1-s2.0-s0029801812002387-main

8/10/2019 1-s2.0-S0029801812002387-main

1/17

M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25 13

Applying t e !" c#ntr#ller #n t e r#ll re$%cti#n an$ trac& &eeping '#r t e ipa$ ancing in *a eMing-C %ng Fang a+n+ ,%- ien in + #- e ang aa "epart ent #' y te 6a al Mec atr#nic Engineering+ 6ati#nal C eng- %ng 8ni er ity+ 9ainan City 70101+ 9ai*an Fi ing #at

Marine Engineering :e earc Center+ 6ati#nal C eng- %ng 8ni er ity+ 9ainan City 70101+ 9ai*an

a r t i c l e i n ' # a t r a c t

Article i t#ry;:ecei e$ 1 an%ary 2012Accepte$ 1 %ly 2012Aaila le #nline 2< %ly 2012

9 i t%$y ai t# $e el#p a !" c#ntr#l y te a e$ #n t e ne%ral net*#r& alg#rit t# re$%ce t e ip r#lling #ti#n in t e$e ire$ trac& t r#%g r%$$er an$ 'in acti#n . 9 e at e atical #$el incl%$ing ea-&eeping an$ ane% ering c aracteri tici $e el#pe$ in t e pre ent paper an$ t e

n#nlinear ti e i t#ry #' ip #ti#n i #l e$ y t e '#%rt #r$er :%nge %tta et #$. =n #r$er t#ey*#r$ ;!" c#ntr#l

6e%ral net*#r& :%$$er ta ili>er 'in

ac ie e t e p%rp# e #' r#ll re$%cti#n an$ trac& &eeping+ t e r%$$er an$ 'in ta ili>er are % e$ a t e c#ntr#l t##l '#r t e ipa$ ancing in t e ea*ay. =n a$$iti#n+ t e !" c#ntr#ller a e$ #n t e el't%ning ne%ral net*#r& alg#rit i applie$ t# ac ie et e g#al #' %lti-inp%t an$ %lti-#%tp%t in t e c#ntr#l y te . F#%r $i''erent type #' c#ntr#l #$e #n a c#ntainer ip#$el are t%$ie$ an$ t e per'#r ance are in e tigate$ in $i''erent ea tate . 9 e re %lt in$icate t at t e !" c#ntr#ller

a e$ #n t e el'-t%ning ne%ral net*#r& alg#rit applying t# t e ta ili>er 'in c#ntr#l '#r r#ll re$%cti#n an$ t e r%$$er c#ntr#l'#r trac& &eeping in t e ea*ay *#%l$ e %gge te$.

2012 El e ier t$. All rig t re er e$.

1. =ntr#$%cti#n

ile a ip ail in t e ea*ay+ t e e?ternal '#rce + i.e. *in$ + *a e #r #cean c%rrent + % %ally ca% e t e ariati#n #n t e #ti#n an$ trac&.9 ere'#re+ # e $e ice nee$ t# e applie$ t# t e ip t# aintain t eta ility an$ #rientati#n.

8 %ally t e r#ll #ti#n i c#n i$ere$ t# e t e # t e ere pr# le ina'ety * ile t e ip ail in t e ea*ay. i ply pea&ing+ t e eri#% r#ll#ti#n *#%l$ a''ect t e ip ta ility+ c# '#rt an$ e''iciency #' cre* +acc%racy #' electrical ec ani + an$ ip c#%r e. 9 ere'#re+ r#ll-re$%cti#ni e pecially a$ antage#% '#r ip a$ ancing in *a e . # e $e ice a e

een *ell e pl#ye$ t# acc# pli t e ip r#ll re$%cti#n+ e.g. ilge &eel +anti-r#ll tan& + gyr# c#pic ta ili>er + # ing *eig t an$ ta ili>er 'in(9rea&le et al.+ 2000 ). A$$iti#nally it i al # *ell &n#*n t at t e r%$$er can

e applie$ t# c#ntr#l t e ip ea$ing+ trac&&eeping an$ e en t e r#ll-re$%cti#n. =n t i t%$y+ t e r%$$er an$ t e ta ili>er 'in *ill e a$#pte$.

Alt #%g t e r%$$er i ainly applie$ t# alter t e ip c#%r e+ it al # can pr#$%ce an a$$iti#nal r#ll # ent a''ecting t e r#ll #ti#n an$c#n e@%ently ay e % e$ a t e r#ll-re$%cti#n $e ice ( Fang+ 1 1 BF# en+1 4 ). =n a$$iti#n t# t e r%$$er+ t e ta ili>er 'in ig t e t e # t e''ecti ean$ *i$ely a$#pte$ r#llre$%cti#n $e ice '#r ip in *a e . #*e er+ in#r$er t# apply

n C#rre p#n$ing a%t #r. 9el.; DD< < 274701D?211B 'a?; DD< < 20D05 2. E- ail a$$re ;'ang c ail.nc&%.e$%.t* (M.-C. Fang).

002 -D01D/ - ee 'r#nt atter 2012 El e ier t$. All rig t re er e$.ttp;//$?.$#i.#rg/10.101er 'in t# re$%ce t e ip r#ll #ti#n+ t e ip pee$ % t reac t ea$e@%ate al%e t# a&e t e ta ili>er 'in '%ncti#n #re e''icient ( err#l$ an$

Mic ael+ 1 ). Henerally+ #t t e r%$$er an$ t e ta ili>er 'in nee$ t#

inc#rp#rate t e a%t# atic c#ntr#ller t# ac ie e t e #pti al r#ll-re$%cti#n '#r t e ip tra eling in r#%g ea . 9 e pre i#% literat%re ( err#l$ an$ Mic ael+1 ) pre ente$ a at e atical #$el c#n i ting #' r#ll- *ay-ya* #ti#n t#$i c% t e r#ll-re$%cti#n e''iciency '#r t e ta ili>er 'in an$ t e r%$$er ya$#pting t e II eparate C#ntr#lJJ an$ IIC# pact C#ntr#lJJ re pecti ely.

#* t# elect a %ita le c#ntr#ller '#r t e ta ili>er 'in an$ t e r%$$er t#re$%ce t e ip r#lling #ti#n in *a e i an i p#rtant tec n#l#gy. e eral&in$ #' c#ntr#ller *ere alrea$y $e el#pe$ in t e pa t+ e.g. !" an$ !="c#ntr#l ( "# e an$ rig t+ 1 1 )+ a$apti e c#ntr#l ( 9>eng an$ in+ 2000 )+'%>>y c#ntr#l (Ca# an$ ee+ 2003 ) an$ li$ing #$e c#ntr#l ( Fang an$ %#+2007 ) etc. A #ng t e + eit er !" #r !=" c#ntr#ller *it 'i?e$-$e ign

para eter i a c#n enti#nal a%t#pil#t y te '#r a ip teering in *a e +* ic i t e # t *i$ely % e$ a #ng any a%t#pil#t y te eca% e #' iti plicity. =n t e pa t+ t e c#ntr#l gain para eter a$#pte$ in t e !" #r !="c#ntr#ller *ere % %ally $eter ine$ a e$ #n t e e?perience #' t e #perat#r+trial-an$err#r et #$ #r e?peri ent + * ic ig t n#t e #pti al. 9 ere'#re+# e appr#ac e *#%l$ e nee$e$ t# pr# #te t e e ''iciency #' t e c#ntr#ller t#re$%ce t e ip r#ll #ti#n+ '#r e?a ple+ t e ne%ral net*#r& alg#rit canan$le %c &in$ #'

pr# le ery *ell. 9 e pre i#% t%$y ( e erly an$ 6a ci ent#+ 1 ) % e$t e ne%ral net*#r& a$apti e c#ntr#l alg#rit t# train t e c#ntr#ller an$i %late c#ntr#l para eter '#r !=" c#ntr#ller. 9 e a%t #r ( i et al.+ 2005 )applie$ t e !=" c#ntr#ller t# t e ip ta ili>er 'in a e$ #n t e *a elet ne%ralnet*#r& i$enti'icati#n an$ t%ning+ * ic can i pr# e t e e''ecti ene an$ t e

per'#r ance #' t e c#ntr#ller. O%r '#r er re earc ( Fang et al.+ 2010 ) al #applie$ t e !=" c#ntr#ller t# an$le t e ta ili>er 'in t# re$%ce t e ip r#lling#ti#n y inc#rp#rating t e el'-t%ning ne%ral net*#r& an$ g##$ per'#r ance*ere # taine$.

Acc#r$ing t# t e pre i#% re earc e ( Fang an$ %#+ 200< +2007 BFang et

al.+ 2010)+ t e

8/10/2019 1-s2.0-S0029801812002387-main

2/17

14 M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25ane% ering c aracteri tic '#r a ip teering in *a e can e treate$eparately in #r$er t# i pli'y t e c# plicate$ c#%pling pr# le . a e$ #nt i #$el+ a !" c#ntr#l y te inc#rp#rating t e el'-t%ning ne%ral net*#r& alg#rit i applie$ t# t e ta ili>er 'in an$ t e r%$$er '#r r#ll re$%cti#n an$trac& &eeping. =n t e '#ll#*ing ecti#n+ t e c#ntr#l y te inc#rp#rate$ in t eat e atical #$el '#r t e ip ane% ering in *a e i $e cri e$. "i''erent*a e c#n$iti#n an$ t e $yna ical en ir#n ent are a$#pte$ t# in e tigate t ee''iciency #' t i c#ntr#l y te .

2. Mat e atical #$el

9 e n#nlinear K#eL* _ * K#eL* F K#0L "F K#eL FF g

K3L

=?? ' =?? y _ c _ ?? K#eLy _ c _ ?? K#eL' ' _ ' _ K, nn, c _ c _ L> :#ll:

F K#0L "F K#eL :F FFK4L

=yyy = ?? c _ ' _

!itc : ?? K#eL' _ c _ yyK#eLy My _ K#eLy _ MyyM* _ K#eL* _ M* K#eL* M F K#0L M "F K#eL M FF

K5L

=>>c =?? y _ ' _ ?? K#eLy _ ' _ >>K#eLc 6 n _ n _ 6 nn 6 c _ c _ 6 c _ 9 c _ 9 c _

9 c _ 9 6 nnc _ n2c _ 6 nc _ c _ nc _ 2 6 ' ' 6 n9 ' 9n9 ' 9 ,a* :

6 c _ 9 ' 9c _ 9 ' 9 K, nn , c _ c _ , n9n9n9n9 , n9 c _ 9 n9 c _ 9 , c9 c _ 9 c _ 9 c _

9 L? 6 F K#0L 6 "F K#eL 6 :F 6 FF

KF are t e c##r$inate #' t e acti#n center #' t e 'in'#rce. ' F i t e angle et*een t e 'in an$ t e pl% line. 9 e relate$e@%ati#n #' t e li't '#rce an$ t e $ra't '#rce can e al # '#%n$ *it re pectt# t e re'erence ( ee+ 1 77 ).

3. C#ntr#l y te

9 e !" c#ntr#ller i % %ally e?pre e$ in t e '#ll#*ing '#r c#ntaining t*#c#ntr#l gain + i.e. pr#p#rti#nal ( ! ) an$ $eri ati#n

( " )

$" %KtLrKtL p" %KtL " K14L $t

* ere r(t) i t e c#ntr#l #%tp%t aria le an$ " %(t) i t e y te err#r.Acc#r$ing t# t e $i''erent # Gecti e i i#n *it re pect t# $i''erent

c#ntr#l t##l + '#%r type #' c#ntr#l c# an$ applie$ t# t e ta ili>er 'inan$ r%$$er are intr#$%ce$ in t e '#ll#*ing+

A-type; t e c# an$ t# c#ntr#l t e r%$$er '#r t e trac& &eeping.-type; t e c# an$ t# c#ntr#l t e r%$$er '#r t e trac& &eeping an$ r#ll

re$%cti#n.C-type; t e c# an$ t# c#ntr#l t e r%$$er '#r t e trac& &eeping an$ t e

ta ili>er 'in '#r r#ll re$%cti#n.

8/10/2019 1-s2.0-S0029801812002387-main

3/17

M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25 15"-type; t e c# an$ t# c#ntr#l t e r%$$er '#r t e trac& &eeping *it r#ll

re$%cti#n+ an$ t e ta ili>er 'in '#r r#ll re$%cti#n.=n Fig. 1 + t e ill% trati#n #* t e $e ire$ *a e ea$ing an$ t e trac& al#ng

*it t e in tantane#% ip p# iti#n. 9 e $e iati#n et*een t e in tantane#%ip p# iti#n an$ t e $e ire$ pat can e calc%late$ y E@. (15).

N08 tan c, 0

E0 @''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i

K15L

tan2 c 1

* ere (N 0+, 0) repre ent t e in tantane#% p# iti#n #' a ip in t e eart -'i?e$c##r$inate+ an$ c in$icate t e $e ire$ ip ea$ing. Henerally+ t e line-#'- ig t( O ) g%i$ance tec ni@%e ( McH##&in et al.+ 2000) i intr#$%ce$ t# g%i$e t eip t# ail t# t e c# an$e$ *ayp#int. 9 e relati#n ip et*een t e act%al

ea$ing ( cr ) an$ $e ire$ ea$ing ( c) i e?pre e$ a '#ll#* .

cec

r c K1

8/10/2019 1-s2.0-S0029801812002387-main

4/17

1< M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 253.1. 9 e A-type an$ -type (i.e. c#ntr#l c# an$ #n r%$$er)

=n t i ecti#n+ A-type an$ -type c#ntr#l y te *#%l$ e in e tigate$.9 e !" c#ntr#ller *it A-type c# an$ i applie$ t# $e'lect t e r%$$er anglet# aintain t e trac& &eeping #nly * erea t e -type c# an$ i t# c#ntr#lt e trac& &eeping an$ r#ll re$%cti#n i %ltane#% ly. 9 e 'l#* c art a e$ #nt e ne%ral net*#r& alg#rit '#r A-type an$ -type are #*n in Fig. 2 (a) an$( )+ re pecti ely.

a e$ #n t e E@. (14)+ t e !" c#ntr#ller c# an$ '#r t e A-type can e

*ritten a $KtL p E0Kt1L $ Kt1L ypc

eKt1L y$c _ Kt1L K17L * ere $(t)

i t e r%$$er angle. p + $ + yp an$ y$ are trac& $e iati#n gain+ *ay el#citygain+ ea$ing err#r gain an$ ya* rate gain+ re pecti ely. C#rre p#n$ingly+

E0(t1)+ (t1)+ ce(t1) an$ c _ Kt1L+ are trac& $e iati#n+ *ay el#city+ ea$ingerr#r an$ ya*ing ang%lar el#city+ re pecti ely.

=n #r$er t# # tain t e #pti al !" c#ntr#ller+ t e el'-t%ning !" c#ntr#ller a e$ #n t e ne%ral net*#r& t e#ry i pre ente$ ere+ i.e. Fig. 2 . 9 e c e ec#n i t #' t*# ne%ral net*#r& ; (i) y te i$enti'icati#n ne%ral net*#r& (661)an$ (ii) para eter el't%ning ne%ral net*#r& (662).

9 e 661 i % e$ t# i$enti'y an$ pre$ict t e n#nlinear $yna ic relati#n ip et*een inp%t ignal an$ #%tp%t ignal . =n t e pre ent ca e+ t e erie -parallel

#$el *it #ne i$$en layer i a$#pte$ in 661. E 0(t1)+ (t1)+ ce(t1) an$ c _

Kt1L are electe$ a t e inp%t n#$e + * erea E^

0KtL+ ^ KtL+c^ eKtL an$ c^_

KtL are et t# e t e #%tp%t n#$e #' t e #%tp%t layer. 9 e err#r '%ncti#n '#r 661 i $e cri e$ a el#*

E& Qg & KtLg & KtL2 K1DL

* ere g &(& 1+ 2+ 3 an$ 4) i plie E 0+ +ce an$ c _ + re pecti ely.eca% e r#ll+ ya* an$ *ay #ti#n can e p# iti e #r negati e+ t e

yper #lic tangent '%ncti#n i t ere'#re a$#pte$ a t e acti ati#n '%ncti#n+ i.e.

'K?L tan K0 :5?L K1 L

An$ t e $eri ati e #' t e acti ati#n '%ncti#n in 661 i t % e al%ate$ a el#*

'0

K?L 0 :5Q1'K?L2

K20L

a e$ #n t e 661 acti ati#n '%ncti#n in E@. (1 ) an$ it $eri ati e in E@.

(20)+ t e '#ll#*ing en iti ity in'#r ati#n+ @g& /@$(t1)+ can e # taine$;

$@Ktg^ &1L 14 NQ1Kg^ & L2R GQ1 G2 G+ & 1+2... 4 K21L

@ G

* ere Gi t e *eig t et*een t e inp%t n#$e an$ t e Gt i$$en n#$e+ an$ R Gi t e *eig t et*een t e Gt i$$en n#$e an$ t e #%tp%t n#$e. Gi t e #%tp%tect#r #' t e i$$en layer.

% e@%ently+ t e ne%ral net*#r& 662 i applie$ t# t%ne t e!" c#ntr#l gain . 9 e err#r '%ncti#n '#r 662 i $e'ine$ a

E& 12Qg & Kt1Lg& KtL22 + & 1+2... 4 K22L

K " g& Kt1LL

eca% e t e c#ntr#l gain are all p# iti e+ t e ig #i$ '%ncti#n *it $# ain et*een 0 an$ 1 i electe$ a t e acti ati#n '%ncti#n+ i.e. E@. (23)+ an$ it$eri ati e i #*n in (24).

1

'K?L 1 ? K23L e

' 0K?L 'K?LQ1'K?L K24L9a le 1!rincipal $i en i#n #' t e c#ntainer ip.

ip

engt ( ) 1D5.5

rea$t ( ) 30.2

"ept ( ) 1

8/10/2019 1-s2.0-S0029801812002387-main

5/17


Fig. 3. (a) 9 e tra er e pr#'ile #' ta ili>er 'inB an$ ( ) t e l#ngit%$inal pr#'ile #' t e r%$$er an$ta ili>er 'in.

C#n e@%ently+ t e #%tp%t al%e #' t e 662 are all et*een 0 an$ 1.9 ere'#re+ # e pr#p#rti#nal 'act#r % t e %ltiplie$ t# eet t e

practical c#ntr#l re@%ire ent. 9 e pr#p#rti#nal 'act#r $epen$ #n t e y tec aracteri tic an$ t e a pling ti e. ince t e # Gecti e al%e #' t e#%tp%t layer are %n&n#*n+ t e ignal al%e #' net*#r& err#r nee$ t# e'%rt er $eri e$ an$ tate$ in t e '#ll#*ing. Fir t+ t e #%tp%t n#$e+ & + i$e'ine$ a

D p + & 1

TTTTU $ + & 2

& yp+ & 3 K25L

8/10/2019 1-s2.0-S0029801812002387-main

6/17

1D M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25

9a le 39 e c# t '%ncti#n al%e #' ip r#lling angle at $i''erent *a e ea$ing.

a e type C#ntr#ller 301 451

8/10/2019 1-s2.0-S0029801812002387-main

7/17

M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25 1TTTT; y$+ & 4

8/10/2019 1-s2.0-S0029801812002387-main

8/17

20 M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25

9 e err#r ignal al%e '#r t e #%tp%t n#$e i

$& " g& Kt1L8 @g& KtL 8@$Kt1L8Q & K1 & L+& 1+2 ... 4K2

8/10/2019 1-s2.0-S0029801812002387-main

9/17


Fig.er 'in #n t er#ll re$%cti#n+ #re c# an$ t an A-an$ -type t# a$G% t t e ta ili>er 'in angle *#%l$ e a$$e$. peci'ically+ t e C-type i % e$ t# $eter ine i' t ee ta li ent #' t e ta ili>er 'in i a le t# re$%ce t e c# t al%e #' c#ntr#ly te + in c# pari #n *it t e A-type * erea t e "-type+ c# paring *it

t e -type+ i t# e?a ine t e e''ect #' t e r%$$er an$ t e ta ili>er 'in #n t er#ll re$%cti#n i %ltane#% ly. 9 e 'l#* c art #' t e c#ntr#l '#r t e ta ili>er 'in i ill% trate$ in Fig. 2 (c).

i ilar t# t e A-type #ne+ t e c# an$ t# c#ntr#l t e ta ili>er 'in intype-C an$ type-" can e pre ente$ a '#ll#* .

aFKtL r'p 8 ' Kt1L r'$ 8' _

Kt1L K34L

* ere a(t) i t e c#ntr#l #%tp%t 'in angle. r'p an$ r'$ are t e r#ll an$ r#llrate gain y t e ta ili>er 'in+ re pecti ely. 9 e #%tp%t n#$e+ & + i t ene?pre e$ a

( r'p + & 1

& r'$ + & 2 K35L

9 e err#r ignal al%e '#r t e #%tp%t n#$e #' t e ta ili>er 'in are;

DU"' Kt1L8 @a@F' KtKtL1L8 @a F @K t &1L 8Q & K1 & L+ & 1

$& ; "' _ Kt1L8@a@F' _ KtKtL1L8 @a F @K t &1L 8Q & K1 & L+ & 2 K3

8/10/2019 1-s2.0-S0029801812002387-main

10/17


@ & ' _ Kt1L+& 2 K L

Time (sec)

Fig. 7. 9 e c#ntr#l gain #n t e r%$$er #perati#n '#r trac& &eeping in l#ng cre te$ *a e *it 1= 3 3 + 9 10 + initial *a e ea$ing 301 an$ initial ip pee$ R 23 &n#t .

K y p

K y d

K s p

K s d

intr#$%ce$ a el#*

(@aFKt1L ' Kt1L+ & 1 37

8/10/2019 1-s2.0-S0029801812002387-main

11/17


3.3. 9 e c# t '%ncti#n an$ r#ll re$%cti#n rate

=n #r$er t# G%$ge t e @%ality #' #perati#n+ t e c# t '%ncti#n ( McH##&in etal.+ 2000) i a$#pte$ ere+ i.e.+

C9#tal N n Qa1K"c iL2 a2E20i a3$i2 a4KaFiL2 a5' 2i K3DLi 0

9 e rig t- an$ i$e #' E@. (3D) i relate$ t# t e trac& &eeping an$ r#ll#ti#n+ in * ic n i t e t#tal n% er #' t e ti e inter al in t e i %lati#n

pr#ce + "c i i t e it ea$ing err#r et*een $e ire$ ea$ing an$ act%alea$ing+ E 0i i t e it trac& $e iati#n et*een t e $e ire$ trac& an$ act%altraGect#ry+$i i t e it r%$$er angle+ aFi i t e it ta ili>er 'in angle an$ ' i i t eit r#ll angle. 9 e a1+a2+a3+a4 an$ a5 are t e *eig t $epen$ing #n t e cale #' eac para eter an$ et t# e 10+ 2.0+ 0.1+ 0.2 an$ 5.0+ re pecti ely+ in t e

pre ent t%$y.

=n #r$er t# G%$ge t e e''iciency #' t e r#ll re$%cti#n rate (:::) '#r t eip ane% ering in ran$# ea % ing t e pre ent !" c#ntr#ller+ t e

percentage #' r#ll re$%cti#n ( Fang an$ %#+ 200DB err#l$ an$ Mic ael+1 ) i $e'ine$ a ;

A!:C::: K ! L 100 K3 L

A! * ere A! i t e tan$ar$ $e iati#n #' r#ll anglecalc%late$ 'r# t e a%t#pil#t c#ntr#ller *it #%t r#ll re$%cti#n+ * erea :Ci t e #ne incl%$ing r#ll-re$%cti#n c#ntr#l.

4. :e %lt an$ $i c% i#n

=n t i paper+ t e c#ntainer ip % e$ y ( Fang an$ %#+ 200< BFang etal.+ 2010) i a$#pte$ '#r calc%lati#n . 9 e principal partic%lar #' t ec#ntainer ip an$ t e ta ili>er 'in are li te$ in 9a le 1 an$ 9a le 2 +re pecti ely. F#r i pli'icati#n+ t e *ater

K r r p

K r r

d

K r f p

K r f

d

8/10/2019 1-s2.0-S0029801812002387-main

12/17


Time (sec)

Fig. D. 9 e c#ntr#l gain #n t e r%$$er an$ 'in #perati#n '#r r#ll re$%cti#n in l#ng cre te$ *a e *it 1= 3 3 + 9 10 + initial *a e ea$ing 301 an$ initial ip pee$ R 23 &n#t .9a le 49 e t#tal c# t '%ncti#n al%e at $i''erent *a e ea$ing.

a e type C#ntr#ller 301 451

8/10/2019 1-s2.0-S0029801812002387-main

13/17

M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25 25=n t i ecti#n+ t e in e tigati#n i '#c% e$ #n t e i %lati#n #' ip

teering in ran$# ea . 9 e c#%r e a$#pte$ ere i a traig t line g%i$ingt e ip t# ail t# t e '#r*ar$ $irecti#n *it re pect t# e eral *a eea$ing + i.e. 301+451+

8/10/2019 1-s2.0-S0029801812002387-main

14/17

2< M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25Fr# t e # erall in e tigati#n #n t e t#tal c# t '%ncti#n *it re pect t# t e

$i''erent *a e ea$ing in 9a le 4 + *e can c#ncl%$e

Time (sec)

Time (sec)

Fig. 10. 9 e ti e ariati#n #' c#ntr#l gain '#r (a) A-type an$ ( ) C-type in l#ng cre te$ *a e *it 1= 3 3 + 9 10 an$ initial ip pee$ R 23 &n#t . 9 e ip ea$ing i't 'r# c 301 t#01 at t 300 .

8/10/2019 1-s2.0-S0029801812002387-main

15/17


t e C-type c#ntr#ller+ i.e. t e c# an$ t# c#ntr#l t e r%$$er '#r t e trac& &eeping an$ t e ta ili>er 'in '#r r#ll re$%cti#n+ ig t e t e e t c #ice '#r t e ip c#ntr#l+ * ic a t e etter trac&ing &eeping an$ r#ll re$%cti#n.

4.2. ip a$ ancing in t e $yna ic ea$ing c ange

9 i ecti#n ai t# in e tigate t e $yna ic e a i#r '#r a ip#perate$ in ran$# *a e y c#n i$ering t e ariati#n #' t e ip ea$ing .ince t e C-type c#ntr#ller a t e etter per'#r ance #n t e a pect #' r#ll-re$%cti#n an$ trac&-&eeping+ t e c# pari #n et*een A-type an$ C-typeare a$e ere t# reali>e t e ip $yna ic e a i#r in t e ea$ing c ange.9 e ip ea$ing i initially et t# e in t e tern @%artering ea *it 301an$ c ange t# 01 #r er 'in t# c#ntr#l t etrac& &eeping an$ re$%ce t e ip r#lling #ti#n+ i %cce '%lly $e el#pe$.Acc#r$ing t# a erie #' n% erical calc%lati#n an$ c# pari #n+ t e el'-t%ningne%ral net*#r& a e$ !" c#ntr#ller i in$ee$ a c#n enient an$ %''icient t##l t#earc '#r t e #pti al c#ntr#l gain . =t i ery %ita le '#r a

30002000-1000 0 1000Y (m)

0

2000

4000

8/10/2019 1-s2.0-S0029801812002387-main

16/17

2D M.-C. Fang et al. / Ocean Engineering 54 (2012) 17 25

ea$ing i't 'r# c 301 t# c er 'in can e applie$ t# re$%ce t e r#lling #ti#n+ it ayincrea e t e re i tance an$ ea$ing err#r+ * ic nee$ care'%l c#n i$erati#n .C# parati ely+ t e re %lt in$icate t at C- #$e+ i.e. t e c# pact c#ntr#ller incl%$ing t e r%$$er '#r trac& &eeping an$ ta ili>er 'in '#r r#ll re$%cti#n+ aya e t e etter per'#r ance #n t e ip a$ ancing at ea t an #t er type #'

c#ntr#ller . =t ean t at peci'ie$ ta & a$ etter e *atc e$ y t e peci'ie$

re p#n i le t##l. Finally+ t e re %lt al # eri'y t at t e el'-t%ning ne%ralnet*#r& a e$ !" c#ntr#ller a$#pte$ ere can re p#n$ t# t e $yna icalea$ing c ange rapi$ly a *ell+ e en '#r t e $i''erent $yna ic #cean

en ir#n ent.

Time (sec)

Time (sec)

Fig. 13. 9 e ti e ariati#n #' c#ntr#l gain '#r (a) A- type an$ ( ) C-type in l#ng cre te$ *a e *it 1= 3 3 + 9 10 an$ initial ip pee$ R 23 &n#t . 9 e ip

8/10/2019 1-s2.0-S0029801812002387-main

17/17


Time (sec)

Fig. 14. 9 e i %lati#n #' (a) traGect#ry an$ ( ) trac&ing err#r '#r A- an$ C-type

in l#ng cre te$ *a e *it 1=3 3 + 9 10 an$ initial ip pee$ R 23 &n#t . 9 e ipea$ing i't 'r# c 301 t# c >y l#gic c#ntr#ller. .ip :e . 47 (2)+ 101130.

"# e+ M. .+ rig t+ C. .+ 1 1. C# p%ter et #$ in arine an$ #'' #re engineering.#%t a pt#n.

Fang+ M.C.+ 1 1. :#ll re$%cti#n y r%$$er c#ntr#l '#r t*# ip $%ring %n$er*ay repleni ent.. ip :e . 35+ 141150.

Fang+ M.C.+ ee+ M. .+ ee+ C. .+ 1 3. 9i e i %lati#n #' *ater ipping '#r a ip a$ ancingin large l#ngit%$inal-*a e . . ip :e . 37 (2)+ 12ati#n #' t e 8 CH MEC 01 clae el. Mar. 9ec n#l. 3er. =n; !r#cee$ing #' t e =EEE+ =nternati#nal C#n'erence #n

Mec atr#nic an$ A%t# ati#n. 6iagara Fall + Cana$a.McH##&in+ E. .+ M%rray- it + ". .+ i+ ,.+ F# en+ 9.=.+ 2000. ip teering c#ntr#l y te

#pti i>ati#n % ing genetic alg#rit . C#ntr#l Eng. !ract. D+ 42 443.9a&a a i+ 9.+ 1 < . Mec ani #' r#lling an$ applicati#n. :ep#rt #' Mit % i i ea y =n$% try

6aga a&i 9ec nical =n tit%te. p. 2D42 (in apane e).9rea&le+ 9. .+ M##&+ ".9.+ iapi + .=.+ 6ay'e + A. .+ 2000. A ti e$# ain et #$ t# e al%ate t e

% e #' # ing *eig t t# re$%ce t e r#ll #ti#n #' a ip. Ocean Eng. 27 (12)+ 13211343.9>eng+ C.,.+ in+ .F.+ 2000. A$apti e ip teering a%t#pil#t $e ign *it at%rating an$ le* rate

li iting act%at#r. =nt. . A$apti e C#ntr#l ignal !r#ce 14+ 41142

1-s2.0-s0029801812002387-main

Documents