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  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 ip a$ancing in *ae Ming-C%ng Fang a+ n + ,%-ien in   + #-e ang a a epartent #' yte  6aal Mecatr#nic Engineering+ 6ati#nal Ceng-%ng 8nierity+ 9ainan City 70101+ 9ai*an   Fiing #at  Marine Engineering :eearc Center+ 6ati#nal Ceng-%ng 8nierity+ 9ainan City 70101+ 9ai*an a r t i c l e i n ' #a   t r a c t Article it#ry;:eceie$ 1 an%ary 2012Accepte$ 1 %ly 2012Aaila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%$$er an$ 'in acti#n. 9e ateatical #$el incl%$ing ea-&eeping an$ ane%ering caracteritici $eel#pe$ in te preent paper an$ ten#nlinear tie it#ry #' ip #ti#n i #le$ y te '#%rt #r$er :%nge–%tta et#$. =n #r$er t# ey*#r$;! c#ntr#l 6e%ral net*#r& :%$$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%$$er c#ntr#l'#r trac& &eeping in te ea*ay *#%l$ e %ggete$. 2012 Eleier t$. All rigt reere$. 1. =ntr#$%cti#nile a ip ail in te ea*ay+ te e?ternal '#rce+ i.e. *in$+ *ae #r #cean c%rrent+ %%ally ca%e te ariati#n #n te #ti#n an$ trac&.9ere'#re+ #e $eice nee$ t# e applie$ t# te ip t# aintain tetaility an$ #rientati#n.8%ally te r#ll #ti#n i c#ni$ere$ t# e te #t eere pr#le ina'ety *ile te ip ail in te ea*ay. iply pea&ing+ te eri#% r#ll#ti#n *#%l$ a''ect te ip taility+ c#'#rt an$ e''iciency #' cre*+acc%racy #' electrical ecani+ an$ ip c#%re. 9ere'#re+ r#ll-re$%cti#ni epecially a$antage#% '#r ip a$ancing in *ae. #e $eice ae een *ell epl#ye$ t# acc#pli te ip r#ll re$%cti#n+ e.g. ilge &eel+anti-r#ll tan&+ gyr#c#pic taili>er+ #ing *eigt an$ taili>er 'in(9rea&le et al.+ 2000). A$$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1B F#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$$re;'angcail.nc&%.e$%.t* (M.-C. Fang).002-D01D/ - ee 'r#nt atter  2012 Eleier t$. All rigt reere$.ttp;//$?.$#i.#rg/10.101</G.#ceaneng.2012.07.00< te taili>er 'in t# re$%ce te ip r#ll #ti#n+ te ip pee$ %t reac tea$e@%ate al%e t# a&e te taili>er 'in '%ncti#n #re e''icient (err#l$ an$Micael+ 1). Henerally+ #t te r%$$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 #' iti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$%ce te ip r#ll #ti#n+ '#r e?aple+ te ne%ral net*#r& alg#rit canan$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<+ 2007B Fang et al.+ 2010)+ te <- OF ateatical #$el incl%$ing ea-&eeping an$ Contents lists available atSciVerse ScienceDirec t  journal homepage: www.elsevier.com/locate/oceanen g Ocean Engineering Ocean Engineering 54 (2012) 13–25  14 M.-C. Fang et al. / Ocean Engineering 54 (2012) 17  –25 ane%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%$$er '#r r#ll re$%cti#n an$trac& &eeping. =n te '#ll#*ing ecti#n+ te c#ntr#l yte inc#rp#rate$ in teateatical #$el '#r te ip ane%ering in *ae i $ecrie$. i''erent*ae c#n$iti#n an$ te $ynaical enir#nent are a$#pte$ t# inetigate tee''iciency #' ti c#ntr#l yte.2. Mateatical #$el9e n#nlinear <- OF e@%ati#n #' #ti#n (Fang an$ %#+ 200<B Fang et al.+ 2010) incl%$ing te c#ntr#l '#rce #' te taili>er 'in an$ te r%$$er are$eel#pe$ an$ #*n in E@. (1)–(<). =n a$$iti#n+ te engine t#r@%e e@%ati#n ial# #*n i%ltane#%ly in E@. (7).K%  _  n c  _ L  K y K # e LN n c  _ L n c  _  ? K # e L%  _   > K # e L* y  _  %rge : K1L N F  K # 0 LN :F  N FF  9K1t  p L:  K n  _  % c  _ L ? K # e L% c  _  y K # e L n  _  , n n , c € c €  , c  _ c  _  , n 9 n 9 n 9 n 9 *ay :  ,  _ n 9 c  _ 9  , c  _ 9 c  _ 9 c  _ 9 c  _ 9  , F  K # 0 L, F K # e L, :F  , FF n 9 c 9 K2Leae : y € K # e L y €  y  _ K # e L y  _   y K # e L y *  _   > K # e L*  _  * K # e L*  F  K # 0 L F K # e L FF  gK3L= ?? '  € = ?? y  _  c  _   ?? K # e L y  _  c  _  ?? K # e L '  €   '   _ '   _  K, n n , c  _ c  _ L>  :#ll :    F  K # 0 L  F K # e L  :F    FF K4L= yy y €  = ?? c  _ '   _  !itc : ?? K # e L '   _ c  _  yy K # e L y € M y  _ K # e L y  _  M y y M *  _ K # e L*  _ M * K # e L*M F  K # 0 LM F K # e LM FF K5L = >> c € = ?? y  _  '   _  ?? K # e L y  _  '   _  >> K # e L c €  6 n  _  n  _   6 n n  6 c  _ c  _  6 c  _ 9 c  _ 9 c  _ 9 c  _ 9  6 nn c  _ n 2 c  _  6 n c  _ c  _ n c  _ 2  6 '  '   6 n 9 '  9 n 9 '  9 ,a* :  6 c  _ 9 '  9 c  _ 9 '  9  K, n n  , c  _ c  _  , n 9 n 9 n 9 n 9  , n 9 c  _ 9 n 9 c  _ 9  , c 9 c  _ 9 c  _ 9 c  _ 9 L?   6 F  K # 0 L6 F K # e L6 :F  6 FF K<LEngine : 2  p K=  pp    pp Ln  _  P F P ! K7L*ere %rge+ *ay an$ eae el#citie are repreente$ y %+  an$ *+repectiely+ *erea r#ll+ pitc an$ ya* $iplaceent are repreente$ y '  + y an$ c + repectiely. : i te ip reitance. 9e %cript F+ :F+ FF an$ Frepreent Fr#%$e– ryl# '#rce+ r%$$er '#rce+ taili>er 'in '#rce an$$i''racti#n '#rce+ repectiely. ince te trip te#ry i applie$+ te $i''racti#n'#rce '#r %rge+ N F + cann#t e calc%late$+ #*eer+ it i generally all $%e t#te len$erne #' te ip. =n E@. (3) an$ (5)+ te c#rrep#n$ingy$r#$ynaic c#e''icient *it repect t# eae an$ pitc can e '#%n$ inre'erence (i et al.+ 1D0)+ an$ tey are calc%late$ y Fran& cl#e-'it et#$. ? +  y an$  > repreent te a$$e$ ae *it repect t# te ?+ y an$ > a?e+repectiely+ *erea  ?? +  yy an$  >> repreent te a$$e$ #ent #' inertia *itrepect t# te ?+ y an$ > a?e+ repectiely. 9e ane%ering $eriatie #' *ay an$ ya* #ti#n+ i.e. , n + , n 9 n 9 + 6 c an$ 6 n 9 '  9 + etc.+ are etiate$ yepirical '#r%la (=n#%e et al.+ 1D1a) ae$ #n te #$el e?perient in cal*ater. 9e r#ll $aping c#e''icient   '   _ can e c#p%te$ 'r# te epirical'#r%la $erie$ y te prei#% t%$y (aa#t# et al.+ 14B 9a&aai+ 1<). 9e relate$ n#nlinear ter '#r ane%ering $eriatie can e '#%n$'r# te re'erence (iran# an$ 9a&aina+ 1D0B =n#%e et al.+ 1D1). 9e Fr#%$e–ryl# '#rce are calc%late$ y integrating te inci$ent*ae pre%re acte$ #n ip %ll t# te *ae %r'ace+ an$ te $i''racti#n'#rce are calc%late$ *it te linear trip te#ry an$ #%rce $itri%ti#net#$. 9ee '#rce $epen$ #n te ip c#n'ig%rati#n el#* teintantane#% *ae %r'ace tat %t e calc%late$ at any intant #' tie(Fang et al.+ 13B Fang an$ %#+ 200D). 9e ter =  pp +   pp + P F + P ! + n in E@.(7) repreent te #ent #' inertia #' pr#peller-a'ting yte+ te pr#peller a$$e$ #ent #' inertia+ te pr#peller t#r@%e+ te ain enginet#r@%e an$ te rp #' pr#peller+ repectiely. 9e r%$$er '#rce can ere'erre$ t# iran# (1D0).9e taili>er 'in-in$%ce$ '#rce an$ #ent can e $erie$ an$ lite$ a'#ll#*+N FF  F : F  KDL, FF  F : c# '  F F  c# '  F KL FF  KF : in '  F  F  in '  F LK10L  FF  Q> F KF : c# '  F F  c# '  F Ly F KF : in '  F F  in '  F LK11LM FF  > F N FF K12L 6 FF  ? F , FF K13L*ere te %cript :+ : +  an$  repreent te 'in-in$%ce$ li't '#rce() an$ $rag '#rce ( ) #n te tar#ar$ i$e (:) an$ p#rt i$e ()+repectiely. ? F + y F an$ > F are te c##r$inate #' te acti#n center #' te 'in'#rce. '  F i te angle et*een te 'in an$ te pl% line. 9e relate$e@%ati#n #' te li't '#rce an$ te $ra't '#rce can e al# '#%n$ *it repectt# te re'erence (ee+ 177).3. C#ntr#l yte9e ! c#ntr#ller i %%ally e?pree$ in te '#ll#*ing '#r c#ntaining t*#c#ntr#l gain+ i.e. pr#p#rti#nal (  ! ) an$ $eriati#n(  )$ %KtLrKtL     p %KtL  K14L $t*ere r(t) i te c#ntr#l #%tp%t ariale an$ %(t) i te yte err#r.Acc#r$ing t# te $i''erent #Gectie ii#n *it repect t# $i''erentc#ntr#l t##l+ '#%r type #' c#ntr#l c#an$ applie$ t# te taili>er 'inan$ r%$$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#llre$%cti#n.C-type; te c#an$ t# c#ntr#l te r%$$er '#r te trac& &eeping an$ tetaili>er 'in '#r r#ll re$%cti#n.  M.-C. Fang et al. / Ocean Engineering 54 (2012) 17  –25 15 -type; te c#an$ t# c#ntr#l te r%$$er '#r te trac& &eeping *it r#llre$%cti#n+ an$ 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).N 0 8 tan c , 0 E 0  @''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i''i K15L tan 2 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$e teip t# ail t# te c#an$e$ *ayp#int. 9e relati#nip et*een te act%alea$ing ( c r  ) an$ $eire$ ea$ing ( c ) i e?pree$ a '#ll#*. c e  c r  c K1<L Fig. 1. 9e ill%trati#n #' te ipJ trac& in te eart-'i?e$ c##r$inate yte. *ere c e i te ea$ing err#r. Fig. 2. 9e 'l#* cart #' te r%$$er c#ntr#l yte '#r (a) A-typeB () - typeB an$ (c) te taili>er 'in c#ntr#l '#r C- an$ -#$e.  1< M.-C. Fang et al. / Ocean Engineering 54 (2012) 17  –25 3.1.9e A-type an$ -type (i.e. c#ntr#l c#an$ #n r%$$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%$$er anglet# aintain te trac& &eeping #nly *erea te -type c#an$ i t# c#ntr#lte trac& &eeping an$ r#ll re$%cti#n i%ltane#%ly. 9e 'l#* cart ae$ #nte ne%ral net*#r& alg#rit '#r A-type an$ -type are #*n in Fig. 2(a) an$()+ repectiely.ae$ #n te E@. (14)+ te ! c#ntr#ller c#an$ '#r te A-type can e*ritten a $ KtL    p E 0 Kt1L  $ Kt1L  yp c e Kt1L  y$ c  _ Kt1L K17L *ere $ (t)i te r%$$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$ingly+E 0 (t1)+ (t1)+ c e (t1) an$ 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$$en layer i a$#pte$ in 661. E 0 (t1)+ (t1)+ c e (t1) an$ c  _  Kt1L are electe$ a te inp%t n#$e+ *erea E ^ 0 KtL+  ^ KtL+ c ^ e KtL an$ c ^_  KtL are et t# e te #%tp%t n#$e #' te #%tp%t layer. 9e err#r '%ncti#n '#r  661 i $ecrie$ a el#*E &  Qg &  KtLg ^ &  KtL 2 K1DL*ere g & (&1+ 2+ 3 an$ 4) iplie E 0 + + c e an$ c  _ + repectiely.eca%e r#ll+ ya* an$ *ay #ti#n can e p#itie #r negatie+ teyper#lic tangent '%ncti#n i tere'#re a$#pte$ a te actiati#n '%ncti#n+ i.e.'K?L  tan K0 : 5?LK1LAn$ te $eriatie #' te actiati#n '%ncti#n in 661 i t% eal%ate$ a el#*' 0 K?L  0 : 5Q1'K?L 2 K20Lae$ #n te 661 actiati#n '%ncti#n in E@. (1) an$ it $eriatie in E@.(20)+ te '#ll#*ing enitiity in'#rati#n+ @ g &  / @ $ (t1)+ can e #taine$; $ @ Kt g ^ & 1L  1 4 NQ1Kg ^ &  L 2 R  G Q1  G2   G + &  1+2 ... 4 K21L @  G *ere   G i te *eigt et*een te inp%t n#$e an$ te Gt i$$en n#$e+ an$ R  G i te *eigt et*een te Gt i$$en n#$e an$ te #%tp%t n#$e.   G i te #%tp%tect#r #' te i$$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 &  12 Qg &  Kt1Lg &  KtL 2 2 +&  1+2 ... 4K22L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' 0 K?L  'K?LQ1'K?LK24L 9ale 1!rincipal $ieni#n #' te c#ntainer ip.ipengt ()1D5.5rea$t ()30.2 ept ()1<.< ra't ()F! 11.0A! 11.0Metacentric eigt ()2eigt #' C. H. ()12.0D%ll i$e area ( 2 )1734.43aterline c#e''icient0.D5<1:#lling peri#$ ()1D.2!r#peller !r#peller $iaeter ()7.45!itc rati#1.0:%$$er :%$$er eigt ()D.4:%$$er area ( 2 )40.42#ngit%$inal $itance 'r# r%$$er t# C. H. ()0.0Rertical $itance 'r# r%$$er t# C. H. ()D.0Ma?i% $e'lecti#n angle ($eg.)  35Ma?i% $e'lecti#n rate ($eg./)3.5Main engineMC: (!)33+7<0100S :!M19ale 29e $ieni#n #' te taili>er 'in.pan ()5.77Fin area ( 2 )15Apect rati#2.22Ma?i% rate ($eg./)4.DMa?i% *ay angle ($eg.)  24#ngit%$inal $itance 'r# i$ip ()21.49ranere p#iti#n 'r# i$ip ()17.7Rertical p#iti#n 'r# i$ip ()10.17Angle *it repect t# pl% line ($eg.)72

Tribes in India

Jul 23, 2017
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