodal polar Coordinates 7 .9 FIL6 14 Polar coordinates of rays 7 .9 FIL8 15 Coefficients of interpolation 7 .9 FIL9 16 Coefficients of extrapolation 7 .9 FIL11 17 Net wave aberrations 7 .9 FIL10

8 .8 FIL1 18 Point-ipread-function 8 .8 FIL2 19 Line-of-sight errors 8 .8 FIL3 20 Energy on detector 8 .8 FIL4 21 Raytrace input

SOURCE CODE EDITOR

3. 1 PURPOSE

This program modifies array sises and data constants for all subsystems in order to minimise the storage requirements of the system. This is done by editing source code to replace parameters by their desired values. The parameters and their values are read from FT09F001. The first record is a symbol (defined in these programs as an ampersand(G)). The regaining inputs define the parameters and their values, one per record. The value of a parameter may be defined by a constant or a sequence of arithmetic operations (or a function which computes the maximum of tuo variables, MAX) applied to a constant or previously defined parameter(s) . Comment records are allowed in the input stream and are defined by an asterisk in column 1. The 'pseudo source code' to be edited is read on FT08F00 1. The resulting output on FT10F001 is compilable FORTRAN source code.

The parameters for each of the subsystems and subroutines where they are used are defined below.

the

3.2 INPUT DEFINITIONS FOR EACH SUBSYSTEM

3.2 1 DYNAMICS

A. Modules Wh ere Parameters Are Used

MODULE M N26 MD2 MD122 N16 MD1 N1 N2 CMA ASN X X X X

BLOCK X X X X X XXX

CAINIT X X X X

CHEKER X

CNTL X X X X X XXX X

COPA X X X X

COPAC X X X

COPO X X X X X X

DERIVP X X X

ETAS X X X X X

FTAB X X X X X X

INPUT X X X X X X

PSINWT X X X X X X

RKETA X X

RKSC X

N2MD2 P MD12

x x X

X

X

X

X

MODULE ASN BLOCK CAINIT CHEKER CNTL COPA COPAC COPO DERIVP ETRQ FTAB INPUT PSIHMT RKETA RKSC

N2C NSEGS MN NT NDIS1 NDIS2 NIC NNORM CMAXN

B. Parameter Definitions

CMAX

CMAXN

M: MD1 ■

MD12 :

MD122

MD2

MN:

NDIS1 NDIS2; NNORM:

NSEGS NT:

Twice the number of modes to be used for structure control (2 * £N1C + 2 * eN2C) The total number of modes to be used for structure control (CN1C + eN2C) Number of force actuators Number of System 1 modes to be used The total number of modes in the system (CMD1 + EMD2) Twice the number of modes in the system (2 * CMDI + 2 * EMD2) Number of System 2 modes to be used The maximum number of nodes in one system (MAX(EN16,CN26)) Number of System 1 disturbances Number of System 2 disturbances The number of normal vectors for each segment (1 or 3) Number of segments in the system Number of entries in table of

Nl I

NIC:

N1MD1 •■

N16:

N2:

N2C:

N2riD2

N26:

P:

System 1 forcing functions Number of System 1 degrees-of- freedom (6 * CN16) Number of truncated states to be used in precision base Number of System 1 degrees-of- freedom times the number of System 1 modes (CN1 * CMDI) Number of System 1 nodes to be used Number of Syst..... 2 degrees-of- freedom (6 * EN26) Number of truncated states to be used in navigation base Number of System 2 dsgrees-of- freedom times the number of System 2 modes (EN2 * EMD2) Number of System 2 nodes to be used Number of sensors

3.2.2 STEADY STRTE

A. Modules Ulhere Paxam^teis Are Used

MODULE NW Nl MD1 N16 NIMDl NDIS1 NNORM NSEGS

MAIN X BLOCK X X X

COO X X

COW X X

FUNC X X X

INPUT X X X

X

X

X

X

B. Parameter Definitions

MD1 i

N0RM3:

NDIS1:

Number of System 1 modes to be used Flag which indicates if three normal vectors will be inputted for each segment Number of System 1 disturbances

8

L

NNAMI

NNORM

NSEGS NM: Nl:

N1I1D1

N16:

Node numbers to be included in System 1 Number of normal vectors per segment (1 or 3) Number of segments in the system Number of frequencies Number of System 1 degrees-of- freedom (6 * GNIG) Number of System 1 degrees-of- freedom times the number of System 1 modes (CNI * CMDI) Number of System 1 nodes to be used

3.2.3 QUASI-STATIC

A. Modules Where Parameters Are Used

MODULE NSEGS NM NODES N0DES3 FMAX FMAX2D NDUM NT NI BLOCK x x INPUT X X

MAIN X X X X

MATCOM X X

PREPRO X X X

SCALE X X X

UOUT X X

X X

X X

B. Parameter Definitions

|

FMAX:

FMAX2D:

NDUM:

Maximum number of force actuators Dimension of an upper triangular matrix of force actuators (CFMAX * (EFMAX + 1) / 2) The amount of space in a common block left over after scratch storage (CN0DES3 * GFMAX + SFMAX2D - CNNODESS)

I

Nl:

NM: KODES:

KODES3:

NSEGS

NT:

Number of time steps or thermal load configurations Number of mirrors Maximum number of nodes in a segment Triple the maximum number of nodes in a segment MaKimum number of segments on each mirror Maximum number of times for scaling

3.2.4 INTERFACE

A. Modules Where Parameters Are Used

MODULE NM NSEGS DEGR DEGTH MAXRT MAXRTNM MTMM NR NTHETA BLOCK X X X

CCMP X X

DBLIN X

DYPREP X X

GLOBC X

GLOBR X

INPUT X X

INTERP X

MAIN X X

OUTPUT X

SEGFND X

MODULE NODES DEGRTH BLOCK

X

X

X

X

X X

X X

X X

X X

COMP DBLIN DYPREP GLOBC GLOBR INPUT INTERP MAIN OUTPUT SEGFND

x x

10

.

r ;

B. Parameter np-Finitions

DEGR:

DEGRTH!

DEGTH:

MRXRT:

MRXRTNri:

tlTMM:

NODES

NR1-

NSEGS:

NTHETA:

NX:

NY:

Number of points needed for interpolation in R direction Number of points needed for interpolation in both R and THETR directions Number of points needed for interpolation in THETR direction Maximum number of rays that will be allowed Total number of points uhere each ray hits each mirror (EtIAXRT * ENM) Scaling factor Number of mirrors Maximum number of nodes in a segment on STRRDYNE tape Maximum Number of different radii in a segment Maximum number of segments in eachnirror Maximum number of different angles in a segment Maximum Number of different X-coordinates in a segment Maximum Number of different Y-coordinates in a segment

3.2.5 OPTICS

A. Modules Where Parameters MS. MsA

MODULE NRT NR N Nl N12 N21 BFOC X X

BLOCK x X X

FILL X X X x INPUTR X X

MAIN X X X X

PROC X X X X

11

:

^^^

z

B. Parameter Definite 9n?

NR: NRT N1 ■

N12.'

K2 1 :

Sise of the detector (must be a power of 2) Number of radii to be used for integration Number of rays One more than the sise of the detector (£N + 1) Number of grid points in the detector (£N1 * CND Number of grid spaces in half a row (or column) of the detector (EN / 2 + 1)

12

mmmmm

/

4. DYNAMICS

4. 1 PURPOSE

This program computes the dynamic equations of motion open loop. It also provides the capability of closing the loop by having a dynamic attitude control and/or structure control. The output at each time-step is a vector of displacements for each support point having six degrees-of-freedom (three translational and three rotational components). This is converted into a deformation for each support point.

4.2 TECHNICAL SUMMARY

of transient dynamic deformations.

An option may be exercised to utilise structure and/or attitude control models, defined in Sections 4.2.2 and 4.2.3 respectively, to generate feedback control vectors. This is performed by passing modal state-vectors from the plant dynamics to the control models at desired times, in order to compute sensor information needed by the control estimators.

A technical overview of the program is illustrated in Figure

4. 1

13

BSSBHHHI

«TTITUOI UHIO» LOCATIONS

1

OISTURIANCES ACTUATOR LOCATIONS

SENSOR LOCATIONS

1

0

1

/,

»ntTUDE

MI»5o«MINT PLANT

/ a- o, 1 SENSOR

MEASUREMENT . i

d'i.OOOl «' I • JE.III

^>

^. t.^.^.e, , »TTlTUOf CONTROL

J is ^»

1 CONTROL CAIN

1 RtOjCEDOROFR EST.MA'O«

I ST IM Aron ■

Figure 4.1 Overview

14

mm me m^amm -r*-T?m

I

.2.1 Plant Kauations o± Motion

r- -i ' » l Ui

i?Z

I A' BiD I

! I 1 BiH F' I

r— —i i— —I

I m' I I BT I I T?1 I + I I I 772

, I I B2 I

\ r\t \ \ I L_ _J L._ _J

I (NDI+MD:)XI I [ (2nDi+2ra2)xi I

i— -i r- "•"' i | I BxUx I

1 U 1 + 1 1 1 | I BsUs I

III I

[MXl 1

[ (MDl+rD2)X(£M01 + CraC) 1

uhere the coefiicient matrices defined by:

A' = [-2 «i uil -<Ji2 1

B, = [-#i b, Ka]

[ 0 I -d bz ^z 1

[(MDl*«02)XHl l(MDl+Ma2)Xll

and their dimensions are

(MDlx2MDl)

(MDlxM)

(nx2MD2)

B 2 ■ I "•*: Ka I

H = I 0 I d b i «i 1

F' -[-2«2"2ri/'2 g'?zl~<J2Zl

BxUx [<?i FDi I

(t1D2xn)

(rix2MDl )

(riD2x2riD2)

(MDlxl)

BsUs - t/z FD21 + 102 bR llRl Is"}] CMDÄXD

b, is a NlxSn System 1 force actuator influence matrix b1 denoted by a' 6x3 matrix of =eroS for -^/fj^ ^

e?ch node. For each actuator an identity matrix is insarted at the translational coordinates of the node to which it is connected. Each actuator may be connected to only one System 1 node. the activated nodes are defined by the vector Al.

b, is a N2x3ri System 2 force actuator inf^^ ^^ denoted by a 6x3 matrix of neros for each actuator at each node. For each actuator an identity matrix is

15

mmmmmmmmm

'

■ . as

inserted at the translational coordinates of the node to which it is connected. Each actuator may be connected to only one System 2 node. the activated nodes are defined by the vector A2.

d is a Mx3M block diagonal force actuator nominal distance matrix defined as follows:

IDJ,.i DJz. ^ DJ3.i 0 I

10 DJi ,m DJ2,m DJ3.m I

Ka is a 3nxM block diagonal force actuator matrix defined as follows 1

r- —' |Ki (DJ,.1 DJ2,1 DJ3. 1 I 0 0 0 I I - ' 10 0 0 Km [DJi.m DJz.m DJs.ml I L_ -J

bR is a N2x3 rotor influence matrix of seros except for a 3x3 identity matrix inserted at the rotational coordinates of the node specified by NR.

g = -bR I IRS' ] bR (N2xN2) Gyroscopic coupling matrix (block diagonal)

IR is a 3x3 resultant rotor inertia matrix composed as follows 1

IIRIN1.1 * CIi IRIN1.2 * CIz IRIN,.3 * CI3I IIRIN1.1 * CIi IRIN1.2 * CI2 IRIN,.3 * CI3I URIN,., * CI, IRIN,.2 * CI2 IRIN,,3 * CI3I

1

llRs'l is a 3x3 skew symmetric rotor body coupling matrix.

r T

lal [IR] (sM = Ibl

Id L J

r- -1

I 0 -c bl [IRS* 1 = I c 0 -al

l-b a 0 1 L_ _J

16

JIMIJ^JIIWIIWUIIWI J.I' '- i ■!.. ■ :- n ■, iLlU!-M .,l.:MU ,..,,_„ ■

/

4.2.2 Structure Control System

From the above plant equations and two input vectors defining the truncated states, the truncated matrices C1', 02', and C3' can be formed for use in the low order system model (estimator). Normally the sensor computation will use untruncated matrices and state vectors.

Sensor computation:

y = (C I El

{ PXl ] [PX(2MD1 + 2MD£) J

where

C = [L, ]

0

0

i— —i

l»7l' I Ul I

lr?2 I i i

IL2 1

(LPl

[ (2riDl + 2MD2)Xl J

10 0 I 01 U, 01 10 0 0 01 10 g*! I I 0 0 0 0 I '_ _J

i i

L [PXJP] /3i 13PX2N1J I 2N1X2HD1 J

[L, 1

0

0

[L2 I

i T— —T r— —i

10 0 I 01 l^2 01 10 0 0 01 10 02 I I 0 0 0 0 I 1~ —' I _J

(LPl

L lPX3Pl /32 [ 3PX2N2 ) l2N2X2t1D2l

L is the sama for C and E. Each Li sets the sensor axis and is a urvt vector

/Si sets which node has a sensor. Also it sets whether position or velocity are measured

Using the same two input vectors, TRCHNIC) and TRC2(N2C),

17

_

-at

the state vectors outputted from the plant can be truncated for use jy the sensor computation.

Estimator (Low-Order System Model):

H=C1,+ CZ'G - KlClE) I (2NlC + aNCC)Xt£HlC*2N2C) 1 ( ( 2N1C+2I-ICC )XM 1 [ ( 2N1C+2N2C ) XP 1

[(2H1C + 2N2C(K(2M1C + 2H2C» 1 I MX(2N1C+2N2C) I I PK(2N1C+2N2C) 1

X' = H x + - K y 03* I (2N102M2C)X1 1 [ (2N1C+2N2C)X1 ) [ PX1 1 [ ( 2N1C+2N2C )X1 1

[ (■:H1C+2H2C)X(CN1C+2M2C) I [ (2N1C+2N2C)XP J

This is a set of first-order differential equations, the initial conditions of which are all sero.

Control Gain:

U = G x [MXll IMX(2H1C + 2H2C) 1 [ ( 2N1C+2N2C )X1 J

4.2.3 Attitude Control

inu output: r— —n r— —i r— —i I— —I

I/3IMU' I ■ IbR 0 I l<?j 0 I \r)l' \ lySlftu I 10 bRllO <f2\ lr?2| I _J I _J L_ _J I _J

[6Xll [6X2N2 1 [2H2X2N2MD2! [ 2MD2X1 J

.00 33 dEg(t)/dt + Eg(t) = ßiw

d,,Ei(t)/dt^ + 2.613 d3Ei{t)/dt3 + 3.414 d2Ei(t)/dt2

+ 2.613 Ei(t)/dt + Ei{t)/dt = Eg(t)

dEw(t)/dt = .15 ld2Ei(t)/dt2 + .0051 dEi(t)/dt + .00005 Ei(t) ]

d3s/dt3 + .001 d2s/dt2 = .5 dEw(t)/dt

4.3 FEATURES AND CONSTRAINTS

A. Independent integration time-steps for plant. and structure and attitude control models.

B. Truncation capability to choose desired nodes and modes for a particular set of disturbances.

18

,,,..V^,,...V ,^:,^..,,.....-V:... ■.'.■ -..;:v^ ' ■■•"*mmm

C. Disturbances may be modeled either analytically or in tabular form.

D. Capability to run the DYNAMIC subsystem four ways: 1 - Open-loop plant dynamics 2 - Closed-loop structure control 3 - Closed-loop attitude control 4 - Closed-loop structure and attitude control

E. Time-histories are printed in both modal and discrete coordinates at a frequency defined by input.

F. Files containing time-histories of selected nodes may be outputted for further analysis at a frequency determined by input.

G. Fixed time-step for each model.

H. Structure and attitude control models must be run at a frequency which is either equal to or an even multiple of the plant time-step.

4.4 SUBSYSTEM ARCHITECTURE

The flow of the DYNAMICS subsytem is shown in Figure 4.2

19

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21

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Subsystem architecture

21

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4.5 SUBROUTINE NESTING HIERARCHY

MAIN

INPUT

■— TABLES

MOVER

ERROR

ABVAL

FORCE (FORGO) I I TABLES I I ERROR

CNTL (CNTLIN) I I TABLES I I ERROR

CHEKER I I ERROR I I NEARZ

AINIT I

■— MOVER

COFO

MOVER

DOT

MTXV

23

Bm—BimmamtmmaaaKmmmassamaD mmmmmmm

I

COPÄ

MXV

CROSS

DOT

COPAC I I MXV I I MOVER

DERIVP I I MXV I I FORCE

TABLES

MOVER

LGRANG

CNTL (DERCO)

DOT

MXM

MOVER

MXV

CAINIT

ETAS I I NEARZ

24

/

■tw— T »Aitu.ii.t.^mjmidm.

I MXV I I DOT

RKETA I

I DERIVP I I MXV

FORCE

TABLES

MOVER

LGRÄNG

CNTL (COCA)

CNTL (COCS)

CNTL (DERIVC) I I RKSC I I MXV

ASN

RKATT I I RKSC

NEARZ

4 . 6 SUBROUTINE SUMMARIES

JVsn'.M) computes attitude sensor information as a function of plant state variables, either when the state is to be saved (N=1) or uhen integration is to be performed

25

mmmmmmmmmiß*. mm ^MIIlipiMillllliWl

(N=2).

Cainit initialises those attitude variables which change as a function of structure control.

Chekez checks for compatibility of size and timing between plant and control models.

Cntl contains all code related to structure control. Derive, Coca, Goes, and Cntlin are all entries.

Derivc(CODE) computes the first derivative of the structure control equations and calls a first- order four step integrator. When the control clock is slower than the plant CODE= 1 and the saved sensor information is used along with current information. Otherwise C0DE=2 and only current sensor information is used.

DercO initialises all structural control variables.

Coca computes the attitude-dependent portions of the control coefficients.

Cocs(CODE) computes sensor information as a function of structure control coefficients and plant state variables. If the control clock is running slower than plant clock this entry is called twice per control time-step, once when the state is to be saved (C0DE=1) and once when the control equations are to be integrated (C0DE=2). If the clocks are running at the same speed, it is only called once with C0DE=2.

Cntlin reads input local to structure control equations.

Copa computes the attitude-dependent portions of the plant coefficients.

Copac computes the portions of the plant coefficients that vary with attitude and/or structure control.

COPO initialises the time-invariant portions of the plant coefficients.

Derivp computes the second derivative of the plant equations.

26

■

Etas, outputs in modal and discrete coordinates.

Force(T) computes the forcing function at aach timed). ForcO is an entry.

ForcO reads input local to the forcing computation. We currently have two versions of this subroutine. One obtains the function by linear interpolation from a table which was input. The other computes them using a sinusoidal function.

Input reads in input

.Eketa second-order Runge-Kutta integrator.

RJisc first-order Runge-Kutta integrator.

Error(N) prints error messages and stops if serious. The parameter, N, defines the message to be printed.

.Phatt performs attitude control updates.

4.7 USER INPUT SPECIFICATTOWS

A. FILE NAME: IN SOURCE: LOCAL

RECORD 1 : FORMAT: NAMELIST 'SYSTEM'

FIELD TYPE NAME 1 L*4 SYS1 2 L*4 SYS2

RECORD 2: FORMAT: NAMELIST 'DPI'

FIELD TYPE NAME 1 1*4 MD1 2 1*4 N16

RECORD 3: FORMAT: RMELIST 'TRUN1'

FIELD UPE NAME

27

I

.. L ..>innp^pi9mi.auii!W...

1 2 3 4

1*4 1*4 L*4 L*4

NNAM1 MNAMI N1ALL M1ALL

RECORD 4: FORMAT: NAMELIST 'NFLAG'

FIELD 1

TYPE L*4

NAME NÜRM3

RECORD 5= FORMAT: (5110)

FIELD 1 2 3 4 5

TYPE 1*4 1*4 1*4 1*4 1*4

NAME NODES(k) NODNOS( 1 NODNOS(2 NODNOS(3 NODNOS(4

,k) ,k) ,k) ,k)

RECORD 6: FORMAT: (3E20.7)

FIELD 1 2 3

TYPE R*4 R*4 R*4

NAME NORM(Kj, NORM(2,j, NORM(3,j,

k) k) k)

RECORD 7: FORMAT: (110)

FIELD 1

TYPE 1*4

NAME 999

RECORD 8: FORMAT: NAMELIST 'TRUP1'

FIELD 1 2 3

TYPE R*4 R*4 R*4

NAME PHI1P W1P PSI1P

28

.. ....... _.. ....

1 ""• ■ IIWPI.UIIII II II "

L

REw'irRD 9 = .ORMAT: NRHELIST ,DP2

FIELD TYPE NAME

2 1*4 N26

RECORD 10: FORMAT: NRMELIST 'TRUNZ'

FIELD TYPE NRME 1 1*4 HNRn2 2 1*4 I1NAri2

L*4 N2ALL 4 L*4 M2ALL

RECORD 11: FORMAT: NAMELIST 'TRUP2

FIELD TYPE NAME 1 R*4 PHI2P 2 R*4 W2P 3 R*4 PSJ2P

F^UORD 12: FORMAT: NAMELIST 'ETAS'

FIELD TYPE NAME 1 R*4 ETA

RECORD 13: FORMAT: NAMELIST 'INR1'

FIELD TYPE NAME 1 R*4 TO 2 R*4 TOPT 3 R*4 DTOPT 4 R*4 TF 5 R*4 TPRINT 6 R*4 DTPRNT 7 L*4 SCNTL 8 L*4 $ÄTT

29

W " jwiiiHiPiPJiwiiw «'.■i|«|l m 'wmmmmmmmmmm

1

RECORD 14r

FORMAT: NAMELIST 'IMPS'

LUM. TYPE NAME 1 R*U K 2 R*4 DJ 3 R*4 IRIN 4 R*4 CI 5 R*it DTP 6 1*4 N

7 1*4 NR 8 1*4 A1

9 1*4 A2

RECORD 15: FORMAT: KAMELIST 'INP4'

JIELD TYPE NAME 1 R*4 FD2

RECORD 16A: FORMAT: NAMELIST 'FORC

FIELD TYPE NAME 1 R*4 P01 2 R*4 OMEGA1 3 1*4 NDIS1 " 1*4 IDIS1 5 i*4 ITUP1

RECORD 16B: FORMAT: NAMELIST 'FORC

HIM TYPE NAME 1 R*4 P01 2 2*^ TTAB 3 R*4 FTAB

4 1*4 NT

5 1*4 NDIS1 6 1*4 IDIS1 7 1*4 ITUP1

RECORD 17: FORMAT: NAMELIST 'DCT

30

■

mmm iipiiimiHiiiipwHiiLiunmi ...^ ■ ,- T^. , ^.^L. ... ummätam

FIELD 1 2 3

TYPE

R*4 R*4

NAME U XHAT DXHAT

RECORD 18: FORMAT:

FIELD 1 2 3 4 5 6 7 8 9

10 1 1 12

NAMELIST 'INCI'

TYPE R'*4 R*^ R*4 R*4 R*4 R*4 1*4 1*4 1*4 1*4 1*4 1*4

NAME G CK LI BET1 BET2 DTC NIC N2C P COPT TRC1 TRC2

RECORD 19: FORMAT: NAMELIST 'DAI*

FIELD 1 2 3

TYPE R*4 R*4 R*4

NAME S EG El

RECORD 20: FORMAT: NAMELIST 'INAI'

FIELD 1

TYPE R*4

NAME DTA

There is one record of type 1. Records 2 through 4 are required if SYS1=T. There is one of each type. One Record 5 is required for each segment if SYS1=T. Each Record 5 must be followed by 3 records of type 6 if SYS1=T and NNORM3=T. One each of Records 7 and 8 are required if SYS1=T. One record each of types 9 through 11 are required if SYS2=T. One record each of types 12 through 15 is always required. Record 16A is required if the System 1 forcing function is

31

W

. .

'' yii!iU!iii|VipMiiii|iilip|piiiiiMipilP mmmmm -^Trrj^rrrr-T'-r-

1

table. one record each of ^vn^9 1^Unc

Jtlon " »iv.n in a

*CNTL= TRUE. One record each ^ H ^ *" required if required. eac:h 0:£ tw*5 ™ and 20 is always

4.8 EXTEP.NflT, STORED DATA BA SES

A. FILE NAME: ITAPE

SOURCE: CDC NASTRAK OR STARDYHE PROGRAMS

RECORD 1 : FORMAT (3110)

FIELD 1 2 3

TYPE

1*4 1*4

RECORD 2: FORMAT: (I12,3E20.7)

FIELD 1 2 3 4

NAME Node Number COORD(1,i) COORD(2,i) COORD(3,i)

(Temporary)

RECORD 3: FORMAT^ (110)

FIELD 1

NAME ID UM

RECORD 4: FORMAT (I12,E20.7)

FIELD 1 2

mm "ode Number (Temporary)

32

gnppngpp^^awOTKiiiHini^nnN.ii i i. r ^ ....-..—-IN-—■ «■w>.> ,. ,—^.,..-..,. ■.„ .-^ .„...<»>■<« <>*< >.>->>■> ■> J.IIII i .iip^i^piiiii

/

RECORD 5: FORMAT: (I12,3E20.7)

FIELD 1 2 3 4

TYPE 1*4 R*4 R*4 R*4

NAME Node Number (Temporary) PHI1P{1,i,j) PHI1P(2,i.j) PHI1P(3,i,j)

RECORD 6= FORMAT: (12X.: JE20.7)

FIELD 1 2 3

TYPE R*4 R*4 R*4

NAME PHI lP(4,i,j ) PHnP(5,i, j ) PHI1P(6,i,j)

RECORD 1■ FORMAT: (2110)

FIELD 1 2

TYPE 1*4 1*4

NAME N2T MD2T

RECORD 8: FORMAT: (112, E20.7)

FIELD 1 2

TYPE 1*4 R*4

NAME Mode Number (Temporary) W2P(j)

RECORD 9: FORMAT: (112, 3E20.7)

FIELD 1 2 3 4

TYPE 1*4 R*4 R*4 R*4

NAME Node Number (Temporary) PHI2P( 1 ,i,j ) PHl2P(2,i, j ) PHI2P(3,i,j )

RECORD 10: FORMAT: ( 12X, 3E20.7)

33

'^^mmmmmmm I. .JJilJU.-LJU-.J-

FIELD. TYPE 1 R*4 2 R*4 3 R*4

NAHE PHI2P(4,i,j) PHI2P(5,i,j) PHI2P(6,i,j)

Records 1 through 6 are required when SYS1=T. One record of type 1 xs required. The number of records of type 2 is Nl? The number of records of type 3 is NELT. The m mber of records of type , xs ND1T. Each record of type i, f^Uowe

4.9 INTERNAL STORED DATA BASES

FILE NAME: IQTAP (unformatted) SOURCE: DYNAMICS

RECORD 1: FIELD

I 2 3

TYPE R*l4 R*4 R*i4

RECORD 2: FIELD

1 2 3

TYPE R*4 R*4 R*lt

RECORD 3: FIELD

1 2 3

TYPE R*l+ R*4 R*i4

RECORD 4: FIELD TYPE

NAME COORD(1,NODNOS(1,k)) C00RD(2,NCDN0S(1,k)) C00RD(3,N0DN0S(1.k))

NAME COORDC 1,N0DN0S(2,k)) COORDCa.NODNOSCa.k)) COORD(3,NODNOS(2,k))

NAME COORD(l,N0DN0S(3,k)) COORD(2,NODNOS(3,k)) COORD(3,NODNOS(3,k))

NAME

34

^i i^z-L.,-:.'^ ._ ...„ ...■■., j-::jsm

!

1 R*14 DELC1) 2 R*4 DEL(2)

3 R*l4 DEL(3)

One record each of types 1 through 3 is produced for each segment in the system. For each time-step, NSEGS records of type 4 are produced.

4.10 GLOSSARY

Al

A2:

BET1

BET2

Cl: CK: C00RD(3,node #)

COPT:

DEL(3):

DJ:

DTA: DTC: DTOPT: DTP: DTPRNT DXHAT: EG :

Node number to be activated as a function of actuator number in the System 1 force actuator influence matrix Node number to be activated as a function of actuator number in the System 2 force actuator influence matrix Sets which node of precision base has a sensor and whether position or velocity is measured Sets which node of na 'igation base has a sensor and whetl.er position or velocity is measurtd Rotor spin axis direction cosines Estimator gain matrix X, Y. and Z coordinates for each node Control option flag 1 = Untruncated sensor computation

Untruncated coefficients 2 = Untruncated sensor computation

Truncated coefficients 3 = Truncated sensor computation

Truncated coefficients Deformations of the three points defining a segment Force actuator axis (nominal distance matrix) Attitude time-step Control time-step size Time between file outputs Time-step size for plant equations Time between prints Current velocity for estimator Attitude inputs

35

.

wmmm imm^^mmm

El: ETA:

FD2(dof): FTABCtime #,dist. #)

G: IDIS1 :

IDUM: ITUP1 :

IRIN:

K': LI: M: MD1 :

MDI :••

NORMS

MD2 •

ND2T'-

MNAMI

MNAM2

tllALL

M2ALL

NDIS1 KELT:

NNAM1

NNAM2

Attitude inputs Vector of modal velocities and coordinates ordered as follows: 1 - all System 1 velocities 2 - all System 1 coordinates 3 - all System 2 velocities 4 - all System 2 coordinates System 2 disturbance Table of System 1 forcing functions Control gain matrix Node numbers in System 1 where disturbances occur Dummy integer Degree-of-freedom within the System 1 node where disturbances occur (must be 1 through 6) Rotor inertia matrix in attached body vector Force actuator spring constant Sets the sensor axis Number of force actuators Number of System 1 modes to be used Total number of System 1 modes in the model Flag which indicates if three normal vectors will be inputted for each segment Number of System 2 mod;;s to bs used Total number of System 2 modes in the model Mode numbers to be included in System 1 Mode numbers to be included in System 2 Flag which is set when all System 1 modes are to be used Flag which is set when all System 2 modes are to be used Number of System 1 disturbances Number of dummy records on file ITAPE Node numbers to be included in System 1 Node numbers to be included in System 2

36

. ■

WPiW

NODES(segment #)■

NODNOSlnode #,sagment #) NR:

NSEGS: NT:

NULL:

NIC:

NIT:

N16:

N2ALL:

N2C:

N2T:

N26 :

OMEGA1: P: PHIIPCdof»node #,mode #)

PHl2P(dof.node #,mode #)

PSI1P(mode #) PSI2P(mode #) P01 : S: SYSI :

SYS2 :

TF: TOPT: TPRINT: TRC1 :

TRC2 :

nodes

nodes to be

Number of nodes in each segment (either 3 or 4) Node numbers for the segment Determines which node in the rotor influence matrix has an activated wheel Number of segments in the system Number of entries in table of System 1 forcing functions Flag which is set when all System 1 nodes are to be used Number of truncated states to be used in precision base Total number of System 1 nodes in the model Number of System 1 nodes to be used Flag which is set when all System 2 nodes are to be used Number of truncated states to be used in navigation base Total number of System 2 nodes in the model Number of System 2 used Forcing frequency Number of sensors Set of normalised mode shapes relative to the mass matrix for System 1 Set of normalised mode shapes relative to the mass matrix for System 2 Damping ratio per mode Damping ratio per mode Amplitude of forcing function Attitude inputs Logical flag which is true if System 1 is present Logical flag which is true if System 2 is present Final time of dynamic simulation Time of next file output Time of next print Precision base states to be used by estimator Navigation base states to be used by estimator

37

/

mmmsm

TTABCtime #)

TO : U: WlP(mode #):

W2P(mode #)

XHaT- $ATT:

*CNTL

Table of times for System 1 forcing functions Initial time of dynamic simulation Current control vector Natural frequency associated uith each mode (rad/sec) Natural frequency associated with each mode (rad/sec) Current position for estimator Flag uhich indicates if attitude control is present Flag uhich indicates if structure control is present

38

"-■"--

STEADY STATE

5. 1 PURPOSE

This program computes the steady-state dynamic equations of motion open-loop. The output at each time step is a vector of displacements for each support point having six degrees- of-freedom (three translational and three rotational components). This is converted into a deformation for each support point.

5.2 TECHNICAL SUMMARY

A set of algebraic equations as defined belou are computed for a number of equally spaced times between t = 0 and t = 27r/oD to produce a set of steady-state dynamic deformation time- histories for each specified frequency of disturbance (UD) . For each mode :

GFJ = 1/UJ2 (Fi fDy.J + Tz *D2.J + ••• + FN *DN. J)

where N is the number of disturbances and Di is the degree- of-freedom at which disturbance I is located

yj = uo /<JJ

AJ = 1 - YJ2

BJ = -2 fj yj

CJ = GFJ / (AJZ + BJ2)

If uj = 0,

GFJ = Ft 0Di,J + F2 ^D2,J + ... + FN ^DN.J

AJ = - 1 /UD2

BJ = 0

CJ = GFJ

For each degree-of-freedom:

ai = A! C! 01.! + Aj Cz *i.2 + ••• + AM CM *I,M

39

/SI " B, Ci 01.1 + Bz Cz «1.2 + ... + BM CM «I.M

where n is the number of modes.

For p equally spaced times between t = 0 and t = 27r/uD:

qi(t) ■ ai sin(uo t) + /3l cos(uD t)

5.3 FEATURES AND rONSTRAINTS

A. Truncation capability to choose desired nodes and modes for u particular set of disturbances.

B. The STEADY STATE subsystem may only be run open loop. There is currently no provision for any control.

C. Only one disturbance frequency may be used at a time.

D. Files containing time-histories of selected nodes may be output for further analysis at a frequency determined by input.

5.4 SUBSYSTEM ABTHTTECTURE

The flow of the STEADY STATE subsystem is shown in Figure

5. 1

!

HO

^

L_

u V. 01

t- o 0) g v -a ^ o) r a u o i: — n o — (U u a

l. V. OJ o c t- OJ en

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m u i_ — c I 'O u I

— — 1

OJ t) e N

+> i/)

— a n ty cv — in 4-

0) u i; *> «• 3 +> a. i T o c O 0

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amm ■Mi tammss^'-::.- ^2:; ■ •-■'^■^^iiWHMpam

■Q c c o

0) c o — o — n c. o +- ß e ._ o — k. —

o o

m 0) k. +> 1^1 o ~ o >♦- a £ o u

I I

c 1 C I U I — I

I a 1 B I

•1 ■*-> r

a i v 1 in

(9 -p 1

L. c i O -P 4- 3 I iu o r

■»^ ' T3 1 03 -

I 0) I a 1

— 1 +> 1

I c-J ll H- i"

/ S T5 I fU I 9 1 w 1 m 1 o 1 O 1

I I I -M C I I 3

I I I O

-►i r i o 1

Figura 5.1 Subsystem architecture

41

/

r J

'

5.5 SUBROUTIKE NESTING HIERARCHY

MAIN

-- INPUT

TABLES

MOVER

ERROR

ABVAL

COO

COM I I MOVER

FUNC I I DOT

NEARZ

5-6 SUBROUTTNF SUMMARIES

CoO computes portions of the coefficients that are independent of frequency.

Cow computes the coefficients for each frequency.

Func computes velocities and coordinates for all degrees-of-

frequency^ ^^ de:£ormatio"s ^ each time for each

.I"P"t. reads all input.

5.7 USER INPUT SPECIFICATIONS

A. FILE NAMLI- IN SOURCE: LOCAL

43

•s-wa

1 "

RECORD 1: FORMAT: NAMELIST 'DPI'

FIELD 1 2

TYPE 1*4 1*4

NAME MD1 N16

RECORD 2= FORMAT: KAMELIST 'TRUN1 i

FIELD 1 2 3 4

TYPE 1*4 1*4 L*4 L*4

NAME NNAM1 MNAM1 N1ALL M1ALL

RECORD 3: FORMAT: NAMELIST 'NFLAG'

FIELD 1

TYPE L*4

NAME NORM3

RECORD 4: FORMAT: (5110)

FIELD 1 2 3 4 5

TYPE 1*4 1*4 1*4 1*4 1*4

NAME NODES(k) NODKOS(1 NODNOS(2 NODNOS(3 NODNOS(4

,k) ,k) ,k) ,k)

RECORD 5: FORMAT: (3E20.7)

FIELD 1 2 3

TYPE R*4 R*4 R*4

NAME NORM( Kj, NORM(2,j, NORMO, j.

k) k) k)

RECORD 6: FORMAT: (110)

44

•'■"T

FIELD TYPE NRME 1 1*4 999

RECORD 7: FORMAT: NAMELIST 'TRUPI'

FIELD 1 2 3

TYPE R*i+

R*4

NAME PHI IP W1P PSI1P

RECORD 8: FORMAT NAMELIST 'INP1

FIELD 1 2 2

TYPE R*4 1*4 1*4

NAME M P NM

RECORD 9: FORMAT NAMELIST 'INPZ'

FIELD TYPE 1 2 3 4

R*4 1*4 1*4 1*4

NAME F NDIS1 IDIS1 ITUP1

RECORD 10: FORMAT: NAMELIST 'INPS*

FIELD 1 2

TYPE 1*4 1*4

NAME PREß NEXTO

There is one record each of types 1 through 3. One Record 4 is required for each segment. Each Record 4 must be followed by 3 records of type 5 if NNORM3=T. One each of Records 6 through 9 are required.

45

. .

np-w"1 ■ ' "mmm***p;mmmm _ ,,L,I!I1

'

5.8 EXTERWAT. STORED DATA BASES

A. FILE NAME: ITAPE SOURCE: CDC NASTRAN OR STARDYNE PROGRAMS

RECORD 1: FORMAT: (3110)

FIELD 1 2 3

TYPE 1*4 1*4 1*4

NAME NIT NELT MD1T

RECORD 2: FORMAT: (I12,3E20.7)

FIELD 1 2 3 4

TYPE 1*4 R*4 R*4 R*4

NAME Node Number COORD(1,i) COORD(2,i) COOkD(3,i)

RECORD 3: FORMAT: (110)

1 TYPE 1*4

NAME IDUM

RECORD 4: FORMAT: (I12,E20.7)

FI^LD 1 2

TYPE 1*4 R*4

NAME Mode Number W1P(j)

RECORD 5: FORMAT: (I12,3E20.7)

FIELD 1 2 3

TYPE 1*4 R*4 R*4

NAME Node Number PHI1P(l.i,j) PHI1P(2.i.i)

(Temporary)

(Temporary)

46

ppilliyiiy^^^

>rtm /

R*4 PHI1P(3,i,j)

RECORD 6= FORMAT ( 12X,3E20.7)

FIELD TYPE NAME 1 R*4 PHIlP(4,i,j) 2 R*4 PHIlP(5,i,j) 3 R*4 PHI1P(6,i,j)

RECORD 7: FORMAT:

FIELD 1 2

(2110)

TYPE 1*4 1*4

NAME N2T MD2T

RECORD 8: FORMAT (I12>E20.7)

FIELD TYPE NAME 1 1*4 Mode Number 2 R*4 W2P(j)

(Temporary)

RECORD 9= FORMAT:

RECORD 10 FORMAT

(n2,3E20.7)

FIELD TYPE NAME 1 1*4 Node Number (Temporary) 2 R*4 PHI2P(1,i,j) 3 R*4 PHI2P(2,i>j) 4 R*4 PHI2P(3,i,j)

(12X,3E20.7)

FIELD TYPE NAME 1 R*4 PHI2P(4,i,j) 2 R*4 PHI2P(5,i>j) 3 R*4 PHI2P(6,i,j)

Records 1 through 6 are required when SYS1=T

47

One record of

"■"I ""■ JliJ.lll|l|«lW ——

'

l""1«'""1'- —'-

type 1 is required. The number of records of type 2 is NIT. The number of records of type 3 is NELT. The number of records of type 4 is MDIT. Each record of type 4 is folloued by NIT sets of records where each set consists of one record of type 5 folloued by one record of type 6. Records 7 through 10 are required when SYS2=T. One record of type 7 is needed. The numijer of records of type 8 is MD2T. Each record of type 8 is followed by N2T sets of records where each set consists of o.ie record of type 9 followed by one record of type 10.

5. 9 INTERNAL STORED DATA BASES

A. FILE NAME: XfiTAPCunformatted)

RECORD 1 : FIELD TYPE

1 R*t4 2 R*4 3 R*4

NAME COORDC 1 ,N0DN0S( 1,k)) C00RD(2,N0DN0S(1,k)) C00RD(3,N0DN0S(1,k))

RECORD 2: FIELD TYPE

1 R*4 2 R*4 3 R*4

NAME COORDC 1 ,N0DN0S(2,k)) C00RD(2,N0DN0S(2,k)) COORD(3,NODNOS(2,k))

RECORD 3: FIELD TYPE

1 R*4 2 R*4 3 R*4

NAME COORDC 1 ,N0DN0SC3,k)) COORDC2,NODNOSC3,k)) COORDC 3,N0DN0SC 3,k))

RECORD 4: FIELD TYPE NAME

1 R*4 DELC1) 2 R*4 DELC2) 3 R*4 DELC3)

One record each of types 1 through 3 is produced for each segment in the system. For each time step, NSEGS records of type 4 are produced.

48

. . ■ . . .■ .

1 wm^mmmpm. _—^ 1 —— » .- ■ I!"

/

5.10 GLOSSARY

C00RD( 3,node #) ■■

DEL(3):

F( frequency # ) '• FREß:

IDIS1 =

IDUH: ITUP 1 ■

MDI :

MDIT:

NORMS:

MNAM1:

MIALL:

NDIS1 : NELT:

NEXTO: NNAMI ■

NODESCsegment #):

NODNOSCnode #,segment #) NORMC3,n,segment #):

NSEGS: NU: N1ALL:

NIT :

N16:

P(frequency #)•

X, Y, and Z coordinates for each node Deformations of the three points refining a segment Amplitude of disturbance Number of time-steps between printouts Node numbers in System 1 uhere disturbances occur Dummy integer Degree-of-freedom within the System 1 node where disturbances occur (must be 1 through 6) Number of System 1 modes to be used Total number of System 1 modes in the model Flag which indicates if three normal vectors will be input for each segment Mode numbers to be included in System 1 Flag which is set when all System 1 modes ar,e to be used Number of System 1 disturbances Number of dummy records on file ITAPE First printout time-step Node numbers to be included in System 1 Number of nodes in each segment (either 3 or 4) Node numbers for the segment Normal vector for the segment n=1 if NN0RM3=F n=3 if NN0RM3=T Number of segments in the system Number of frequencies Flag which is set when all System 1 nodes are to be used Total number of System 1 nodes in the model Number of System 1 nodes to be used Number of time-steps

49

mmm

I Bmmmmmmm ?T3*M(

PHIIPCdof»node «,mode #)

PSIIPCmode #): WCfrequency #) WlPdnode #):

Set of normalised mode shapes relative to the mass matrix for System 1 Damping ratio per mode (fj) Frequencies (uo) Natural frequency associated with each mode (UJ)

(rad/sec)

50

Sga wmmmmaa5zz.-zz^

i -J— -JL

6. fiUASI-STATIC

6. 1 PURPOSE

This program corrects the thermally induced displacements of the optical surfaces by the use of position and figure control actuators.

6 . 2 TECHNICAL SUMMARY

For each node n in segment s of mirror m in the system, the component of deflection normal to the mirror surface is:

E0(n,s,m) = N(3,n,s,m) • U0(3,n,s,m)

where N is the normal vector at the node and UO is the total deflection of the node.

The initial surface deflection of each mirror is:

E0(3,m) = -S N(3,n,s,m) E0(n,s,m) s,N

Each element of the 3x3 rigid body sensitivity matrix for each mirror is:

E(j,k,m) = S NCj,n,m) N(k,n,m) S,N

The rigid-body movement of each mirror due to the thermal load is:

R(3,m) = E(3,3>m)-1 £0(3,1.0

The deflection due to the optical train <--> backup truss actuators is '•

Ul(3,n,m,s) = U0(3,n,m,s) - R(3.m)

The initial surface deflection of each segment is:

51

61

. ...

wm^ßmKfmmmim^^m^nßmifmm^iii^ - ^a»^: .nimm . ■ ■

E0(3,s,m) = -2 N(3,n,s,m) EO(n,s,m) s

Each element of the 3x3 rigid-body sensitivity matrix for each segment is:

E(j,k,s,m) = Z NCj^n^.m) N(k,n,s,m) N

The rigid-body movement of each segment due to the thermal load is!

R(3,s,m) = E(3,3,s,m)-1 E0(3,s,m)

The deflection due to the backup truss <—> segment actuators is•

U2(3,n,m,s) = Ul(3,n,m,s) - R(3,s,m)

The residual deformation of each segment due to the thermal load after implementstion of the quasi-static control system is i

T T T

U3(3,n,m,s) = U2(3,n,m,s) (I - A(A A)"1A ) + UA*

where k is the actur. :.->r influence matrix of the segment and LA* is the deflection dun to ram-om aetuatoz errors.

6 . 3 FEATURES AND CONSTRAINTS

A. Rigid-body actuators can be used to remove piston and/or tilt motions.

B. Surface actuators correct surface deformations.

C. Any combination of corrections may be performed.

D. Output may be produced before corrections and/or after any corrections.

6.4 SUBSYSTEH ARCHITECTURE

The flou of the ßUASI-STATIC subsystem is shown in Figure 6. 1

52

BHHBBBBBHBHHBBBBHBHHI wmmm

mm

mm m

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L cn o C k.

C

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in o — i. ** k. o R) ■♦-> V. 3 n k. *» C — u z:

k OTJ

«1 k. 4- ra <> n o «0 4- in

H- +> ^ in c mm

r lit m V) o p e

D> k. ■M ■M lU u> 0) O in£

01 ^ +> k

4- or c lil k. o M O k. «n

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a u g| o n c in t) JC

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— — — - _ RI fc Q_ k. o 11) o £ -1 f* »-

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k. o B k. in k r UJ Ul Ü) i

n r 4' n n T; 3 t 4* n <J o: <

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Hppwiipji ..»»■■imiiiii.Piiwii."^^^" i. vwni ^mvmmMmmm.m ^mmmmm nspn^pppvnpain

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to

6

51

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in ■o— c — o o 0) — +> +> a — o

c « k. M — O 4- k. Cl Cl k. £ r^ — *>

E U 4) O (0 £ I. 1-

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„my.M ^.ui.,imi..MU.Ui.Wl.M|?yM .,.„..,1 ; ^m.HMBJ.IIIIHIHW.l KIMi,,! .1 . »jw^www PWWSSBIW^B

c u E +* Ü c > tt) O E r tn

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(D E £ »( +> > o 0) £ > O X E tJ ai o

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■** * "" * ' ' m F 1. 0) £ u

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O c c v +* s n l."p

0) t +• +> 7) — — m O in L F « O k » 3 0) O E (7

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a c ao a o

V) k. Cl 0 k. a> ir k. 0) o

JJ « 0) 4- 4-

+> C (3 k. 3 J Q. M — lf> «= (0 ft ■o o-e a

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k. IU £

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wmmmmammnc^^szjL- - warn vommmm IBBra^EJi'■.:..-: .^ _: ..:.:'.. yy^m I ,..,..:!,,»

51

\. ■

V. ■M o +» k. C k. 3

O rH £ O +

in Al +» M •V c in m U) ■n (; tr. ■->

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k. 0) o+> k. c k. 3 — O rH l:0 +

E u a ■>

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V ro k. E V k. -M OJ C r4 X 3 ♦ (- O —

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+> -o IS CO

TJ O Ü.-I 3

^ J

Figure 6.1 Subsystem architecture

53

■

Vouli < II, ä.M'MLC'msiQTtET^, TOTAL, 1,%) computes the deformation for each node in the normal direction and prints them with the root-mean-square. If TOTAL=TRUE, the total root-mean-square for the mirror is printed. The deformations are also written onto one or more files, scaled if required.

Er5toP prints error messages and stops if severe.

Random(VIC,N) currently inserts N zeros into a vector.

InPut Reads and echoes local input and sets up files for scaling results if required.

ilatcom ( ROM. U2 » U 3 , NVEC , N ) Computes: T T

U3 = U2 (I - A(A A)-1A ) + U3 using ROW as a holding vector.

PrePro computes normal vectors and rigid-body sensitivity matrices.

6.7 USER IKPUT SPECIFICATIONS

A. FILE NAME: IN SOURCE: LOCAL

RECORD 1 : FORMAT: NAMELIST INPT

FIELD TYPE NAME 1 1*4 NI 2 1*4 NM 3 1*4 NSEGS 4 1*4 NODES 5 1*4 EXROUS 6 L*4 $MAT 7 L*4 $MRIT'l 8 L*4 $WRIT2 9 L*4 $1

10 L*4 *2 1 1 L*4 $3 12 L*4 PUSH 13 L*4 TILT

56

»i^ _.. /

6.b SUBROUTINE NESTING HIERARCHY

MAIN i INPUT

PREPRO I I MOVER I I— SI

MOVER

DOT

MXVSYM

UOUT I I DOT

RANDOM

MATCOM

DOT

SI

MOVER

SCALE

6.6 SUBROUTINE SUMMARIES

Scale consolidates scaled deformations into one file for each type of correction. This routine is only invoked when *SCALE=TRUE.

55

,

ILout (IJ,2J , NO , liVEC , RMSTOT , NTOI. TOTAL , I. M )

J&rstoE prints error messages and stops if severe.

MM^(VEC,H) currently inserts H 2eros into a vector.

Input Reads and echoic i„„..i

scaling results0" re^^^ *** '**' UP fileS for

üatcom(R0H.Ul.U3.NYEC,N) Computes: T T

U3 = U2 (I - A(A A)-iA ) + U3 using ROW as a holding vector.

PrePro computes normal vectors and rir,^ », ^ matrices. ectors and rigid-body sensitivity

6-7 USER INPUT SPECIFTrBTTn^

A. FILE NAME: IN SOURCE: LOCAL

ORD 1 • FORMAT: KAMELIST INPT

FIELD TYPE NAME 1 1*4 NI 2 1*4 NM 3 1*4 NSEGS 4 1*4 NODES 5 1*4 EXROWS 6 L*4 $MAT 7 L*4 *WRIT1 8 L*4 $WRIT2 9 L*4 $1

10 L*4 $2 1 1 L*4 $3 12 L*4 PUSH 13 L*4 TILT

56

I

RECORD 2 : FORMAT: NAMELIST IN2

FIELD 1 2 3

TYPE R*8 1*4 L*^

NAME FACT NT $SCALE

There is one record each of types 1 and 2

6.8 EXTERNAL STORED DATA BASES

A. FILE NAME: FIL1 SOURCE: CDC NASTRAN OR STARDYNE PROGRAMS

RECORD 1 : FORMAT: (3E20 7]

FIELD 1 2 3

TYPE R*4 R*i4 R*4

NAME IK 1,J) U(2,J) U(3.J)

There is one record of type 1 for each node and each thermal load .

B. FILE NAME: FIL5 SOURCE: CDC NASTRAN OR STARDYNE PROGRAMS

RECORD 1 : FORMAT: (110)

FIELD TYPE NAME 1 1*4 FIN

57

' .

/

RECORD 2- FORMAT:

FIELD 1 2 3 4 5

(5E16.6)

TYPE R*4 R*4 R*^ R*4 R*U

NRNE A( 1 , 1 , A(2, 1 A(3, 1 A( 1 ,2 A(2.2

There mirror The number of

is

for each segment of each

s o * (FIN

y t determined by the number of segments in the system.

is one record of type 1 , , . records of type 2 needed for each

+ EXR0WS)/5. The number of segment is 3*N0DESCS,M) sets of Record 1 followed by the proper number of^Records 2

C. FILE NAME: FIL7 SOURCE: CDC NASTRAN OR STARDYNE PROGRAMS

RECORD 1: FORMAT:

FIELD 1

(F10.5)

TYPE R*'4

NA?;E RC

RECORD 2: FORMAT:

FIELD 1 2

(2E20.10)

TYPE R*4 R*4

NAME X Y

Thert. is one record of type 1 for each mirror. The number of records of type 2 is determined by the total number of nodes on the mirror. The number of sets of Record 1 followed by the proper number of Records 2 is determined by the number of mirrors in the system.

1 This format was changed from (8F10.7) on September 19, 1978

58

. .

/ I

'

6.9 INTERNftL STORED DATA BASES

A. FILE NAME: FIL2(unformatted)

RECORD 1 : FIELD TYPE NAME

1 R*4 NVEC( 1,1) 2 R*4 NVZC(2, n 3 R*4

R*4 R-^U R*^

NVECO, 1 )

R*4 NVEC(1,J) R*4 NVEC(2,J) R*4 NVECC 3,J)

One record of type 1 is produced for eauh segment of each mirror. Each record has ANODES(S,M) fields.

B. FILE NAME: FIL6>: unformatted)

RECORD 1: FIELD

1 2 3

TYPE R*4 R*4

R*4 R*4 R*4 R«t» R«4 R*^

NAME ROU(1,1) R0W(2, 1 ) R0M(3, 1 )

ROW( 1,NODES(S,M) ) ROW(2,NODES(S,M) ) R0W(3,N0DESCS,M) )

Both the number of fields per record and the number of records per segment is 3*N0DES(S,M).

C. FILE NAME: UFIL(unformatted)

RECORD 1 1 R*4 DELTU)

59

, 'SÜSPPSF

J-

R*4 R*4 R*^ DELT(J)

One record o-* type 1 is produced for each segment of each mirror. Each record has NODES(S,n) fields. There are four of these files .

6.10 GLOSSARY

]U3,node #,actuator # + EXR0WS):

DELTCnode #): EXROWS:

FACTCmirror #,time #,thermal #) FIN:

J: M: Nl:

Nfl: NKthermal #): NODESCsegment #,mirror #):

NSEGSCmirror #) ••

MVEC(3,node#) '• PUSH:

RC: R0M(3,node «)

S: TILT:

U(3,node #):

Ul(3,node #)«

Actuator influence matrix for a segment Deformation of a node Number of rows added to A for dependent push and tilt removal Scale factor Number of figure actuators for a segment Node number Mirror number Number of time-steps or thermal loads Number of mirrors Number of times for scaling Number of nodes in each segment Number of segments in each mirror Normal vector for each node Flag which indicates if mirror rigid body actuators should remove push motion in mirror rigid-bod>' computation Radius of curvature Row of the matrix used for figure control Segment number Flag which indicates if mirror rigid-body actuators should remove tilt motion Initial displacements for each node Displacement for each node

60

■

. ..

7 ^B^H^^p^, -.-„ ,,.v- • ^^jsppr ^IBBIB

U2(3,node #)

U3(3,node #)

$SCALE:

$URIT1i

$WRIT2:

*1

$2:

*3:

after mirror rigid-body correction Displacement for each node after segment rigid-body correction Displacement for each node after random actuator correction X coordinate of node Y coordinate of node Flag which indicates whether matrix used for figure control will be computed Flag which indicates whether scaling is to be done T - scale F - no scaling Flag which indicates wlu.'ther output is desired after mirror rigid-body computation Flag which indicates whether output is desired after segment rigid-body computation Flag which indicates whether computation of mirror rigid-body deformations is desired Flag which indicates whether computation of segment rigid-body deformations is desired Flag which indicates whether computation of figure control deformations is desired

61

Wmm

L

7. INTERFACE

7. 1 PURPOSE

This program interpolate«; racH itiiei ^^x the DYNAMICS ox STEADY STATE an^

0rma^0nS Produced ^ "i oitrtui iiAit, and/or the OUfl^T-^TBT-rr- Programs at the structural points, to obtain deformations f?

CoL0P iC.al. P01ntS- The UaVe Serrations produced by the

combined deformations are calculated using the ravtrace data

free «H ^"^ SyStem and are added *' the disturbance free aberratxons of the system to obtain the total aberrations of the deformed system. wave

7.2 TECHNICflT. SUnnflRY

The INTERFACE subsystem can presently utili,. A *

^-^■^^^^

7 ■ 2 . 1 D y n a m i r:

The deformation, Um, at the ith raytrace point on is computed as follows: pomx on mirror M

<5DM =f yi(Xc-xB) + yeCxi-xc) + yc( XB-XI ) ]*HA

+ yi(HA-XC) + yA(xC-Xl) + yC(xl-XA) JÖNB + yifXB-XA) + yA(xi-XB) + yB(xA-Xl)1ÖNC}/

[yA(xc-xB) + yB(xA-xc) + yc(xB-xA)J

having associated deformations, ön.ön «ndVnc

7-2.2 guasi-st^f-i r

ihs\t:1z:rT-io^s-t the tth "'*"" '^ •- ^ ror M

62

■ BSHUpipi •nrnnmrnm*****^' ^msmm^g.

JL

3*1 R + l S+l R + l

ÖQM = Z S { IT I (yi-yK)/(yN-yK) 1 n I ( XI-XJ)/(XL-XJ) J} öLN

N=l L=l K=l J=l

K#N J^L

uhere R and s are the orders of interpolation desired in each direction respectively and the x's a^d y's are the nodal coordinates for interpolation.

7.2.3 Ket Wave Aberrations

The deformations obtained by the methods in Sections 7.2.1 and 7.2.2 are nou combined on each mirror and summed over N mirrors to produce the total aberration W of the ith ray by the following expression:

N

Wi = U0+ Z ±2 COSIM (ÖQM +5DM) M=I

7.3 FEATURES AKD CONSTRAINTS

A. Coefficients of interpolation may be saved and reused.

B. Interpolated deformations may be saved and reused.

C. Cartesian or polar coordinates may be specified.

D. Interpolation orders may be specified in both directions,

E. There are six running options:

1 - Use deformation dans frosrt thr tUA^I-STATIC subsystem onlj".

2 - Use deformation data from the DYNAMIC subsystem only .

3 - Use deformation data from both the ßUASI-STATIC an the DYNAMIC subsystems.

4 - Use deformation data from the DYNAMIC subsystem with saved interpolated ßUASI-STATIC data.

5 - Use deformation data from the fiUASI-STATIC subsystem with saved interpolated DYNAMIC data.

6 - Use saved interpolated SUASI-STATIC and DYNAMIC data.

63

.

wamm

'

I««I"..«!, • ...i

7.4 SUBSYSTEM ARCHITECTURE

The flow of the INTERFACE subsystem is shown in Figure 7.1

64

. .

\m<mm.^.m i i| i

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-

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M ■"•• ^

4» &

n ^ 3

. L —J

111

si K M -ig SS IH U a. ui o o <

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O U (A DC M Z t»- o Z < W O H K Ü W < ui M o: Sen o < u. (0 3 in MOO

in ■i r ui Ui ►- t- UI

S25 OTS S j i I.,

— — • § M 1- t , DC UI UI O O H M 10 i/) Z Ui o a D

ID a H ui z ■

a M 5 o. in ui |f a x MO E M

gi < z

H in ui in e fc . 25 M r a o a ui g in o UI

uiiE u < UI

P5 E V ex < UI a H

Ui •H D ml < g u. ■M — •

.

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5 lil H m t- < 31« o < a. f- a < u,o

tu

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a o o u

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C1 u. M O

UI O UI O M -I O H 3 zB8 K- UJ

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z o M DC

H O CE O O U

UI U 111 < a.

5§ a CE

-i O

HS < M

O

o u |8 z g

§

■

INPUT

1 IN

TER-

1 PO

LATE

Dl

DYNAMIC!

DEFO

RM-1

ATIONS1 1

^

i in i o r in t CE 1- M M CE Z b ui < OT r- O O D. h- -> < < U. M Z Z O 3 1- ui H M M a. cr w o <

-^

-

INPUT

I INTER-

I POLATED

! DYNAMIC

1 DEFORM-

1 AT^SNS

1 1

1 INTER-

1 POLATE

1 USING

I Q.-S.

1 DATA

1 BASE OF

1 DE

FOR.

.

INTE

R-

1 PO

LATE

1 USING

1 DYNAMIC

1 DATA

1 3A

SE OF

I DEFOR.I

1 INPUT

1 IN

TER-

1 POLATED

1 QUASI-

I STATIC

1 DEFORM-

1 ATIONS

-

INTER-

1 POLATE

1 USING

1 DYNAMIC

1 DATA

I BASE OF

I DEFOR.I

INTER-

POLA

TE

1 Q.-S.

| DATA

| BASE OF

DEFORM-

ATIONS

1

111 UL IT. H O Z •too -J (9 M UI M o z r OT »- a. M < < < cv: OT Z CD X: m b >-

o < g

UI U U. OT t- •H O Z

3 t- o (9 < UI M

o T. 1- OT 1- E n W < < ■ OT r CE IS 111 M a & m to

«< 1- u. M 3 < in

a oo

■V

~ ^_: „,.. -r—

PI|lpillWJP.Mi,,ili.i! 'I „ mmmv^mm •>■-" - PWPP

i

1

■

in z oo D. H V> <

o IU

<

si HI

Si is H H Si:

DC -»a < u U ID M < a in

"I

I!.

■ .

.-. -

'Jt

Figure 7.1 Subsystem architecture

65

1

i

3

'"«H^PÄPf.w^ mm^mmmmm^'''

1

7.5 SUBROUTINK NESTING HIERARCHY

MAIN

SEGFND I I ERSTOP I I NEARZ

INPUT

DYPREP

SCALE

GLOBC

CONVRT

NEARZ

ERSTOP

GLOBR

GLOBXY I I NEARZ I I ERSTOP

CONVRT

INTERP I I DBLIN I I

67

atü«—..-■.,■■*,.»■■■.. _,*«

-— LGRANG I I MOVER

•— CINT I I DOT

CIKT I I DOT

COMP

OUTPUT

DMOVER

7.6 SUBROUTINK SUMHARIFS

Cint finds an interpolated vtlue given a two-dimensional table, pointers into the table in both directions, a set of coefficients for each direction, and the order of interpolation in each direction.

Convr± converts the coordinates of one point from cartesian to polar.

Dblin performs two-dimensional interpolation and also returns the coefficients of interpolation in both directions together with pointers for them. The actual interpolation in each direction is performed by Lcrrana.

Erstop urites an error message and either stops or returns depending on the severity of the error.

Globe converts the global coordinates for one mirror from cartesian to polar. Error checking is performed, and the polar coordinates are output. The actual conversion is done by calling Convrt

GlobKY performs error checking for one mirror when cartesian coordinates are desired

68

.

z_

Giobr reads in the polar coordinates for one mirror

Input reads data in namelist form Variables which have "default values may optionally be overridsn by input. Variables which do not have default values must be inputted.

Interp interpolates the quasi-static displacements to get the displacement at a point on a mirror. If the coefficients of interpolation are also to be computed and filed, Dblin is used. If the coefficients are to be read in, Cint is used.

Larang performs Lagrangian interpolation of any order and also returns the coefficients of interpolation together with a pointer for them.

Scale computes scale factors for data on each mirror if required

Output writes the updated raytrace file for the OPTICS program.

Seqfnd finds the segment of the mirror which contains a certain point.

7,7 USER INPUT SPECIFICATIONS

Ä. FILE NAME: I>J SOURCE: LOCAL

RECORD 1: FORMAT: NAMELIST 'INI'

FIELD TYPE NAME 1 1*4 NM 2 1*4 MAXRT 3 1*4 NODES 4 1*4 NSEGS 5 1*4 GLFLAG 6 1*4 RTCFLG 7 1*4 RUNTYP 8 1*4 NT

RECORD 2:

69

f 1 !■

FORMAT: NÄMELIST 'RT

1 R*4 ZR1

RECORD 3: FORMAT:

1 2 3

NAMELIST 'n^'

1*4 DEGR 1*4 DEGTH 1*4 COFLAG

RECORD l» : FORMAT

1

NAMELIST 'REU'

L*4 *REWD2

RECORD 5 FORMAT: NAMELIST 'DYN'

1 L*4 DYCFLG

RECORD 6: FORMAT: NAMELIST 'IN3'

1 2 3

R*4 SGN 1*4 FREß 1*4 NEXT

There is oi ̂e reeorrt oa^v.

7-8 EXTERNAL STORKn DATA BAS'i ES

A. FILE NAME: FIL5

SOURCE: CDC NASTRAN OR STARDYNE PROGRAMS

70

RECORD 1■ FORMAT: (F10.5)

FIELD 1

TYPE R*4

NAME RC

RECORD 2: FORMAT: (2E20. 10)

FIELD TYPE NAME 1 R*4 X 2 R*4 Y

There is one record of type 1 for each mirror followed by NODES(S,M) records of type 2.

It is

B. FILE NAME: riL7 SOURCE: RAYTRACE FORMATTER

RECORD 1: FORMAT (3I5,F15.6)

FIELD 1 2 3 4

TYPE 1*4 1*4 1*4 R*4

NAME IND IC(NRT) JC(NRT) T

RECORD 2: FORMAT: (4F20.6)

FIELD TYPE NAME 1 R*4 XRT(NRT,1) 2 R*4 YRTCNRT, 1 ) 3 R*4 COSI(NRT,1) 4 R*4 XRT(NRT,2)

RECORD 3: FORMAT (4F20.6)

FIELD TYPE NAME 1 R*4 YRTCNRT,2)

71

"" iniiip.niji.ijii i

2 3

R*l+ R*4 R*4

COSKNRT,2) XRTCNRT,3) YRTCNRT,3)

RECORD 4: FORMAT: (4F20.6)

FIELD 1 2 3 M

TYPE R*4 R*4 R*4 R 4

NAME COSKNRT, 3) WIO(NRT) XR(NRT) YR(NRT)

RECORD 5= FORMAT: (F20.6)

FIELD 1

TYPE R*4

NAME ZR(NRT)

There is one record each of types 1 through 5 for each ray

7.9 INTERNAL STORED DATA BASES

A. FILE NAME: FIL_L( unformatted) SOURCE: 2UASI-STATIC

RECORD 1 : FIELD

1 TYPE R*4 R*4 R*4 R*^ R*4

NAME DELßl(1)

DELßl(J)

One record of type 1 is required for each segment of each mirror. Each record has NODES(S,M) fields.

B. FILE NAME: FIL3(unformatted)

SOURCE: DYNAMICS

72

. . . . .

mmm mpiwipuAwii« üw^. ••

1

•fmmi^mmmmmn

RECORD 1: FIELD TYPE

1 R*4 2 R*4 3 R*4

NAME XDYN(1,S,M) YDYNC1.S^M) ZDYN(1,3,n)

RECORD 2: FIELD TYPE

1 R*4 2 R*4 3 R*t

HflME XDYN(2,S,M) YDYN(2.S.M) ZDYN(2,S,M)

RECORD 3: FIELD TYPE

1 R*4 2 R*4 3 R*4

NAME XDYN(3,S,M) YDYN(3,S,M> ZDYN(3,S,M)

RECORD 4: FIELD TYPE

1 R'*4 2 R*l4 3 R*«!

NAME DELDK 1 ,S) DELD1(2,S) DELD1(3,S)

One record each of types 1 through 3 is required for each segment in the system. Theue are followed by NSEGS records of type 4 for each time-step.

C. FILE NAME: FILICunformatted)

RECORD 1 i FIELD TYPE NAME

1 R*4 DELe2

NRT records of type 1 are produced for each time-step or thermal load whenever quasi-static interpolation is performed.

D. FILE NAME: FILjH unformatted)

73

"■I""1»"' "«"■

-

RECORD 1 « FIELD TYPE NAHE

1 R*^ DELD2

NRT records of type 1 are produced for each time step or thermal lo'aC whenever dynamic interpolation is performed.

E. FILE NAME: FIL6(unformatted)

RECORD 1: FIELD

1 2

TYPE 1*4 R*4 R*4 R*i4 R*4 R*4 1*4 R*4 R-»;4 R-*4 R*4 R*4

NAME KRS R(1,S)

R(NRS,S) NTHS THETA( 1 ,S)

THETA(NTHS,S)

One record of type 1 is produced for each segment in the system.

F. FILE NAME: FIL8(unformatted)

RECORD 1 : FIELD TYPE NAME

1 R*4 RTR 2 R*4 RTTH 3 1*4 RTSEG

One record of type 1 is produced for each ray in the system

G. FILE NAME: FIL9(unformatted)

74

. . .

• -..",-■ '■ ■'■ '"

1

.

RECORD 1• FIELD

1 2

TYPE R*4 R*4 R*4 R*4 R*4 1*4 1*4

NAME CRTHC 1 ) CRTH(2)

RPT THPT

One record of type 1 is produced for each ray for each mirror in the system whenever quasi-static interpolation is

performed.

H. FILE NAME: FIL11(unformatted^

RECORD 1■ FIELD TYPE

1 R*4 2 R*4 3 R*4

NAME C( 1 ) C(2) C(3)

One record of type 1 is produced for each ray for each mirror in the system whenever dynamic extrapolation is

performed.

I. FILE NAME: FIL10(unformatted)

ECORD 1= FIELD TYPE NAME

1 1*4 NRT 2 1*4 IC( 1) 3 1*4 JC( 1) 4 R*8 WI0( 1) 5 R*8 XR( 1) 6 R*8 YR( 1) 7 R*8

R*8 ZR( 1)

R*8 . R*8 ,

1*4 IC(NRT) 1*4 JC(NRT)

75

!

wm

7 mm

• R*8 MIO(NRT) • R*8 XR(NRT) • R*8 yR(NRT) • R*8 ZR(NRT)

RECORD 2 : FIELD TYPE NAME

1 R*8 TOTWC 1) • R*8 • R*8

R*8 •

KRT R*8 TOTW(NRT)

One record of type 1 is produced. One record of tvn* » i Produced for each time-step or thermal'load ^ ' 1S

7.10 PLOTTING OUTPUTS

A. Nominal wave aberrations

B. Time-history of net wave aberrations

7-11 GLOSSARY

C(3) :

COFLAG

COSKray #,mirror #) CRTH(DEGR*DEGTH)t

DELD1(3,segment #):

DEGR:

DEGTH:

PTLDI:

DELD2(ray ») :

Coefficients of DYNAMIC extrapolation Flag which determines whether interpolation coefficients for SUASI-STATIC interpolation will be computed or read 1 = Computed 2 = Read Cosine of the angle of incidence Coefficients of SUASI-STATIC interpolation Displacements of the three points defining a segment Number of points needed for interpolation in R direction Number of points needed for interpolation in THETA direction Displacement at the DYNAMIC support points Displacements from the DYNAMICS

76

wsmmBSSEMBBSM ffWoTg

Z

DEL21 •

DEL22(ray #)

DELTH = DYCFLG

DYFLAG:

FREQ: GLFLRG

ICCray »):

IND: JCCray #):

n ■■ I1AXRT:

HEXT!

HM: NODES(segment

HRS:

HRT ■

HT:

R(7 adiv;i * f

RPT '•

#,mirror #):

> 5

Twe ■'"' » )

program interpolated to the raytrace points Displacement at the QUASI-STATIC nodes Displacements from the fiUASI- STATIC program interpolated to the raytrace points Displacement of a node Flag uhich determines whether extrapolation coefficients for DYNAMIC extrapolation will be computed or read F = Computed T = Read Flag uhich determines formula for DYNAMIC computation Frequency of print output Global coordinate flag 1 = Convert to polar 2 = Read in polar 3 = Not needed in polar

(RUNTYP = 6) 4 = Used in rectangular I coordinate in the grid Ray identifier j coordinate in the grid Mirror number Maximum number of rays that will

be allowed Time or thermal load number of next print output Number of mirrors Number of nodes in each segment on STARDYNE tape Number of different radii in a

.•egment Number of rays Number of segments in each

mirror Number of time-steps or thermal

loads Number of different angles in a

segment Radius Radius of curvature Pointer to array of radii for ßUASI-STATIC interpolation Raytrace coordinate flag

7 7

1^^^^^™™"^^^™^"""^™^^^^^"«^»*^"'"*"*™™"™

1.

RTR: RTSEG:

RTTH: RUNTYP

SGNCmirror *)

T«

THETACangle *,segment #): THPT:

TOTMCray #)t UI0(ray #)•

KDYN(3,segment t,mirror t)

XRCray #):

XRTCray t,mirror #): Y: YDYN(3,segment #,mirror #)

YRCray #):

YRTCray #,mirror #): ZDYN( B.secrment #,mirror *)

1 = Convert to polar 2 = Read in polar 3 = Not needed in polar

(RUNTYP = 6) 4 = Used in rectangular Radius of the raytrace point Segment number of the raytrace point Angle of the raytrace point Deformation data from 1 = Suasi-static 2 = Dynamic 3 = Suasi-static and Dynamic 4 = fiuasi-static (from file) and

Dynamic 5 = Quasi-static and Dynamic

(from file) 6 = ßuasi-static and Dynamic

(both from file) Segment number Sign of the factor to be used in computing the total wave aberration Transmission constant (may only be 1.0 or 0.0) Angle Pointer to array of angles for ßUASI-STATIC interpolation Wave aberration (Wi) Nominal wave aberration (W0) X coordinate of node X coordinates for the three points which define a segment in the DYNAMICS program X-coordinate of the incidence point of the ray on the original reference sphere X coordinate of ray Y coordinate of node Y coordinates for the three points which define a segment in the DYNAMICS program Y-coordinate of the incidence point of the ray on the original reference sphere Y coordinate of ray Z coordinates for the three points which define a segment in

78

w*mm~~mrr*i*~Bm "■ • ■" UII.J.J

7

ZRKray *,mirror *) ZRCray t)i

$REUD2 i

the DYNANICS program Z coordinate of ray Z-coordinate of the incidence point of the ray on the original reference sphere Flag which is true if the interpolated quasi-static file is to be rewound and reread

79

„•■-,. ' * "-w. -^r^smmm

8. OPTICS

8. 1 PURPOSE

This program computes the point-spread-function of the deformed system and generates the line-of-sight and amount of signal energy reaching a detector element as a function of time in order to evaluate the optical performance.

8.2 TECHHICAL SUHMARY

The OPTICS subsystem computes the following:

• Pupil function, F

• Irradiance point-spread-function, I

• Ensquared power. P

for every a (field angle) in the system. These computations are performed for the:

• Nominal or disturbance free aberrations, W0 with respect to nomiral focus.

• Net wave aberrations. Mi (including time-history thermal and/or dynamic deformations) with respect to nominal focus.

• Net wave aberrations, WF with respect to a ntw reference sphere centered at a best focus for which the variance of the wavefront error is minimum.

For each time and field angle the followin'j are also commutedi

• Transverse and longitudinal defocus

• LOS error

• Average variation in the ensquared power for both Mi and MF.

The pupil function is computed as follows for M=M0(tf),

80

■■■■. ,

Ul(a,t), and WF(of,t) to obtain F0(a), Fi(a,t) and FF(of,t) respectively.

r i

F(u,v) = IEXP( (27ri/X ) M(u,v)l Inside Exit Pupil I I 0 Outside Exit Pupil I

where X is the optical wavelength.

The irradiance pojit-spread-function is computed as follows for F = F0(a), FiU:,t) and FF(a,t) to obtain I0(a), Ii(a,t) and lF(a,t) respectively.

I(x,y) = (1/X2R2) l//F(u,v) EXP( (-27r/XR) (KU+yv) Idu dvl2

where (x,y) is in the Image Plane and (u.v) is in the Exit Pupil Plane.

The above integral is a Fourier transform of the pupil function, and R is the radius of the reference sphe'-s.

The ensquared power of the PSF is computed as follows for I = I0(a), Il(a,t) and lF(a,t) to obtain P0(a), PiCa.t) and PF(ot,t) respectively.

P = f //I(x,y) dx dy

where the integration is performed over detector, and then normalised by a factor f.

the desired

The average variation in the ensquared power is computed as follows for P = Pi(a,t) and PF(of,t) to obtain APi(a) and APF(a) respectively.

(1/L) Z P - P0

t=l

The transverse and longitudinal defocus is computed as follows for rFtor.t) to obtain Ar(a,t)

I Arx I irr L

rFX - rx0 I rFY - ry0 I

Arz = rFZ - rz"

transverse

longitudinal

81

■ ■ ■ ■

The line-of-sight error (LOSCcr.t)) is computed from Ar(a,t) as follows:

LOS = (Arxz + ArY2)•5/f

whi»re f is the system focal length.

8.3 FEATURES AND CONSTRAINTS

A. Multiple field angles

B. Dynamic point-spread-function

C. Matrix of data points representing the pupil function must be a rectangle with dimensions equal to powers of two

D. Clear region of pupil may be y sire or shape and be placed anywhere in the exit pupil grid.

E. The detector must be square. It may be of any size and positioned anywhere in the image plane grid.

F. Multiple detectors may be employed, one at a time, to analyse tha data.

8.4 SUBSYSTEM ARCHITECTURE

The flew of the OPTICS subsystem is shown in Figure 8.1.

82

/ ■ ■■■■■■ : '

■Mi MW -

in c o

■f IS L C S £}

■ö < 10 ^- t) t) CK >

IS 3

« C g Q z

— _ J

c w o c ~ o

cok.ro o H- (1) k. ~ v> O-i. ■P C O 0) U (D £3 C k. 0) < 3 t- k. u. ro «)

W 3 > — (U er P3 — —«0 3

§-b , _ OT — Q. O 3 ß

ü- — C 1) 3 ~ W +> "D E 3 Irt O o

ig r z

c 0) o o — C -M <o o ~ c ■O 3 (S U. k. t -D w Cl

V C k. .- a (S v>

■M I .Q +- o c o o

+> a.

ES

k. k. 0) O 3

+» o 0 D. u

+> k. t) o b

k. v 01 -P > 0) o a

+> <u a tn D> O 1) -P

fg M (U

k.

■

+> (S Ik c

ID X) U < a u >

(0 3

in — 3 IS O i. coo — 4- k. •O OJ i. 3 O UJ

+« — 0) W D> in O C k. J O 0) -I >**

in o> »CO! +> ID

E A) OTJ

ID

in in w CD u o u _ o — o V. I- +"♦- 3 IS ID O 3 k. V u. IT i in

m u a) +> xi Ja in in < ID 3 k. u. _ |) «J

3 > +» -"B ra H- c o 3 ID " " . — *> i. +> Tl 0) O o c z ^ C ID V 3 C k. u. E O O

k. H- — O C « — t-OSi a m — 3 C4> k. a ID ID o

k. k.£ 0) I- 0) +> in a.— 3 o u

4) O

gc — o TJ — ID *>

Ü u.

C — "O ID ID

+> I» Si k. o a

in o I +> +» c r— *> o o a D

k. 0) O 3 ■P O u a 4> k. u o

y k. (U 0) V > 0) o o 0)+»

+> u ID 0)

0)0

ll

— —-• r 1 L

oi in K. 8 E "a 01 ^ — «3 n s- t~ O L. k. <

3 (DO) „ 1. I) — 5g?S " ID i a B o +5 E 0) o 0|» t w £fe J:^ k-X t-4> O-P Oh- o >t- in

c oi oi a> — +> ID CD ll B ID _ ■Ü 0 ■*!

01 XJ fi -ü &s 0 i a

1

a £ V) +> it o — o> i. c o <

CS 0) 4, —

01 Q:

Figure 8.1 Subsystem architecture

83

^J~~~~ ^

/

8.5 SUBROUTINE NESTING HIERARCHY

MAIN

INPUT

INPUTA

FILL I I FUNC I I CHOVER

FFT I I REVBIT

MAPR

OUT I I SOUT

INTSET I I INTEG

OUT1

DMOVER

BFOC

DMOVER

CROUT

ERSTOP

85

I .

I MXV

PROC

FILL I I FUNC I I CMOVER

FFT I I REVBIT

MAPR

OUT I I SOUT

INTSET I I INTEG

OUT1

8.6 SUBROUTIKE SUMMARIES

Bfoc computes best focus and variance.

Fill computes the functions for all sets of coordinates, and stores them in a two-dimensional complex array.

Inputa reads input which may vary with field angle.

Proc(MI.PK) subsystem executive for one set of wave aberrations (WI) either before or after best focus. The energy on the detector is added to that from other time periods in PK.

Erstop(N) prints error messages and stops if serious.

86

Func(ARG) computes and returns: (COS(ARG),i SIN(ARG))

Input reads invariant input.

Intejl(DJLTA,ANS,NIM.N,XCTR,YCTR) integrates a two- dimensional array (DATA) in the square extending NINT units in both directions from the point (XCTR^YCTR).

Xnts^(AlN'AM'MMUS'XCTR,YCTR,C) computes the radius of the square-of-integration and scales the results o± integration by C.

Mapr(CIN.ROUT,N,NPT) maps an NxN complex array into alternating elements of a 2xNxN real array by squaring the absolute value of each element and inserting it into the same position of a different quadrant as

follows: I <■--> IV II < —> III

Out(ANS,N) Outputs alternate elements of a 2xNxN real array.

Outl(P,N) outputs a linear array of length N.

0ut2(ANSrN,XCTR,YCTB.R) outputs the portion of an NxN array(ANS) lying within the square extending R units from (XCTRrYCTR).

Sout(JLNS.N) outputs the real single-precision portion of a complex double-precision vector(ANS).

8.7 USER INPUT «^PFrTFTCATIONS

A. FILE NAME: IN SOURCE: LOCAL

RECORD 1 : FORMAT: NAMELIST 'INI'

FIELD 1 2 3 4

TYPE R*8 R*8 1*4 1*4

NAME F LAMBDA N NALPHA

87

/ SW;- ' -■.:,:.;,.;.--.,■,,■,...,■. -;..,,,,„.;.,. ..;.,;

RECORD 2: FORMAT

FIELD 1 Z 3

NAMELIST 'INIA'

TYPE

1*4 1*4

NAME FREß FIRST LEVEL

RECORD 3= FORMAT:

FIELD 1 2 3 4 5 6 7 8

NAMELIST '^2'

TYPE 1*4 1*4 1*4 1*4 1*4 1*4 1*4 L*4

NAME NT xos YOS R OPT NIN NR WO

RECORD 4 FORMAT NAMELIST 'IN3'

FIELD 1 2 3 4 5 6

TYPE R*8 R*8 R*8 R*8 R*8 L*4

NAME NP R1 XP YP ZP $DELP

There is one each of Records 1 and 2. One record each of types 3 and 4 are required for each field angle.

B. FILE NAME: FIL5 SOURCE: LOCAL

RECORD 1: FORMAT:

FIELD 1 2 3

(3D20.12) TYPE NAME R*8 R*8 R*8

DELPC 1) DELP(2) DELP(3)

88

.

There is one Records 1 for each time at each field angle

8.8 TNTERNAL STORED DATA BASES

A. FILE NAME: FIL1(unformatted) SOURCE: INTERFACE

RECORD 1 : FIELD TYPE NAME

1 1*4 NRT 2 1*4 IR( 1) 3 1*4 JCM) 4 R*8 UI0( 1) 5 R*8 XR( 1 )

6 R*8 YR( 1)

7 R*8 ZR( 1) R*8 .

R*8 . R*8 1*4 IR(NRT) 1*4 JC(NRT)

R*8 WIO(NRT)

R*8 XR(NRT) R*8 YR(NRT)

R*8 ZR(NRT)

RECORD 2: FIELD TYPE NAME

1 R*8 WI( n • R*8

R*8 •

,. R*8 ,

N RT R*8 MI(NRT)

One record of type 1 is required for each field angle must be followed by NT records of type 2.

This

B. FILE NAME: FIL2(unformatted)

RECORD 1 : FIELD

1 TYPE R*4 R*4

NAME DATASfiC1,1)

89

- "-^ -_■' ■

N R*4 R*4

R*4

R*4

DATASß(N, 1 )

DATASß(M,N)

If OPT is 1 or 2, then the number of records produced is NT^NALPHA+1. If OPT = 3, then the number of records produced is 2«NT*NALPHA+1.

C. FILE NAME: FIL3(unformatted)

RECORD 1 = FIELD TYPE NAME

1 R*8 ELOS

The number of records produced is NT*NALPHA

D. FILE NAME: FILU(unformatted)

RECORD 1 i FIELD TYPE NAME

1 R*8 P(1) , R*8 . . R*8 . , R*8 .

N R*8 P(N)

If OPT is 1 or 2, then the number of records produced is NR*(NALPHA*NT+NALPHA+1). If OPT = 3, then the number of records produced is 2*NR*(NALPHA*NT+NALPHA+1 ) .

8.9 PLOTTING OUTPUTS

A. A Point-spread-function for each time step.

B. Time history of line-of-sight errors.

C. Time history of ensquared pouer for each detector.

90

-

8.10 GLOSSARY

DATASß(N,N) DELP(3)f

F: FIRST: FREß: IR(ray #)> JC(ray #):

LAMBDA: LEVEL:

N:

NALPHA NIH:

N?: NR: NRT: NT: OPT:

R(radius # ) • R1 : WKray #) ' WlOCray #): WO :

XOS(radius »)

XP: XR(ray #)■

YOSCradius #)

YP: YRCray t):

Point-spread-function Displacement of best focus point from the old reference point System focal length Time-step of first printout Frequency of print output I coordinate in the exit pupil grid j coordinate in the exit pupil grid Optical wavelength Amount of printout desired 1 - Minimum 2 - All except mod2 data 3 - All Size of the exit pupil grid (must be a power

of 2) Number of field angles Grid size of the portion of the exit pupil containing rays Index of refraction in the image space Number of radii to be used for integration Number of rays Number of time-steps or thermal loads Run type option 1 - Use wave aberrations as read 2 - Use wave aberrations after best focus 3 - Use both wave aberrations 14 - Use neither; compute best focus only Energy on the d«tector Radius of detector Radius of the original reference sphere Wave aberration at each time-step Nominal wave aberration Flag which determines whether to bypass reading wave aberrations (use only nominal when true) X-direction offset of the center of integration X-coordinate of the old reference ray point X-coordinate of the incidence point of the ray on the original reference sphere Y-direction offset of the center of integration . Y-coordinate of the old reference ray point Y-coordinate of the incidence point of the ray on the original reference sphere

91

ZP: ZR(ray #)

*DELP:

Z-coordinate of the old reference ray point Z-coordinate of the incidence point of the ray on the original reference sphere Flag which determines whether the displacement of the best f' sus point from the old reference point will be computed or read F - computed T - read

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SAMPLE TEST CASE

9. 1 NQDEL DESCRIPTION

A sample problem is presented to illustrate the flow of data through the different modules of the simulation. A simplified model of a typical large space structure is used. This system, shown in Figure 9.1, contains three mirrors. The primary and tertiary mirrors each have one segment and the secondary mirror has three segments. The mirror support structure is made up of graphite epoKy hollow tubes. A finite element model was created and analysed using NASTRAN in order to determine the natural frequencies and mode shapes of the stru bure. These are listed in Table 9.1. The system was subjected to a dynamic disturbance on the secondary support truss and analysed using the DYNAMICS, INTERFACE, and OPTICS modules. The local input to the DYNAMICS module is shown in Tables 9.2 and 9.3. The local input to the INTERFACE and OPTICS modules are shown in Tables 9.4 and 9.5 respectively.

The output of the system illustrates the degradation of the image due to the system disturbances. Plots of the nominal point-spread-function and the point-spread-function at 0.0040 seconds are shown in Figure 9.2.

The CPU time and storage requirements of each module are listed in Table 9.6.

93

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w

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m M 3

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■P W

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• • • A • >

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94

•

Table 9.1 Natural Frequencies and Mode Shapes

Mode Freq(Hn) Description

1 - 6 0.0 Rigid Body

7 43.96 \ Bending 8 44.08 / of 9 65.45 > Secondary

10 73.90 1 Mirror 1 1 73.92 '

12 98. 13 Torsion

95

Table 9.2 Dynamic local inputs

Computer Input Value I Defi nition

MD1 N16 MNRtll

NNAM1

NORMS

6 13

7,8,9,10,11, 12

1,2,3,4,5,6, 7,8,9,10,11,

12,22 TRUE

I No. of odes iNo. of nodes iMode numbers to be I used in analysis iNode numbers to I be used in I analysis iFlag to indicate that normals at I mirror support points follow

4 4152 0 4152

7 1687 1687

-0.3375 10

, 1687 3375 1687

9 1687 3375 1687

1 0 0 0

12

11

0 0

-0

-0 -0 0

0 0

-0

0 0 0

0 0 0

6 .7193 .8303 .7193

8 .2922 .2922 .0

12 2922 0 2922

10 2922 0 2922

3 0 0 0

999

-0.5573 -0.5573 -0.5573

0.9413 0.9413 0. 9413

0.9413 0.9413 0.9413

0.9413 0. 9413 0.9413

■I .0 1 .0 1 .0

96

Table 9.3 Dynamic local inputs (continued)

I Computer I Input I IPSI1P I TO ITOPT t DTOPT ITF ITPRINT I DTPR'tT ICNTL I ATT 1DTP IPOI I OMEGA 1 INDIS1 IIDIS1

1 IITUP1

Value Definition

6* 005 0 0 0016 024 0 ,0016 FALSE FALSE 0.0008 0.5

464.32 1

22

Damping Ratio per mode Initial time Initial time to output to file Time interval for file ouput Final time Initial printout time Time interval for printout No structure control present No attitude control present Plant time-step Amplitude of forcing function Frequency of forcing function No. of disturbances present Node number indicating where

disturbance should be located Degree-of-freedom where

disturbance occurs

97

•

Table 9.4 Interface local inputs

Computer Input Value Definition

NN 3 No. of mirrors MAXRT 12 No. of raytrace points NODES 5*4 No. of nodes used to define

each segment NSEGS 1,3,1 No. of segments in each mirror GLFLAG 1 Convert segment definitions to

polar coordinates RTCFLG 1 Convert rayTrace data to

polar coordinates RUNTYP 2 Type of input-' 2 = Dynamics NT 15 No. of time-steps on input file FRES 1 Frequency of printout NEXT 1 First time-step to be printed SGN 3*-1 .0 Sign of factor for total

uave aberrations L J

98

■

Table 9.5 Optics local inputs

r

I Computer 1 1 I Input 1 Value 1 Definition

i — I |

IF 1 -10.0

1 — ISystem focal length

ILAMBDA 1 1.0E-6 ISystem wavelength

IN 1 64 ISize of Detector

INALPHA 1 INO. of field angles

IFRE'2 1 iFrequency of printout

INEXT 1 iFirst time-step for printout

ILEVEL I

3 iLevel of output: I Level 3 = PSF for input wave

! I aberrations and best focus

INT 5 INo. of time-steps

IXOS, YOS 0.0, 0.0 lOffsets for center of integration

IR 1 llntegration radius

INR I 1 iNumber of radii

ININ 1

1 5 jRaytrace grid size I in each direction

IWO I FALSE iRead nominal wave aberrations

IR1 1 -5.33 1 Radius of the reference sphere

|XP,YP,ZP

I

10.0,0.0,-5 33 [Coordinates of old reference 1 ray point

99

NOMINAL DEFORMED

t = 0.004 s

Figure 9.2 Plots

100

Table 9.6 CPU time and storage requirements

Time (sec)

Storage (K bytes)

I DYNAMICS I INTERFACE I OPTICS

1 .40 2.31

36.291

1 12 144 172

1 The PSF uas calculated for nominal and best focus at each time-step.

101