Feeding an information determine optic atmosphere turbulence into the simulation model of a seeker of homing missiles

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1 6h WSEAS Innainal Cnfnc n SYSTE SCIENCE and SIULATION in ENGINEERING, Vnic, Ialy, Nvmb 2123, Fding an infmain dmin pic amsph ubulnc in h simulain mdl f a s f hming missils TEODOR BALÁŽ, RADEK DOSKOČIL, ARTIN ACKO Dpamn f Wapns and Ammuniin, Dpamn f Ai Dfnc Sysms Univsiy f Dfnc a Bn Kunicva 65, Bn, CZECH REPUBLIC d.balaz@unb.cz, ad.dscil@unb.cz, main.mac@unb.cz Absac: Pssibl way f implmnain f masud and cmpud daa abu amsph ubulnc in h simulain mdl f an plcnic s (cdina) f a hming missils is dscibd in his aicl. Th gnal mhd allws analyzing f impac f h amsph ubulnc n upu signal f an plcnic acing cdina f hming missils. KyWds: Tubulnc, Amsph, Rang, S, Cdina, Hming, Rc, Simulain 1 Inducin A hming cs VSHORAD and SHORAD h plcnic (OE) acing cdinas (TC) wih ngyscp acing acuaing mchanism a us h ms [3, 8] ha is mvably plac n h bad f a hming c. Th psiin f h pic axis f a cdina is cnlld fllw h ag all h im. I is allw g ncssay paams f alizain usd guidanc mhd (aiming angl and angula vlciy f ag ). Funcin cha f h OE TC wih gyscp acing acuaing mchanism f h vical plan is in h Fig.1. Opical U OE sysm sysm Gyscp ϑ Tqu Suc Fig.1 Funcin cha f h OE TC wih gyscp f h vical plan Th masumn f dsid paams is basd n h dcin pic adiain ppaga in h amsph fm ins ag OE TC. Th amsph has an unngligibl impac n ppagad adiain (Fig.2). In idal amsph cndiins h ffc f anuain (abspin, scaing) and ubulnc n qualiy f imag ds n assum. Tass f ang f h OE TCs a slvd nly accding ngy gmical fmulas. Th ffc f anuain and ubulnc has analyz whn w sach ang and accuacy f h masumn f OE TCs in al amsph [10]. g B a c u n d T a g b a c s ca ing Φ 3 Φ 1 Φ 4 Φ 5 A msp h i nh n adiain f a m s p h jammi ng Φ 2 OE a p p a aus p si i n f a g a c ing f a g a n g u l a v l ciy f ag Fig.2 Cha f adiain in sysm f ag, amsph and OE appaaus Th impac f anuain and scaing f pic adiain n h suling imag cad by OE sysm xpsss spcially n innsiy dcasing f pic adiain duing h ppagain in amsph and n dcasing f cnas ag/bacgund. I dcass ang f OE appaaus n h givn ag. Nih abspin n scaing causs an angula f aiming. Bsids w a abl cmpnsa a scaing sufficinly duing masumn f a disanc. Tubulnc f amsph chaic chang f facin indx f ai can chang f dimnsin and shap f ag imag, pducd flucuain f adiain ampliud, pducd andm changs f psiin ag imag and caus andm in aiming ag and in masumn angula psiin ag, pssibly angula vlciy, and in h nd influnc f ang f TC [1,]. 2 Pblm Fmulain Funcin cha fm Fig.1 is pssibl ansfm in sucual cha f OE TC wih gyscp acing acuaing mchanism, in h Fig.3, accding Laplac ansfmain uls [4, 7].

2 6h WSEAS Innainal Cnfnc n SYSTE SCIENCE and SIULATION in ENGINEERING, Vnic, Ialy, Nvmb 2123, (p) p 1 ϑ p (p) (p) p F (p) U (p) F (p) (p) K (p) (p) (p) ϕ p F G(p) p Fig.3 Sucual cha f OE TC wih gyscp f h vical plan [3] In sucual cha in h Fig.3 psn: U K F = = sandad ansf funcin ϕ p + p T f OE sysm includs an bjciv; (1) F p K = = sandad ansf funcin + U p p T f a qu suc; (2) F G 1 K = = = p p L p G sandad ansf funcin f a f gyscp; (3) wh is magniud f angula vlciy jump f a chang dicin f ag aiming lin. Fm caid u analysis and fm minal fmula (5) fllw ha sabilizd valu f cnl dviain ϕ is ppinal angula vlciy f h chang f ; dicin f h ag aiming lin TC wih a paial ansf funcins (1 3) bhavs as a sysm wih fis asaism, i.. h sysm has a z sabilizd dviain f psiin and cnsan dviain f vlciy; h using f gyscp acing acuaing mchanism lads in ffciv suppssin f c lngiudinal vibains n pain f TC. Fllwd cnclusins a cnvnin f h mhd f ppinal guidanc and hi mdificains ha usd a hming c VSHORAD and SHORAD h ms. Ths cnclusins fm analysis f TC a pssibl chc and nlag wih h hlp f h simulain mdl (SldKd1.mdl) in infac alab [8] (Fig.4). K ficin cfficin in baings f gyscp. Inpu infmain f TC abu angula psiin (vnually angula vlciy) f acd ag is psnd by valu f psiin angl (vnually angula vlciy f chang f h aiming lin f ag ). Gal f cnl is h pic axis f TC aim h ag all h im. This siuain is pssibl dscib by m =, and cnl dviain ϕ = 0 ad. Lngiudinal vibains f c ϑ a nx inpu quaniy ( hamful ), ha influnc mus b liminad. Accding hy f aumaic cnl [3, 8], whn i is u a cndiin K 0, f h cnl dviain f TC (Fig.3) valid fmula 2 p T T + p ( T + T ) + 1 ϕ 3 2 = p T T + p T + T + p + K, (4), = F p p wh K = K K KG is whl amplificain givn as pduc amplificain f OE sysm, suc f a qu and invs valu f a mmn f mmnum f h gyscp; F ϕ, is a ansf funcin f a cnl dviain; T a T a im cnsans f fil clls f h lcnic blc and suc f qu. Thn f h sabilizd valu f cnl dviain is valid 1 ϕus = lim p ϕ lim p F ϕ, p 0 = p 0 p (5) K Fig.4 Cha f simulain mdl OE TC wih gyscp a infac ATLAB Simulin (SldKd1.mdl) F h simulain f funcin [7] h OE TC f hming cs VSHORAD and SHORAD hav dmin as sn as h fllwing paams (h dmind f h OE TC sysm VSHORAD Sla2) [8, 9]: gain f pic sysm K = 100 sysm K = 100 (fil), gain f lcnic, im cnsan f lcnic sysm T = f = 100 s = 10 ms ; 1 1 gain f suc f qu K = 0, 001, im cnsan f h suc f qu T m = 0,1 ms ; gain (a mmn f mmnum) f gyscp KG = L = 0,12 g m s 8,33 g m s, ficin cfficin in baings f gyscp angula vlciy f ag ( ) 3 K = 1 10 ; 1 0, 2 ad s ; fquncy f h lngiudinal vibains f c f = 900 min = 15 s, i.. ω = 94,5 s, ampliud f vibains ang 0, 01 ad 0, 2 ad.

3 6h WSEAS Innainal Cnfnc n SYSTE SCIENCE and SIULATION in ENGINEERING, Vnic, Ialy, Nvmb 2123, Th suls f simulain f funcin h OE TC, i.. cuss f signals in mdl SldKd1.mdl (Fig.4), 0 1 s and abv a shwd f im ang mnind paams and f w chaacisic cass and al A( ϑ ) 0,1 ad (idalizd A( ϑ ) << 0,1 ad siuain) in diagams in h Fig.5a and Fig.5b. (Tp ad = f, h diagams xpss a inpu funcin [ ] middl funcin f a cnl dviain ϕ [ ad] = f ( ) 1 and bm upu funcin d / d ad s = Fig.5a Signals f h ampliud vibains and K 0 A( ϑ ) << 0,1 ad f.) is pssibl us f masumn f valu ( ), b valid ( > 0,1 s) = ( ). If cndiins a fulfilld, xcp valu f ampliud f h lngiudinal vibains f c, ha is, hn cuss f signals a shwd n h A( ϑ ) 0,1 ad Fig.5b. I nws ha ( ) vay. Cus f ( > 0,1 s) > 0,1 s ns., bu valus can appximaly xpss by fmula > 0,1 s = + A sin 2 π f, _ ns _ pm ( ϑ ) ( ) wh _ ( ) is ampliud f masumn f pm A ϑ angula vlciy f TC pic lin, ha valu is funcin A ϑ. By simulain i is pssibl shw f ampliud ha a ampliud pidical vaiain a quaniy _ pm ( > 0,1 s) iss wih ising a valu diagams in h Fig. 5b s ha ϕ ( ) spi f = A ϑ. Fm > 0,1 s ns. In, whn w implmnd fmula (5) h f masumn aiss h m h bigg is valu A( ϑ ). Nw w can as lgiimaly: Wh is h pblm? W s ha usd mahmaical mdl (1 5) ds n allw dic analysis (implmnain) f impacs f amsph ubulnc upu signal f OE TC. Th mdl ds n cnain any dic pic quaniis ha dmin amsph ubulnc and ha influnc funcin f OE TC. Sluin is add sm inpu funcin in OE TC ha xpss chang in inpu quaniy pducd by ubulnc. F h fis xplanain (appach) w will us a mdl f cus quaniy wih man squa dviain σ [1, 8], Fig.6. Fig.5b Signals f h ampliud vibains and K 0 A( ϑ ) 0,1 ad Fm p diagam in h Fig.5a fllws, if h ag = ns (i.. mvs cnsan angula vlciy ( ) ) a vical plan and if ficin cfficin in baings is minimal ( K 0 ), and a h sam im, ampliud f h lngiudinal vibains A( ϑ ) << 0,1 ad s cuss f signals cspnd hical assumpins. Fm h las diagam in h Fig.5a can 1 > 0,1 s 0, 2 ad s = ns., ha ad valu 1 cspnd chsn inpu valu ( ) = 0, 2 ad s b valid ( > 0,1 s) = ( ) =, and hus cnl dviain ϕ ( > 0,1 s). S ha. Nx s, Fig.6 dl f inpu signal ( ) ns wih σ

4 6h WSEAS Innainal Cnfnc n SYSTE SCIENCE and SIULATION in ENGINEERING, Vnic, Ialy, Nvmb 2123, Pblm Sluin W will analyz h cas whn ( ) ns (Fig.6). I is mans ha h chang cus f angl ( ) in im is n lina ising, i.. ( ), bu valus f angl a dispsd abu σ fm man valu. This mdl cus cspnds cas whn h changs a pducd by ppagain pic adiain in amsph fm ag. Th simulain mdl SldKd2.mdl was fmd f an invsigain mann f h OE TC and his upu signals includ h impac f ubulnc flucuain insananus psiin f cn in dicin axis x [1, 2, 6], Fig.7. Th lmn paams f OE TC a h sam as pvius xampls. Fig.9a Signals f vibains A( ϑ ) << 0,1 ad and man squa dviain σ ad Fig.7 dl f flucuain f insananus psiin f cn f ag in dc plan [1] Fig.9b Signals f vibains A( ϑ ) << 0,1 ad and man squa dviain σ ad inpu funcin f mdl f ubulnc amsph Fig.8 Cha f h simulain mdl SldKd2.mdl Th suls f simulain funcin h OE TC by mans f mdl SldKd2.mdl (Fig.8) wih inpu funcin (YT.ma) influncd f mdl f al amsph a 0 1 s in diagams in h Fig.9a, shwd f im ang Fig.9b and Fig.9c. Fig.9c Signals f vibains A( ϑ ) << 0,1 ad and dispsin σ 4 Cnclusin ad Fm cmpud cuss in h Fig.9a,b,c w can s and angula vlciy ha signals f dviain

5 6h WSEAS Innainal Cnfnc n SYSTE SCIENCE and SIULATION in ENGINEERING, Vnic, Ialy, Nvmb 2123, ( ) a impacd n amsph vy subsanially cnay signals in h diagams in h Fig.5a,b. And i m h bigg is valu f dispsin σ f inpu signal ( ). If man squa dviain appximaly 5 σ 1 10 ad, implmnain f fils wuld lad suppssin f highfquncy pa f signal ϕ and, and his smhing. Cus f signal wuld b appximaly cnsan, i.. ϕ 0,1 s ns 0,1 s ns. ( ) and Subsqunly i wuld allw using f fmula = f alizain ppinal mhd f guidanc. If man squa dviain σ ad, signals f dviain ( ) and angula vlciy ( ) a impacd n amsph s m ha using f filain and alizain ppinal mhd f guidanc wuld b vy pblmaic and inffciv. F pacical applicabiliy f his mdl f OE TC is ncssay plac mdl f inpu funcin by xpimnal an daa abu amsphically ubulnc [6, 8]. I is nx as f u jb. Rfncs: [1] BALÁŽ, T., DOSKOČIL, R., KRIST, Z., ACKO,. Flucuain f Dicin Pins in h Fild f Viw f h Oplcnic Dvic by Tubuln Amsph. Budaps: 4h Innainal Cnfnc Nw Challngs in h Filds f h iliay Scincs 2006, Zinyi ils Nainal Dfnc Univsiy, Hungay, ISSN: [2] BALÁŽ, T., DOSKOČIL, R., ACKO,., ŘEHOŘ, Z. Chyba zamířní způsbná ubulncí amsféy (Aiming causs by amsph ubulnc). Lipvsý iuláš : 12h Innainal Scinific Cnfnc Amamn and Tchnics f Land Fcs 2006, Aadémi zbjných sil gn.. R. Šfánia, Kada sjásva, Lipvsý iuláš, Slvns, p. ISBN [3] HATIL, I., DOSKOČIL, R. Oplnicé dináy avých sysémů (Oplcnic cdinas f c sysms). Bn : Vjnsá aadmi v Bně, [4] HOLST, C. G. Tsing and Evaluain f Infad Imaging Sysms. Scnd diin. Win Pa and Washingn : JCD Publishing and SPIE Opical Engining Pss, Bllingham, Washingn, USA, [5] HOLST, C. G. Elpical Imaging sysm Pfmanc. Scnd diin. Washingn : JCD Publishing and SPIE Opical Engining Pss, Bllingham, Washingn, USA, [6] BALÁŽ, T., DOSKOČIL, R., ACKO,., ELŠA, P., ŘEHOŘ, Z. Expimnal Dminain f a Claiv Dpndnc f h Imag Fams fm Dicin and asu Lin f a Passiv Rangfind in h Tubuln Amsph Cndiins. Tnčín: 1s Innainal Cnfnc Advanc in chanics, Alxand Dubč Univsiy f Tnčín, Slvaia, ISBN , EAN [7] BOREAN, G. D. dulain Tansf Funcin in Opical and ElcOpical Sysms. Washingn : SPIE Pss, Th Innainal Sciy f Opical Engining, Bllingham, Washingn, USA, [8] DOSKOČIL, R. Oplnicý diná univzálníh avéh mplu blízéh dsahu (Oplcnic s f a gnal SHORAD c sysm). Bn : [Dissain], Univsiy f Dfnc, [9] DOSKOČIL, R. dlvání plnicéh sysému s dinám avých mplů VSHORAD (Th mdling f plcnic sysm wih s f VSHORAD c sysm). Lipvsý iuláš : Sbní Aadmi zbjných sil gn.. R. Šfánia Vjnsj aadémi v Lipvsm iuláši, Simulácia a mdlvani v PVO, Slvnsá publia [10] HOUGHTON J. Th Physics f Amsphs. Thid diin. Cambig: Cambidg Univsiy Pss, Unid Kingdm, 2002.