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Honeywell REFERENCES STRUCTURED UNCERTAINTY J.F.P 1/26/8
ANALYSIS
Refercncr
[I] J.C. Doyle, k t m Notes, 1984 ONR/Honeywell Workshop on Advrncea in Multivariable Control
121 J.C. Duyle, 'Analyrir of feedback system with structured uncertainty,' I&E Pmcudinpr, Part 0, v129, No. 6, Nov., I982
131 J.C. Doyle, J.E Wall, and G. Stein, 'Performance and r+ burtneu analyiu with itnxtured uncertainty,. I982 CDC
141 J.C. Doyle,'Syntheau of robust controllem and fiItemlm 1983 CDC
[SI C.C. Chu and J.C. Doyle, 'On inner-outer and rpect-I fac- torirationr,' 1984 CDC
161 C.C. Chu and J.C. Doyle, T h e g e n d dirtvlce problem in ff- rynthais,' 19s CDC
17l I.M. Homwitr, Syntihcrw of Feed6ack Syrtcmr, 1963 181 C . Zacna, 'Feedback and optimal renaitivity: model d e r -
ence traadocmationr, multiplicative seminorms and approx- imate inverses,' IEEE %nr. Ado. Control, AC-26, 1981
[9] C. Zama a d B.A. Ran&, 'Feedback, minimu sensitivity, and optimal rohuatnaa,' I&&E Itom. Auto. Control, AC- 28, April, I983
'
(101 K. vkiyuagar, to appear [I21 CL Z u n a , 'On the input-output rtability of sonlinear t i n e
varying feedback rydcmr, p a r b I urd-n,. I&&E 7bans. Ado. Contd, AC-11, 1966
(131 J.C. Doyle and C. Skin, 'Multivariable feedback design: comccpta €or-% ckricrl/modun rynthair; L&E& h n r . Ado. C d d , AC-26, Feb., I981
[I41 M. Fan and A. Tit.,'Ch-teriration and efficient compu- tation of the r h c t u m i r i g u l u value,' rnbmitted to I&&E Itam. Ado. C o n t d
[IS] M.G. Safouor m d J.C. Doyle, '.Minimiring conaeemtivenesa of robutnew aiagulu valua,* in S.C. Trefatu (ed.), Mal- tivariable C d d , 1984, D. Reidel Publishing Compaay
1161 D.C. Youla, HA. Jabr, and JJ. Bongiorno, Jr., 'Modern Wiener-Hopi daign of optimal controllen: Part IT, IEEE 12tanr. Arb. Contmf, AC-21,1976
[ I l l C. Davis, W X Kahn, and H.F. Weinbcrger, .Norm- p r d n g dilatioas-and their applicatioaa to optimal e m r bounds,* SIAM J. Num And., 1982
C k q ' U opts Hankel-nom rppmximationr of lin- e= m a l t i d a b l e ryrtemr and their L'-emr bound*,' Int.
[lo] M.C. Sdoncn,'optimrl diagonal wrling for infinity norm
[W J. Corlrd, 1984
ophairatmn,' l96S ACC
HONEY
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1 PI - Frequency (rrd/sec) 1 IC
Nu-Plot For 10% Uncertainty In Three Modal Frequencies
* Shows System Stable With Up To 4.54% Uncertainty On Modal Frequency.
1 /2.2 * 10% = 4.54%
J.F.P. 1 /29/€
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I-
L. ;, ' * ORIGINAL PAGE Ts
OE: POOR QUALITY ~
P- D a t e : .' F e b r u a r y 24 , 1986 c c : H. C i e l d e r l o o s c : (0 To: - J .F .L . L e e
J . Y e i c h n e r R . P l a t u i e n k o N. M c S u t r e
F r o m : M.;. K a i n d l i+ :
C . s u t l J & C t : S c o c h % s t l c C r e w ruil: l t lon N o ~ e i s F o r F i e x l b l ~ S p a c e S t a t i o n u R e s p o n s e A n a l y s i s
I-
t-:
R e f e r e n c e : I . " H z n l ? t ~ o k o n A s t . r o n a u t C r e w M o t i o n D i s f u r b k n c e s fo ' r r' 8..
i,' C o n t r o l S y s t e r n U e s i g n " , &&.SA R e t ' e r e n c e B u b l i c z t i o n 1025
.- ..
CI-.
j::
Two s t o c h a s t i c c r e w m o t i o n d i s t u r h a n c e m o d e l s w e r e y e n e r a t . e d f o r u s e i n f le:.;; t t l e S p a c e S t a t i o n respl :~n;e a n a l y s e s . T h e m o d e l s a r e c o n s e r v a t i v e , s i r n p ! e , a n d r e p r e s e n t a t i v e , b a s e d o n d a t a p r e s e n t e d i n r e f . 1. T h e F i r s t rf7i;del r e p r e 5 e n t s B h i g h : + v e l c r e u m o t i o n u h i r h e n c o r n ; ~ ~ ~ s e s i i i i c r e w a c t i v i t i e s . T h e d + t a u s e d t o c h z r a c t e r i z e t h e a c t i v i t i e ~ t o tie r e c u g n i z e d as h i g h l e v e l i s g i v e n i n r e i . . 1 u n d e r
Eow i n g M o t I o n Arm F i a p p i n g C r o u c h a n a P u s h o f i S o a r I n g - -
O n e - m a n hiorma1 iSne-man F o r c e f u l T w o - m a n N o r m a l T w o - m a n F o r c e f u l
The.seccrnd m o d e l r e p r e s e n t s c r e w m o t . i o n w h i c t r i s r e s t r i c t e d - t o i n c l u d e
i n r e i . 1 t o c h a r a c t e r i z e t h i s l o w l e v e l a r e 65 o n i y l o w ! e v e 1 a c t i v i t i e s . ~ t t e a c t i v i t i e s s e ~ e c t e c ~ f r o m t h o s e a n a ~ y z e d
i :.
C o n s o l e C i g e r a t i oris ice s p i r a t i o n, .Arm M o t i o n L e 3 M o t i o n a d a y i rig M o t i o n
Co u g ! I i 173, Sn e c 2 i n 3
.-
~ :a ~ t : t i i e ~ G e n e r a t i o n :
A . T h e f o l i o w i n g c r i t e r i a w e r e u s e d i n s e l e i t ; n ~ t .he c r e w s o t l o r i r i i o d e i s . ,e L.;*
c"
c:
c
c ' - .
w h e r e s i s t h e L a F ' l r c e v z r i a h l e .
2 . T h e - m o d e l m u s t b e c o n s e r v a t i v e , w i t h t h e m o d e l ' s PSI) a t l e s s t a s s t r o n g a s t h e PfD b e i e g a p p r ~ ~ i ~ ~ i a t . & + b , a t a l I f r e q u e n c i e s .
3. T h e m o d e l mus t . b e r e p r e s e n t a t i v e , w i t h a Psi) as c l o s e t o t h e FSD b e i n g a p p r o x i m a t e d a s p o s s i t l i e w i l i l e s i i i I s a t i s f y i n g c r i t e p - i a 1 a n d 2 .
4. T h e t i m k h i s t o r i e s o f t h e r r o d e i r r i us t t i E v e m r t ; p e z k ~ s i r n i l a r to t h e i i ) l : f ; l eaks o i t h e d a t a p r e s e n t e d i n r e f . 1.
c: 3. M e t h o d o f S e l e c t i n g a P o r e r S p e c t r a l D e n s i t y t o W o l r e l
T h e PSU t o h e r n o d e l i e d i n e a c h c a s e was c h o s e n by t r k i n g t h e m a x i m u m PSI) v a l u e o v e r a l l t h r e e a x e s , f o r a l l a c t i v i t i e s i n t h e s e t , a t e a c h f r e q u e n c y .
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ORIGINAL PA-GE Ts OF POOR QUALITY
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$ TYPE DESIGN.COH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P I "OLE "OPT I HAL" CONTROLLER DES I GN COtlHAHD F I LE
$! I NPUTS : * $! *
KP KP*KRI ----> lPS.D l KP PORPORTIONAL IPS GAlH * ----> IPS,D2 KR IPS RATE GAIN *
$! ALPHA ----> LOS PENALTY FUNCTION URLUE * f i fKP]
$! R --0- > CONTROL EFFORT PENALTY UALUE * $! RHO ----> D I STURBANCE/NO I SE UE I GHT I NG FUNC, * $! * ............................................................. $ I $! $! THE CLOSED LOOP IPS CONTROLLER S ! $flPY POF3YJ3,B IPS,Dl TEtlP $flPY TEflP POF3YA,Cl TEHP $SUBT POF3YAI A TEtlP PLT-I P S A , A $MPY POF3YA, B IPS, 02 PLT-I P S J , B $! $! $! THE CLOSED LOOP IPS COHTROLLER $! SnPY POF3Y.B IPS.01 TEHP $flPY TEnP POF3Y,C1 TEtlP SSUBT POF3Y, A TEflP PLT-I PSI A $HPY POF3Y. B I PS , D2 PLT-I PS , B
dr $ 1 $! UHERE THE COST FUNCTION I S S ! $! J INT O->OO ( X " BETA" * ALPHA * BETA X)+(X"*ALPHA*BETA*U)+(U"*R*U) dt $! $! INPUTS: (1 1 SYSAAHE. A $! $! (2) SYSSSFlHE , B $! $! (3) SYSJJAtlE,HC ---> Q HATRlX STATE "x" UElGHTlNG tlATRlX
$! $! (4 ) SYSAAHE,HD ---> R HATRIX : CONTROL "u" UElGHTlHG M T R l X $! R = r $COPY R,DAT PLT I P S A , H D $L GN PLT-IPSA- $ H h PLT-I P S J , B PLT-I P S J , KC TEHP SSUBT PLT I P S A , A TEllP TEtlP $EIG TEtlP- $RENAME TEHP . E REGULATOR E SR I FD REGULATOR. E $! $!
* * * p
GENERATING THE REDUCED ORDER PLANT EQUATION UHlCH INCLUDES
GENERATING THE PLAHT EQUATIOH UHlCH IWCLUDES
GENERATING THE REGULATOR GAIN tlATRIX Kc
$! Q= ALPHA*~ETA
SnPY FILPHA BETA PLT-I PSA. HC
GENERATING THE KALHAN FILTER GAIN tlATRlX KO 8 I NPUTS : ( 1 )SYSAAtlE, A
$! (2)SYSNAHE. C
'3' 1' ' = S Y S J I I IEsU1 'DISTURBflNCCE PENflLTY FUNCTION'
( 4 1 R = SYSNAflE . U2 " flEASUREflENT NO I SE PENALTY FUNCT I ON"
DlAG 7 RHO G)
$! $MPY GYK RHO TEflP SD I A TEflP PLT-I P S A . U1 $KF I LT PLT-I P S A $flPY PLT-I P S A , KO PLT-I P S A . C TEHP SSUBT PLT 1PSA.A TEflP TEflP $EIG TEflP- SRENAflE TEflP e E KALflAN .E SR I FD KALtlAN . E S! $! $! $! $! $SCL PLT-1PS.B TEtlP -1 , O
GENERATING THE CLOSED LOOP SYSTEfl "Acl " flATRlX AND CHECKING FOR STABILITY BY FINDING ROOTS OF THE CLOSED LOOP "Acl" flATRlX
$MPV TEflP PLT-I P S A I KC TEf lP l2 SflPY PLT-I P S A . KO PLT- I PS e C TEflP2 1 $flPY PLT- I P S A B PLT-I P S A . KC TEtlP22 1 SflPY PLT- I P S A I KO PLT- I P U . C TEflP222 $SUBT PLT-I P S J I A TEflP221 TEflP SSUBT TEflP TEflP222 TEHP22 $! $! SAUING THE Y-AXIS CONTROLLER
OPY TEflP22 I DAT CONTROLELY. OAT I G TEflP22
$R I FD TEflP22. E $RUG PLT,IPSsA TEflP21 TEflPl 0,l SAUG TEt lP l2 TEflP22 TEflP2 0 , l $RUG TEflPl TEflP2 ACL , A 1 ,O SEIG ACL,A f R l F D RCL,E SOEL TEMP*. * , * S! $I S! S ! $SCL PLT-1PS.B TEflP -1.0 $MPY TEMP PLT- I P S A . KC TEHP 1 2 SllPY PLT- I P S A KO C J L , C TEflP21 SflPY PLT- I P S J i . B PLT- I P S A e KC TEflP221 $flPY PLT- I P S A I KO PLT- I P S A e C TEflP222 SSUBT PLT-l P S J i . A TEflP221 TEnP $SUB1 TEIP TEflP222 TEflP22 $AUG PLT-I PS I A TEtlP21 TEflPl 0,l $RUG TEflP12 TEflP22 TEflP2 0,l SAUG TEtlPl TEHP2 A O U O S , A 1 ,O $CON TEflPl 10,1,0 SnPY PLT-I P S J I KO BDELTA TEflP2
GENERATING THE OPEN LOOP LOS SYSTEfl flATRlX " A O U O S "
&L TEflP2 TEflP21 A 4/P EL TEflP2 TEflP22 A 5 L TEflP2 TEflP23 A 6
DO TEHP21 TEllP22 TEflP2 SAD0 TEflP2 TEflP23 TEflP2/P
$RUG TEtlPl TEtlP2 A O U O S , B 0 , l SSEL PLT-IPS,C TEtlPl 4 A SSEL PLT-1PSJ.C TEHP2 4 A a UG TEtlPl TEtlP2 A O U O S , C 1,0 $DEL TEtlP* , * , * s
CL TEtlP2 TEtlP2 0,O
S TYPE ANALYSISaCOfl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ii* * P I "OLE ANALYS I S COflflAND F I LE
FUNCT I ONS : $!* , S ! *
3: ti: $!* $!* $! * $I* $!* $!* $! * $!* $! * $!* $!* $! * $!*
( 1 1 CREATES CLOSED LOOP STOCHASTIC T l f l E RESPONSE DATA
(2) CALCULATES flu FOR UNCERTAINTY I N FREQUENCY * * * * * * * * *
(3) C~LCULATE THE OPEN LOOP FREQUENCY RESPONSE * FROfl LOS command ---> LOS sensed
I NPUTS : * * ( 1 ) K, ZETA, OflEGA ---> CREU HOTlOti SHAPPING
FILTER COIF I C I ENTS
$!* (2) AflPLlTUDE ---> CREU HOTION DIST. AflPLlTUDE * $!* * $!* (3) ACL,A,B,C ---> CLOSED LOOP SYSTEfl flRTRIX * S!* * $I* $!* SI *
* * * * 4: * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . si $! $! $COPY [ P I NHOLEA, HBU D ] A O U & , * *, * $!SCL R 0 U O S . C A O U 0 S . C - 1 , O $PACK A O U O S A O U O S $FRESP A O L L O S 0 a 001 j lOOj50 $! $! $! CREU IIOTION $! $COPY P I NHOLEA. HBU . D ACL, A *, * $COPY P I "OLEA . HBU , 0 1 PLT-I PS , * * , * $CON TEflP31 2,8,0 $Con TEflP32 2,6,0 $COPY [ P I NHOLEA, HBU I DIGZ, OAT *. * $tlPY GZ DIST,C TEflP13 $CON TEMP23 6 2,O SAUG TEHP31 T h l P 3 2 TEtlP2 1 ,O $RUG ACL,A TEflP2 TEflPl 0,l $RUG TEf lP l3 TEtlP23 TEMP2 0 , l $RUG TEtlP2 DIST,A TEflP2 0,l $RUG TEtlPl TEflP2 S Y S D , A 1 , O
UG TEflP 0 I S T . B S Y S J , B 0 , l ti TEHP 4,8 0
SAUG PLT-IPS.6 TEflP S Y S D , C 1,0 SPACK S Y S D S Y L D
GENERATING THE FREQUENCY RESPONSE FOR OPEN LOOP LOS
GENERATING THE CLOSED LOOP T l f l E RESPONSE TO STOCASTIC
GN TEMP 14,1,0
- _
STHIST S Y S D 4OJO.01 JO.O1
f ! $COPY P I NHOLEA I HBU, DIACL. A *, * $COPY E P I NHOLEA .HBU. DIPLT-I PS. * * .* $CON TEtlP31 2,8,0 $CON TEtlP32 2,6,0 $COPY P I NHOLEA HBU , DIG2 . OAT * . * $nPY G2 DISTH,C TEtlP13 $CON TEMP23 6,2,0 $RUG TEtlP31 TEtlP32 TEtlP2 1 ,O SFIUG ACL F1 TEtlP2 TEtlPl 0,l
$RUG TEtlPl TEtlP2 SVSDH,A 1 ,O $CON TEMP 1 4 , l J O
$AUG PLT-IPS. C TEMP SYSDH, C 1 ,O $PACK S Y S D H S Y S D H $THIST S Y S A H 4Oj0,01,0,01 $! S ! $I SI $COPY S Y S D H I OAT SYS-XO I OAT STH I ST S Y S A O 25,O. 05 0 . 0 1
GENERATING THE CLOSED LOOP T l t l E RESPONSE TO STOCASTIC CREU MOTION "HIGH LEUAL" ----> DlSTH 1M
SAUG TEMP13 TEtlP23 TEtlP2 081 $RUG TEtlP2 0ISTH.A TEtlP2 O j 1
$RUG TEMP DI STHeB SYSDHeB O j 1 $CON TEtlP 4,8jO
GENERATING THE CLOSED LOOP STEP RESPONSE TO FOR THETAips =,5 degrees and n l - 2 degrees
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