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0 P VIHDETT BSo(Bng), D P h l l » J 0 FLOWER B3o(Eng), PhD, M I E E , CBng*t Ats-tract Thora l p a n I n c r e a a l n ^ n e e d to produce B i o a l l - a l g n a l c o n t r o l n o d e l s o f a h l p a behaviour I n r o l l a n d yaw I n ö r d e r to f a o l l i t a t o the b o t t e r dealgn o fa t a b l l i a a t i o n and s t e e r i n g syotema. T h i a p a p u r d i a c u s o e s a method o f ayatem i d e n t i f i c a t i o n u s i n g pseudo-random b i n a r y oecpjonco t e c h n l q u e a . Thoae
teohnlques a l t h o u ^ a p p l i e d with some Gucoeas i n r e c e n t y o a r s a r e not well-known i n the marine i n d u s t r y and so aoma n e o e a s a i y baokground f o r t h e i r a p p r o o i a t i o n i a given h e r o . P r a c t i c a l l y t h e i r advantage i s t h a t the p e r t u r b a t i o n needed t o d i s t u r b the ayaton under i n v e s t i g a t i o n need be s m a l l . S m a l l p e r t u r b a t i o n s Imply t h a t " l i n e a r i B a t i c n " c o n d i t i o n s a r e more n e a r l y mot. A d d i t i o n a l l y , i t i s shown t h a t w e l l - p l a n n e d ezporlnontB may bo performed q u i c k l y and w i t h minlmua of t r i a l s equipment. To domonatrate t h e i r use an a p p l i o a t i o n to the measurement of the r o l l dynamios o f a s h i p i a g i v e n . Tho method u s e d i a dlaouBsed a l o n g with the r s B u l t s of the expeiMment.
1.- ^Introductioa
An e v e r i n o r e a s i n g raqulremant e z i e t s f o r b e t t e r performance o f s h i p ' s ooureo keeping a n d s t a b i l i B a t i o n systems. I n o r d e r t o d e s i g n c o n t r o l aystems to M e t t h i e neod b e t t e r c o n t r o l ' modola o f s h i p s a r e r e q u i r e d . Such B M d e l s can ba d s r t v e d from tho hydrodynamic e q u a t i o n s , from t a n k t e s t a on modela, o r from a c t u a l s h i p t r i a l s , A l t h o u ^ aaoh approooh has i t s advantages and d i e -advantages t h a l a a t method, I n g e n e r a l , p r o v i d e s d a t a from whloh models oan be b ^ h ^ v i t i r " * * * confidence o f t h e i r a c t u a l r e p r e s e n t a t i o n o f the ahlpa
Ship t r i a l s , however, are expensive and t r t a l s time i s u s u a l l y a o a w e , thua a aolhod of i d e n t i f y i n g tho system r e q u i r i n g minimum i n s t i u m o n t a t i o n and a a h o r t A i r i t l o n t r i a l l o sought. Covontional t a s t s u s e d on s h i p t r i a l s i d e n t i f y o p « o . n o paranetera and a comprehensive s e t r e q u i w a oonaidarable time, honoe *n a i u m a l l v e approach must be sought.
^ r . ' w . n c y - d o a a i n technlquea u s i n g a T r a n a f o r F u n c t i o n A n a l y s e r ( T P A ) have b . . r -MM to produce miocoaaful r e s u l t s but a g a i n the t r i a l s time l a long
. '°"-''""I"on''y oe-iaureoonta a r * needed and i n tha p r e a . n o o o f * ^ ; * " ™ « however hae g r e a t advantages. J f c T ' - ü r l A t !!Ü ^ ^ ' ' " ^ • U o w i n g erroneous r f n u l t a t o be Z l JwtT, r r « q u . n o y ^ o a » l n r . p r . . o n t a t l o n I s moat e a s i l y used I n model
JT
h .^' *
1t ^ ' ^ ^ f " T f
r » < ? u l r . d can lead to U r g e output d l a t u r t a n o e e-.^ ^ ^ " f r r * "
' • ' ' ^ ' l ^ " TwAnn n o i M input* have been d e - « M > « < l . ' t . . - « i > . ^ t • t , « » i . » « . It, a,f>»r«,; \ha I«i>iiii4 I I M f u r Ih*»* M~ * - ' » - « l 't < u » i i . 4 » ^ . « . . * . Pn^im, VK Tha
^ ' ^ ' ' O ' o t o i l u m « o o r S c h o o p 8 h y d r o m e c h a n f e « M e k e l w e g 2 . 2 6 2 8 C D D e H I V E R T I C A L H E A D I N G R E F E R E N C E REFERENCE 1 \ F I H S I R V O S
RUOOER
SEBVOS
DEHODULATORS
J
I
C O N O I T I O N I N C A M P L I F I E R S/
C H A N N E L CORI C O R R E L A T I O N S E L E C T I O N P . R . B I S . G E N E R A T O R C R O S S C O R R E L A T O R ANO D I S P L A Y A N A L O G U E T A P E R E C O R O t R yPEM-l 9 p.Ukti PERTURfiATIOH C H A N N E L S E L E C T I O N — y * ' ^ " ^ e o , > , v M r . c y r o R ^ , r o Y . A M , . . . » ,are r e l a t l v o l y short exoopt f o r tho methods whloh produoo vory simple out-puts (og Dtop-reuponns) oomputor proooBBlng i s r i q u i r e d to obtain tho r e s u l t a .
An i d e a l t e s t i n g toohnlque would require a short t e s t i n g time, have a hig}» noiaa immunity, provide immodiate repulte to ohook the B U O O B B B o f the t e s t , and aleb p r o v i d i n g e ; r t e n B i v e infonnation about the aystem t e s t e d . T h i s paper attempts to show how tho i d e a l oan bo approached by tbe use of time-domain toohniquos baaed on pooudo-random b i n a i y sequence e i o i t a t i o n of the ship responee and a oombinatlon of immediate and longei^torm p r o c e s s i n g techaiquea. The use of one of the methoda io demonstrated by the measurement o f tho r o l l dynamics of a s h i p .
2 . Ounoral Phtlotiophy
The i d e n t i f i c a t i o n method oeto out to produce data ouitable f o r generating s m a l l - s i p i a l l i n e o r models of tho eystom. I t l a oonsidsred t h a t at l e a s t impulse and frequency responao p l o t s should r e s u l t from the measurements. The neamireaenta oust be teken with s m o l l - s i g n a j disturbanoee and,as a l r e a d y s t a t e d , the t e s t s should be ohort. During t e s t i n g i n anything other than an i d e a l f l a t calm s e a there w i l l be a measurable noise dieturbaaoe introduced by the s e a s t a t e .
Techniques based on the paeudo-random b i n a r y e i ^ i a l aa a p e r t u r b a t i o n method meet the requirements and a l s o o f f e r reasonable noise r e j e c t i o n . I n these mothods t h o pseudo-random b i n a r y s i g n a l l a applied to the system input, whloh i n the case here oan be the rudder o r the b t a b i l i s e r f i n a , and the response i s moaaured at the output which here w i l l be the s h i p ' s head o r the s h i p ' s r o l l .
I n order to provide s u f f i c i e n t d a t a f o r ship c o n t r o l models i t i s neceasary to take meaaurementa of tho rosponae of tho ship i n r o l l and i n yaw when t h e rudder l a perturbed and a l s o the reaponse i n r o l l and i n yaw to a t a b i l l B e r p e r t u r b a t i o p a ,
Tho measuremento can ba analysed i n a v a r i e t y of ways to produce the required rosponaea. Simple o r o a s - c c r r o l a t i o n of the input and output oan be used to produce tha impulse rooponoe and tha aqaipaant r e q u i r e d f o r t h e
anolyBls l a r e l a t i v e l y olraplo. The methods that muet be used to produce t h * frsquenoy response from t h i a data or to produce a l i n e a r t r a o s f e r f u n c t i o n
g e n e r a l l y r e q u i r e oomputor prooesBlng. 1 I t i s d e s i r a b l e to havo an iomadiate check cn a t o s t ao that a t r i a l I s not
wftated due to say a malfunotioning tmnaduoor o r aa i n c o r r e c t l y a e t s w i t c h . While with the expense of t r i a l s i t I B a l s o deoirablo to e x t r a c t the maximum information from the d a t a .
Both these objeotivea can be net u e i n g pseudo-random b i n a i y s i g n a l methods as, due to the B i m p l i o i t y of o r o s s - o o r r e l a t i c n techniques, these oan be c a r r i e d out on board while tho data l a a l s o recorded on moanetic tape f o r f u t u r e ooBiwter proceBBlng. The equipmont r e q u i r e d i o minimal and a t y p i c a l con-f i g u r a t i o n BB shown i n con-f i g u r e 1.
The pseudo-random b i n a r y s i g n a l generator i s used to perturbate the rudder-servo and then the f i n - s e r v o . During eaoh t e s t the response of the ship i n heading and i n r o l l i s recorded f o r computer p r o c e s s i n g . The o r o o s - o o i r a i a t o r i o used to c a r r y out immediate impulse response generation to v a l i d a t e that no gross e r r o r s i u the t e s t a have occurred.
The paoudo-rwdora M n a i y elgnol i s a p e r i o d i c telegraph s l g n o l that haa - i t h l n i t s period tha property of random n o i s e . The s i g n a l i a aimple to ,7onerate hy a o h i f t - r o g i s t e r and modulo^two foedhaok. The a u t o - o o r i a l a t i o n function and a t y p i c a l sequonoa i s shown i n f i g u r e 2 . Tho a u t o - o o r r o l a t i o n Junction i s given by
«X ( t ) - a ' ' j l - M T j f o r - A t < r < t ( 5 a )
( r ) - - a ^ A f o r A t « r « ( i J - l ) A t — ( 5 b )
r/'ti!
the pseudo-random binary a i g n a l a m p l i t u d e , Zl t the b i t p e r i o d andL ™ ^ ^ ? »
f v * ^ ' Boquenoe. I f tho s e q u e n c e i s o h o s e n such t h a t A t i s s m a l l3 e ^ t w t J ^ " "ï^^ " ' ^ J i ' ^ ' . r ' i ' ^ * °^ t e s t a n d H A t U
g r e a t e r than the s e t t l i n g tijns t h e n fl ^ a p p e a r s as an i j u p u l e a o f s t r e n g t h
j2=+jj
» A t with a do b i a s o f - 2 / H . I f t h i a i s a p p l i e d to equation4
J^xy (0)
- a ^
^ l ^ g (0)- a i
ƒ
g(u) du ( 6 a )g(u) du t o Y ' A i ^ r ^ M . i ) M
( 6 b )
(the d
^^'^si
^nJTi *^"<»:^Y'"i"?*' ota^le systam the integral tenn is a constant
o a l ™ ? « t ^ f + J oroSB-oorrelation function is
Jhe integral torn deduced by other means the impulse roapcnae of
tha system may be found from equation 6 a and 6 b , A detailed ^proach tS th^
^ i ^ ' r ^ l ' Z l ^ l T f l ^ ' r
IdentifioatSSn'lTgJeei''
5 '
FrofTuenrv Repnonoo from Iinpijls^ RoopoiiBO Data
' » (Jw) g(t) e-J*^ dt
3. P r a o t i c f i l c-x;ioriniico
A ship t r i a l WHO c a r r i e d out u o l n g the paoudo-randon bin.-vi-y u l g n a l
Itothoilo thouflh duo to tho luok o f a o u i t a h l o c o r r e l a t o r no i m i o d l a t ó ohocke Hoy^ppunlblo. Tlia t r i a l waa ooniluotod t o produce tho impulaa rcoponoo by
oixioa^borrolatior. ojid then t t ^ J i a r a t o from « H o the flötittenoy ruaponno. Later tho aaao iiioaïiüroir.iinta Moro pixscoouod by iuBximuni l l k o l l h o o d teohniquos t o produoo tho iapuloo ranponao, frotpicnoy rooponoo aiid t r a n o f o r f u n o t i o n a of the
oyotem. (Tliu l a t t e r r o u u l t u uro roporlod I n roforonoe l ) . Although tho
method o f pnoudo-rajidoiii b i n a r y o i c n a l and o o r r o l a t i o n i a now woll-dovolopod i t o u p p l i c a t i o n to t h t o typo o f oyutoui io oomowhat noval honce f o r
oomplotonean i t i u doaorihod I n thu noxt uaotloiia.
4 , Pnmido-Randon Binary ü l f i n a l aiid CroDo-norrelntion I d a n t l f l o a t l o n
Conoidor a l i n o a r ayotota with an iopulBB itiaponoo givon aa e ( t ) . The
input x ( t ) and output y ( t ) of tho syotoa are r o l a t o d by tho c o n v o l u t i o n
i n t o f i i ' a l ouch t h a t
y ( t ) - / * g U ) r ( t - u )
^
(1)0
F u r t h e r a q u a n t i t a t i v e maouure o f tho Interdopondonoo of two aignala a ( t )
and b ( t ) lo glvon by tho o r o a a - o o r r o l a t l o n f u n c t i o n
J ( a b ( r ) - ^ _ L l m ^ ^ y ^ ^ ( t ) m + r ) d t (2) - T
I f t h i a i t a p p l i e d t o tho i n p u t and output o f a l i n o a r oyBtom and tho
output i o erprocaud i n toruia o f tho i n p u t by equation 1 then , , T , t
^Xr ( t ) - Lim 1 / i ( t ) f g(u) x(t + T - u) du
T-*- <D W J J - J " '
For a Btable phyaiaally rsalieablo Byatoa t h i s oim ba re-arranged to give
<^ xy ( T ) - 7 g(u) L i a 1 ƒ ^'C* + T M I ) dt du-(3l,
Tho" inner integral can be reoogniaed ao tho auto-conelation function henoe equation i beoomea
( 4 )
l^xy
( T ) -f
eM ^ rx
( T - u ) duI f J< X I woo a d e l t a funtion then xy ( r ) - g C t )
Thie r e s u l t l a well-known ond forms the baaia of system i d e n t i f i c a t i o n • using a random noioa s i g n a l . The use of random noise i s r a s t r i o t a d by the d i f f i c u l t y of i t s generation and delay and th6 f a c t that p xx I T ) « d I <•' only f o r an i n f i n i t e integration period.
Conaldar » aignal d«aarlb«d by K auiplaa at I n t e r v a l s ipoosd T . Ths froiiuonoy opeotrura of the •ooplod function a» (nT) oan be given by tha DlBcreto F o u r i e r Tronufom . .
K-1
j A n k T
where n " 2 7r
I t con be shown ^^Uhat i f a(t) oontoino only a f i n i t e nunber of froquenoioo {< H) and that lhaaa ore only at frequonoios that aro a m i l t i p l o of II then
D i s c r e t e F o u r i e r Transform ( a» (nT) •• Ftouriep Tranafonn
I f i t l a noted that a pseudo-random binary s i g n a l hao a l i n o frequency apeotruM with space and, i f g» ( n A t ) l a computed from th* pseudo-random binary s i g n a l and oorrelation i d e n t i f i c a t i o n of tha system, then
DPT ( g» ( n M ) ) . r r i g(t) ! at n A t - 0, 2 A t , . . . ( B - l ) A t
ÏSrTiw'iI""^??^'^
rosponae may be computed from the time r^aponae v i a the DPT.^IZZ
t'.r""^
"«ohanisod byth.
Past F o u r i e r T r a n a f o m u s i n g a computer to c a r r y out the prooeos hence the frequency response may e a s i l y be obtained.KeaOTroBont o f R o l l RBOPOIISO ó f a Small F r i g a t e
"^^ i ^ f ^ ^ * ^ ? ? deeoribed in SBotion 2 and f i g u r e 1 wero applied to the
Z y. J^" ""P»»"» of & S a a " F r i g a t e . The ship wae Induced to roll
J ^ e ' ^ ^ n ^ " " " ° ' B t a b i l i e e r f i n s and a l . c by perturbation of the r^dS^r. I5aira"e":n"?h"":h"tp."" * '""^"'^^ « ^ - ^ o
ooi l ^ L S ^ ^ ? ' * " ? ' ' ^ ' ' ; ^ ^^^'^ "^«""^ " ' ' O " " * ° ' ^ ^ f i l the requirsmentB s e t t r l a l e =«!^t f J : " " " - a v a i l a b i l i t y of a c o r r o l a t o r , at the time of the
in'ilo^e°'ta^'
I^HAII^':' °'
« . t J ï d . M o T I ^ r ï h * ! ° " ™ " the helm wa. a p . ^ l » ^ r L i r ^ i o ™ / " t j 8 < l " c . d Into the a t a b U i a e r c o n t r o l to oauae
f » . r « . w a C r ^ t r l ^ ^ i i i ! ^ ; ['"•"^'' P"*^" recorded was r . , t - . ^ ^ ) . ' r i " : t f ^ « » « n u to s e t t l e . The
P.R. B.S
+ Q
-- -
a-1 1 1 1 I - 1 1
le • i;. • 13 • « 3 -O -3 - « • » " U " I S = 10
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P.R.8.S. SEQUENCE LENSTH»63 BITS. BIT P E R I O D - 3 SEC,
P.R.as. AMPLITUOE t 6 Dq.
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Data PTOoanninff
The onadogue r o c o r d i n g B of tbo toots Here d i g l t i B o d and p r o o e s s e d on a d i g i t a l o o m p u t e r u s i n g s i m p l e programmes to o a r r y O u t the o r o a e - o o r r e l a t i o n and the impuloe-to-frequency r a s p o n a e c o n v e r s i o n . These programmes p r o d u c e d the r e s p o n a o s shown^ i n the next s e c t i o n * The same d a t a MOO l a t e r prooeaaad u s i n g maximum l i k e l i h o o d mothods and the r e s u l t s o f t h i s are p r e s e n t e d i n pef e r e n c e 1,
8 , Timo-ana F r e c p i e n c Y - f c a i n Holl RecponBe
The p r b s c h o s e n to p e r t u r b a t e the f i n e was a 63 b i t s e q u e n c e w i t h a p e r i o d of 2 s e o o a d s . Tho r e e p o n B * p r o d u c e d b y o r o s B - o o r r o l a t i o n a n a l y s i s i s shown i n f i g u r e 3 a . '
I n order to p e r t u r b a t e the rudder b o t h a 63 and a 127 b i t Bequenoe w a s t r i e d . The p e r i o d used f o r b o t h s e q u e n c e B was 2 s e c o n d s . F i g u r e 3b shows the i m p u l s e r e s p o n s e d a d u o a d by o r o a o - c o r r e l a t i o n and a n l y s i o of the 1 2 7 b i t sequence.
Tho f r e q u e n c y r e a p o n s e f o r both t h e s e i m p u l s e responses waa d e d u c e d by the method d i a o u s s e d e a r l i e r and the r e s u l t s are shown i n f i g u r e s 4 and 5 r a s p e c t i v e l y .
Due to the v e r y c a l m c o n d i t i o n s d u r i n g the t r i a l i t was not n o c o s a a r y to c a n y out o r o a s - e o r r o l a t i o n over more t h a n one sequence l e n g t h . The i m p r o v e d gain by c o r r e l a t i o n o v e r s e v e r a l periode was found to show no c h a n g e i n the i o p u l s a r e a p o n s e a f t e r 60 s e c o n d s . A f t e r t h i s p e r i o d of t i m o some change i n the r « B i d u e appeared that ohowed t h a t the r e s p o n s e o f f i g u r e 3b a f t e r 60 B e c o n d a i a due to n o i a e and not s h i p ' s t r u e d y n a m i c a .
g , Diaoncnlon of muthoA
Tho ebip w h i c h was uaed to c a r r y out the t r i a l s was f i t t e d w i t h a v e r t i c a l reforonoo gyro ao all the e q u i p m e n t needed f o r the t r i a l i s t h a t shown i n f i g u r e 1. The e q u i p m e n t i a p h y s i c a l l y small and h e n o e e a s i l y passed t h r o u ^ b a t c h e s e t c .
A B a l r e a d y s t a t e d the c r o s s - c o r r e l a t o r was not a v a i l a b l e and h e n c e no
i m m e d i a t e r e s u l t s could bo p r o d u c e d . T h i s was a s i g n i f i c a n t d i a a d v a n t a g a aa d u r i n g one t e s t a f w i l t i n tha p r b s t r a i n c a u s e d a c o n s i d e r a b l e l o s s of i n f o r m a t i o n . T h i s f a c t w o u l d not have gone u n d e t e c t e d i f the r e s u l t e oould have been c h e c k e d on board.
Some i d e a of tha order o f d y n a n i c a of the ship was known b e f o r e the t e s t i n g . T h i s allowed tho p r b a to be chosen c o r r e c t l y f i r s t t i m e . Had t h i a knowledge of tha d y n a m i c s not been a v a i l a b l e the need f o r the onboard c o r r e l a t o r i n order to ensure a s u i t a b l e prba had been c h o s e n w o u l d have been i m p e r a t i v e .
Tho r o B u l t B were p r o c e a e e d u o i n g a very Bimple programme f o r the
o o r r e l a t i o n and f r e q u e n c y r e a p o n a e c o n v e r s i o n . The d i g i t i s a t i o n o f the o i g n a l was c a r r i e d out by u s i n g a c o m p u t e r and a c c m p u t o i x - c o n t r o l l e d a n o l o g u e - t o - d i g i t o i c o n v e r t e r . The f o i r o o r p r o g r a m M S were w r i t t e n i n F o r t r a n w h i l e the s a m p l i n g programme was w r i t t e n i n a s s e m b l e r l a n g u a g e . Any m i n - c o m p u t e r w i t h 4K as s t o r e and a f a c i l i t y f o r input V i a an A-to-P c o n v e r t e r would be s u i t a b l e f o r the t a s K .
impulse reaponoo, fiRuro 3b, ehowa T o l ^ B i n frequency range. The i ^ I i M ^ n ' ' " ' ^ *^ ^ - t o r ' d e n e o t i c n r^ ihe d i " "'^^^ < = h » r a c t e r i e U o i n i t i a l l y reived i n f i e i t i v , 4 t i „ i , d i r e c t i o n cppoalte to t h a t 4 + behaviour io not, h o L " e r : ^ " ^ ' n ^ L ' ^ i h T L l i ^ J ^ ^ r ; : ^ - ^ ' " " * ^ - " ) ^ 11. Ccncluaione ° ^ ~ i . u n > phase ayatema.
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v a r i a b l e syatems o r , frequenovdomain • methods f o r m u l t i -Phase systems i s an o c o u p ^ t i o ^ l i a b l " t o t T T ^ i " « « " " t i a l l y „ o n ï ï n i ^ u m a s s o c i a t e d i d e n t i f i c a t i o n
tooLlLea
a o n e ^ t"^^^
f r u s t r a t i o n . PrSTand«lohioving the n e c e s s a i y k n o w j o ï g ^ *° ''^^'^ ° « ° h to o f f e r i n
DiSolalmeT-d r a „ n ^ r : ; i t : X = r a i e " t t : : Ï X l
- " f u s i o n sthose o f the HOD of the UK. n e o e s e a r i l y
M s t of HafDr«.„„.„
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""'P < ^ ^ i o « x p e r l m e n t s u s i n . t h „ Applied s c i e n c e s . 'ini:e"^sft"''of°s"u]:et^W;*««^«rtrsoh'cörof
- - i a . . . , . . S y e t e m , d , n t . f i c a t i o n for S e l f . . . a p t l v a C o n t r o l , , wa., , , , ,
/ ' i ' l ' " t o a t i r . ^ tiir.o u u i i l f t tho molhod d o u o r i b o d wae v o i y o h o r t , Tlio j / ' p r o o o a t r i n g timo wati i c c u them ii\ h o u r i i i o l u d i n s t h o p l o t t i n g o f rosponooB cmd
t h e d i g i t i o a t i o n o f tho analocuo t a p o c . Tho pro^^aoinog r o q u i r e d t o o a r i y o u t
t h o t o o k t o o k l o u B than 3 dayo l o w r i t o and p r o v e . Howovor, t h e FJT was n o t
u r i t t o n i n t h i s p e r i o d an i t waa a l r e a d y a v a i l a b l e . )
I t o o u l d be ooncluded t h a t the Dothod i a r e l a t i v e l y aiinplo t o uQo and the hardware and u o f i w a r o r o q u i r o d i o o n l y a e m a i l i n v o o t i o o n t i n r e l a t i o n t o tho
i - o o u l t u w h i c h i t i a capable o f p r o d u c i n g .
I t i o w o r t h n o t i n g t h a t tha tnothod nao a l a o a p p l i e d t o t h e yaw dynaraioo. However t h o r a u u l t s woro n o t u u c o e a a f u l when pracoaned b y a i m p l e c o i - r e l a t l o n
u a a l y D i D . T h i s was p r i n a r i l y due t o tho f a c t t h a t tho yaw waa o b t a i n e d by
c a o o u r i n K E b i p ' o haaa v i a tho course coicpaen and the m t i t c h i n g o f t h o prba to ^
tho ya-.! d y a j w i c t i i a s o o n o t a n t a waa f a r f r o a i d e a l , I n v e o t i g a t i o n o f tha sys.toia f o i - uuoh ooaauroicantu ohowa t h a t i n e f f e c t an open-loop i n t o j t r a t o r
o x i a t u a t t h e o u t p u t . P r o b l c c a i n i d e n t i f y i n g Duoh ayytem wlien u a i n f ; prba and o o r r o l a t i o n touhsiiquoo are w e l l - t a i o w n . Again hov/avor t h e anoloeuo tape r e c o r d i n g o f t h a t e s t a -.IOB prooooccd l a t e r by niiuciffiiuo i i k o l i h o o d methoda and
good r e i r a l t s wore o b t a i n e d (cee r o f o r o n c o 1 . ) I f i n s t e a d o f u a i n g s h i p ' s
hoad aa t h o y a u i c s a n u r e i e n t p a r u m o t e r , y a w - r a t o waa u s e d tho problem o f the o p o n - l o o p i n t o g r a t o r c o u l d bo ovoroomo.
P i n a U y i t o h o u l d bo n o t o d t h a t t h u o o p l i t u d o n o f t h o t e a t s i g n a l wore r e l a t i v o l y s m a l l a n i t h o r o i i u l t a n t a h i p r . o t i o n waa v o r y cin.-\ll, thus tho
objaoti\'0 o f p r o d u c i n c a teat nathod t h a t was a p p l i c a b l e t o the i d e n t i f i o a t i o n of a l i n o a r sraall s l i ^ u l model was a c h i e v e d .
10. B i B o n o B ' o n o f i-emiltB
Althou.^h t h e \;ork d a a o r i b o d horo waa aimod, e v e n t u a l l y , a t v e r i f y i n g tho ! u p p l i o a b i l i t y o f prba t t e l i n i q u o a t o l U l l - u o a l o c h i p d y n o a i o i n v a a t i g a t i o n B i t
io w o r t h oonimonting on the r e e u l t a o b t a i n e d f o r t h o y i l l u a t r a t e an irapoi-tant
d e f i c i e n c y i n knowlodgo o f a h i p dynamic o f f o o t n . Tho r o a u l t n p r o u o n t e d h e r o
uro f r « ; s a a i o i l d r a h i p t o t h a t uued by C a r l a y and D u b o r l e y V") i n o b t a i n i n g j
conventional frequency response d a t a on r o l l i n g to f i n p e r t u r b a t i o n s . ' F i g u r e 4 ohOHB good affreeraent w i t h the r e s u l t s p r e v l ó u a l y p u b l i s h e d by t h e s e
a u t h o r s . .
P c B s l b l y t h o most s t r i k i n g f e a t u r e of F i g u r e 4 l a tho l a r g e p h a s e - • advance oi,)erienoed at low f r e q u e n c i o s . C a r l e y and Duborley suggest that t h i a
i s due to c r O B B - o o u p l i n g e f f o o t B between yaw and r o l l . Theory shows that these e f f e c t s muet o o r t a i n l y bo present but are normally considered n e g l i g i b l e f o r amoll dieturbanoes of g o t i o n . The mailoium r o l l experienced i n t h e s e oxpejimenta was, however 3 and f o r the vaat m a j o r i t y o f tha t i m e waa l e s s thao
+ I J - . Hence, i f I n t e r a c t i o n i s s l g n i f i o a t i t t h e n those o r o s B - c o u p l i n g
e f f e c t s would a p p e a r to bo c o n s i d e r a b l y g r e a t o r t h a n has been imagined to d a t o .
A n o t h e r p o a s i b l e e x p l a n a t i o n i s t h a t non-minimum phase behaviour o f the o o t i o n i e a r i a i n g . Such behaviour hem been p r e v i ö u o l y evidenced i n s h i p s t e e r i n g work (77 (0) but haa n o t , to tha authors knowledge, been s a r i o u s l y disoussed i n marine woric. T h i s phenomenon i s , however, a w e l l known oonsideratW i n f l i ^ t dynanios I n the a e r o n a u t i c a l w o r l d . Whether t h e s e e f f e c t s a r i s e f r c a h u l l hydrodynamic o r f i n hydrodynamics, o r a combination o f b o t h , i s unknown.
Dynamic experiments on i o o l a t e d h y d r o f o i l oaotions h a v e produoed unusual c h a r a o t o r i e t i c a , The i n t e r e s t i n g f e a t u r e i a that tha g a i n c o n t i n u o »
RiiloB f o r chooDlnK a uultable prbo
1. A prba c u o t ba ohoaen uuoh that the period i e g r e a t e r than the s e t t l i n g t i n e of tho oyatoa.
2 . The b i t longth reuat be at leaat 4 times emaller than the s n a l l e a t time
constant of tho oystom.
3 . "Vho ojiiplitude of tho teat aignal should be aa l a r g e as p o s s i b l a compared with ooooptablo plant diuturbancoo and q u a a l - l i n e a r i t y .
4 . Tho p a r i o d of oorrolation f o r the teat nuat be an i n t e g e r m l t i p l * of tha
aequonoo l e n g t h .
5 . Tho poriod of the t e s t ohould be as long aa p o s s i b l e oompatible with
plant s t a t i o n a r i t y .
6. Tho t e s t a i g n a l ohould bo i n j e c t e d f o r at l e a s t one c y o l e before meaauramont coomancoa i n order to allow t r a a a l a n t a to s e t t l e .
7. Caution should be exerted when reduoing the time o f the b i t length a«
t h i s inoroaaes tha varl.oaoe of the e r r o r due to high frequency n o i s o . 8. Caution should be exerted i n systema with d r i f t as the moment o f the prbs w i l l appear on the i d e n t i f i o a t i o n impulse responao.
9 . Cara should bo taken i n the ohoioa of transduoora as t h e i r o f f e o t oan bo l a r g e oa tho f i n a l i d e n t i f i o a t i o n .
8. Coolowoki, J and Oolb, k, 'Dyiimnioa of a n a u t o n u t i o ohip B t u o r i n g oyotom', I E E E I'luna on Auto C o n t r o l , Vol AC11, J u l y , I 9 6 Ö .
9. KloDO, C J , a n d Aooota, A J , 'Unatomiy f o r c e m e a s u r o m a n t D on
f u l l y H o t t e d h y d r o f o i l e i n heaving motion", Journ of Ship Roooarch, Karch I p é S .
