Stabilization and Control of a UAV Flight Attitude Angles using the Backstepping Method

Transcription

1 ttio Jou of Mhi os Egiig 6 tiitio oto of U Fight ttitu gs usig th kstig Mtho Mihi Lugu stt h sts th sig of ii-u ttitu oto usig th kstig tho ttig fo th oi i utios of th ii-u usig th kstig tho th utho of this oti th ssios of th vto u io ftios whih stii th U t h ot to th si vus of th ttitu gs h ttitu oto otos th ttitu gs th gu ts th gu tios oth vis tht si th U ogitui t otios o sig th oi oto usig th kstig thiu th oi utios th Luov sis hv it us h sig oto hs it i Mt/iuik viot its fftivss hs tst with ig of ui siutios usig t fo th U fight tsts h oti suts v goo th tt th th os fou i vious woks Kwos ttitu gs kstig oto U NRODUON LL ov th wo U i his hv o g of ivi iit itios ot of sitists sig Us tht hv to t so ttios gig thi iiit ow ost s si so o so foth th oi of s-si Us th ost ssts sti o s otots us of thi k of iiit hi iiit is iovig thi oig thi fight oto ssts [] Moig siutio sis fight tstig of fu-si ifts o g Us v w st i ots of sitifi woks ov th st fw s [] Fig h o of th kw U this th utios of th fig ojt otio oi [] th kstig tho ig us h fo th oto of th U ttitu gs h ot of thius fo th oto of fig ojts wh thi fight is si oi utios: i ivsio oi itiv oto o thius tht us uo twoks [] h sst oiitis os oo i sst is oti usig th fist tho his tho isvtg is th ist of M Lugu is with th Uivsit of iov Fut of Eti Egiig viois Divisio 7 D tt iov Doj Roi (i: L@hooo ugu@thuvo) oiitis thi ivtivs his is sious o us th oi fos ots whih si th sst ot o t high isio g [5] ttiv to th i ivsio is th kstig tho; it is si tho its ost iott vtg is tht th oiitis ust ot ss i th oto w this th ttitu oto is ojt fo th kw U (Fig ) [6] s of th kstig tho his U is hti oi t ss i o to iii th g fo h sig of th ttitu gs oto (utoiot) s th titio of th th ftios (vto ios u ftios) so tht th gs htiig th U ttitu t to thi ios vus h Dfs P ft uit (DP) h of th outh fi oui fo itifi usti Rsh (R) uh so s go th kw og; th i ojtiv of this sh og ws to ostt th vtgs of Us with vi t ss [6] h i htistis of this U th k of th vti g th wig; ths thiks to s g fos suio oi fos h o isvtg th stiit of th U; s osu th sig utoiot ust v ffiit h uos of th fight oto sst ws to is th tu U stiit so tht it is hti oi stti stiit its otio vis stii tow thi si vus h i ssos tht us o Us : th ots (fo th sut of th i tios u v w whih itgtig to voitis u v w) th gots (fo th sut of th gu voitis ) ssos fo stti i ssu (th fist fo th titio of th oti titu th oth ssos fo th titio of th fight voit) io-tit o oth sst fo th sut of th U s hight with st to th gou so o [789] otst with [6] i this th U fight oto is usig th kstig tho th ffii of this tho wi ostt ig of ui siutios usig t fo th U fight tsts Most U utoiots us ssi ootio-itg-ivtiv (PD) otos -ho thos to tu th oto gis uig th fight his thooog is ot th st o us it hs high isks us th ot of iittios i th Us fos oustss t is iott to oti itgt fwok tht s it to i sthsi it vit oto ofigutio usig ittiv vot s [-] 9

2 ttio Jou of Mhi os Egiig 6 h thti ou of usig th kstig tho to th stiitio oto of ii U th titio of th oto ws (ftios of th vto u ios) whih ssu th oto of ii U th w oto softw ittio st th oigiit ts of this h is ogi s foows: th i utios of th kw U is giv i stio th oto sig fo th ith g h is st i stio ; i stio th utho tis th oto ws fo th stiitio oto of th o w gs stio th sig oto is it i Mt/iuik viot its fftivss is tst with ig of ui siutios usig t fo th U fight tsts; fi so ousios sh i stio DYNM EQUON OF HE EKW MN-U h ot of thos to fi th o of th Us [5-7] s o s i [8] th oto sst hitttu gt siifi juiious ssig th ift is fu stig th vis tht to oto hus th oit of th utoti iot is gt u ost sig thius o v ffiit [6] Fig h iti f sst o to oti th thti o of th kw U o s to fi th is ssts h fist o is th iti f sst th Nwto s ws sussfu i with st to this f o us this f it is ssu tht th suf of th Eth is ft o-ottig his f [9] fis tht is tgti to th Eth suf (Fig ); th sst t is ovit hos s oit fo th uw h so f (OXYZ) is th o is sst with its oigi i th t ss of th fig ojt h OX is is th ogitui is of th U th OY is th t is oitig out th ift ight sto wig whi OZ is is th vti is it is fi to si withi th U s of st h thi f is th w kow oi f its oigi ig th s with th oigi of th iti f; th OX is hs this ti th itio of th U tot voit his f is v iott us th titio of th stiit ivts is with st to this is sst Fig h o sufs th tutos of th kw U h U hs 6 tutos ssoit to th vto ios u ftios 5 6 (Fig ) tuto fo tuto fo th tt ig g G th st os wh tuto fo th o of th tust (ousio) fo ( ) us i th sit ittu o uss th ssi os of th o sufs ( th vto ftio th ios ftio th u ftio) it is ss to stish so tioshis tw th ssi ftios th ftios of th kw U h ftio of oto suf is fi i is with ositiv ftio usig gtiv ot t is si to wok with o tuto wig fo oto uoss thfo shou ov togth 5 shou ov togth too; thus 6 5 [6] h tioshis tw th ssi ftios ( ) U kw ftios ( ) [6]: ( 5 ) / ( 5 ) ( ) / 6 / 5 o oti th U is th U is osi to igi o with si g of fo [68] o siif th ivtio of th U o stti t of ss ositio is ssu h is of th U is osi to th sutt tw th kitis th kitis of th U us th uos of this is ot to u th i utios of th kw U wi ott o th U oto sig usig th kstig tho; th kw U is is st i ti i [6] [8] hus th kitis of th U is [68]: t os si ( si os ) si os os h ssios of th o ith w ots L M N [68]: 6 () () 5

3 ttio Jou of Mhi os Egiig 6 L M N ( ) ( ) ( ) () whi oths whih ot ss to [5]; th oto w is si o to us th kstig tho th sst ust witt u th foowig fo: wh is th i ssu th wig suf ttk sisi gs th wig s oi ho os os si si () th oi ot offiits hv th ssios [6]: (o ith w stiv) ( ) ( ) () is th stti ot offiit it hs vus os to o; tht is wh i siutios wi osi u h utios siig th ojtios of th U gu voitis og OXYZ f s [6]: with [ ( ) ] [ ( ) ] [ ( ) ] ; () (5) (6) ( ) f ( ) f ( ) (7) f u wh f f f oi futios s th o of vitu oto fo th o of th vi tow o without tkig ito out th is of h is us s vitu oto fo th ovg to o of th vi Fi th iut vi u is th o tht stiis th vi ONROLLER DEGN FOR HE PH NGLE HNNEL o stii th U ith g th utho osis th ios (si) vu of th ith g fis th o [5] t is vit tht tkig ito out () it is: si os (8) os with ositiv ostt h sig i is ; s sut it is si tht: si si (9) os os h utio of th o usig (9) os: ; () i o to ostt tht () osos to st sst th Luov futio hs hos [5] outig ( ) it foows: th i iti ots Fo th sig of th kw U oto fo th stiitio oto of th ttitu g ( ) th kitis utios of th U th utios of th oi ot offiits th utios siig th ojtios of th U gu voitis og th OXYZ f (utios () () (5)) O of th st oto sig ous is th kstig tho h kstig thiu is s o Luov tho it offs uti ossiiitis fo th us of oiitis with st to th i ivsio thiu hus so oiitis iti ( ) < ( ) > () h Luov futio is gtiv s osu th sst () is st o it ovgs to o h so o vi is ow hos s with hvig th fo (9) i: si () os 5

4 ttio Jou of Mhi os Egiig 6 s sut th foowig utio sst is oti: os () th sustitutio of with th fo (5) i th so utio () it foows: [ ( ) ( )] ; () tkig ito out th ssio of () os: ( ) ( ) ( ) fo () (5) wt to stii th o to o s w Fo this th foowig Luov futio ( ) (6) is hos outig ( ) it foows: ( ) with ( os ) ositiv ostt (7) h fist two ts i th ight si of (7) gtiv fo stiit sos it is si tht: ( os ) (8) o os ( ) ( ) ; (9) thus th fist tioshi tw th ftios of th vto ios u is: () with os ( ) ONROLLER DEGN FOR HE ROLL NGLE HNNEL () h ou is sii to th o st i stio ; th utho of th osis th si (ios) vu of th o g h fis th o [5] Fo ostt it foows ; tkig ito out th ssio of it suts: [ ( t si t os) ] () Fo th ovg of th o to o () ust hv th fo with ositiv ostt s osu th o gu voit hs th ssio [5]: t si t os () hoosig th Luov futio ( ) ( ) < ( ) > o gts: () hus th sst is st o ovgt to o ( ) h so o vi is ow hos: ; hs th fo: t si t os (5) U ths oitios oti th foowig sst: (6) ig with th fo i (5) ito th so utio (6) it foows: 5

5 ; (7) tkig ito out th ssios of it suts: (8) h o ust o Fo this th Luov futio (9) is hos outig it suts: () wh is ositiv ostt h fist two ts i th ight si of () gtiv us it is si tht < it is: () Rig hvig th fo (8) i th () oti: ; () thus th so tioshi tw th ftios of th vto ios u is oti s foows: () wh () ONROLLER DEGN FOR HE YW NGLE HNNEL Fo th w g stiitio th oh is th s with th o us i stios h o vis (5) us h; is th ios (si) vu of th w g whi hs th fo [5] os si os os (6) h Luov futios whih hv us th foowig os: (7) oti i this s too tioshi (th thi o) tw th ftios of th vto ios u: (8) with (9) ttio Jou of Mhi os Egiig 6 5

6 h titio of th vto ios u ftios is sovig th sst fo utios () () (8) hus it suts th sst: () with i i i i ig si () () (9) h utio sst () hs th ti fo: () with th soutio () o [ ] [ ] [ ] t t t () wh t () Fig ttitu oto fo th oto of th kw U fight Fig 5 Mt/iuik o of th U ttitu oto usig th kstig tho ttio Jou of Mhi os Egiig 6 5

7 ] ] ] ] ttio Jou of Mhi os Egiig 6 ousio th utho hs sussfu it th oi ttitu oto o th oi U ift o h ttitu oto otos th ttitu gs th gu ts th gu tios oth vis tht si th is of U Puttig togth utios () () (5) () () () (6) (9) () () th ssio of th si os th ok ig fo th ostutig of th ttitu oto hs oti (Fig ) MULON REUL this stio st th oti suts ft foig th ui siutios h sig oto sst hs it i Mt/iuik viot its fftivss hs tst with ig of ui siutios h Mt/iuik o of th stutu i Fig is st i Fig 5 h U hs s isios: wig s 7 wig suf 9 oi ho 8 ss kg h siutio t hv oti fo ittu; thus th vus of th oi offiits of th iti ots [6]: [g] [g/s] [ g kg i [s] i [s] i [s] kg [g] [g/s] [ g i [s] i [s] i [s] kg Fig 6 i vitios of th vis t t t t t t t t ( t) (5) i [s] 5 h ti oitios v iott us th th sttig vus of th vis; th ti oitios : [ g [g/s] [ g i [s] i [s] u 8 /s g/s g - g 5 g g g ; (6) th si vus of th ttitu gs hv hos s: 5 g g g Fig 6 st th ti voutios of th vis ( t) ( t) ( t) ( t) ( t) ( t) ( t) ( t) ( t) O ks th o futio of th kstig tho us th gs whih fi th U ttitu (th o g th ith g th w g) tk thi ios vus Ro g of th U [g] i [s] Fig 7 i vitio of th U o g fo ifft vus of tw Pith g of th U [g] - Fig 8 i vitio of th U ith g fo ifft vus of tw Yw g of th U [g] i [s] i [s] Fig 9 i vitio of th U w g fo ifft vus of tw 8 55

8 ttio Jou of Mhi os Egiig 6 h hoi of th vus fo th ositiv ostts ifu th soss of th sst Whi th ostts ositiv th sst is st; th igg th vus of ostts th tt th sst otis (th ovshoot th tsit gi io s) Fig 7 Fig 8 Fig 9 st th ti vitios of th th ttitu gs fo ifft vus of th ostts (vus tw ) h st suts oti fo th iu vu (i this s ) Fo if o osis th s of th o g stiitio fo th ovshoot is g whi fo it ss t tis to th vu g h s ousio oti gig th tsit gi io th is of th ostts fo th vus to th vus s to th s of th tsit gi io fo sos to 5 sos (65% s); s ks fo th ith w gs ONLUON h fous of th kstig oto sthsis oss ws th hoi of th o vis of th Luov futios h ftios of th oto sufs hv oti utios () () h oti ttitu oto it o Us; th thiu tht hs us fo its sig is g o us to ki of fig ojts offig v goo otio htistis of th outut sigs h sig of th th otos th kstig thiu hs it us th oi utios th Luov sis h tho hs iott vtg with st to th ssi thius (fo th sig of PD otos): th oi sst (siig th is of U) ust ot iis i ti oit his iitio ust o if w wt to sig PD otos h iitio of th U is iits th iiit of PD otos Usig th kstig tho th utho oti th ssios of th vto u io ftios tht oto th U t v ot stii it to th si vus of th ttitu gs gu ts h utho o siutios i Mt/ iuik usig t fo th U fight tsts h oti suts v goo (U ttitu gs th U gu ts t to thi ios vus i o tsit gi without ig ovshoots) Whi th ostts hv ositiv vus th sst is st; th igg th vus of ostts th tt th sst otis (th ovshoot th tsit gi io s) s o th otio tiv itgtio of th o io iti ssos i ow ost twoks with high g of u o/ REFERENE [] H ho Y o Y h utoiots fo s fi-wig u i vhi: suv EEE ttio of o Mhtois utotio 7-9 [] Y Pw thsis itio of Fight oto fo U Dissttio suitt to th Fut of th Gut hoo of th Uivsit of Misot D 9 [] NM Joh P u Wo Dvot of s u i vhi sh tfo: Moig siutig with fight tst vitio Moig iutio hoogis of Ehiit o [] NK P K Ghosh ift t stitio usig w fitig thiu s uo u twok Guss-Nwto tho outi Jou i 9 () -5 [5] Y Pw ttitu oto of Mii-U usig kstig oto Noi sts Pojt ME88 Oto 7 [6] D w Fight oto st fo i tiit -wig- o U i hi Mst of i hsis Uivsit of tosh outh fi Mh 9 [7] L Gigoi t-ow iti vigtio ssts Otiitio stuis ith Puish iov 7 6 [8] L Gigoi L Di J ou ifts titu Msut Usig Pssu fotio: oti titu Dsit titu WE stios o iuits sts [9] L Gigoi DG u h ifus of th go ssos os o th ttitu uus EEE ig Possig oit - 9 th ttio osiu ELMR-7 fous o Moi Mutii Z oti - t [] D Jug P siots Moig hw-i-th-oo siutio fo s u i vhi Gui Nvigtio oto of Ehiit o [] Ki O Ykiko Dookhoov K Jos Ri fight tst oto-tig sst th ft of Us Ms t th v ostgut shoo Poigs of th U Uiit hi of [] J Rfow Li J Dh F- fight oto w sig vifitio vitio usig out i giig toos Poigs of th hi EEE of o oto itios vo [] M ish vs i ift fight oto o Fis Lt 996 [] L Di J ou ED EF ssts o o of o tsot ift th ttio of o i hoti Etiit iov Roi [5] M ook Fight Dis Piis Esvi uttwoth- Hi 997 [6] JH kok utoti oto of ift Missis Wi- tsi 99 [7] Etki LD Ri Dis of Fight tiit oto Joh Wi & os 996 [8] K P tio s Muv Fight oto st fo U i his Uivsit of tosh 7 [9] Ki oiso of oto sts fo th Fight sitio of OL U i his Uivsit of tosh 8 [] M hioti G Mgi oto ws fo fotio of utooous fight vhis outi Jou i 9 (7) KNOWLEDGMEN his wok ws suot N-UEFU ojt PN -RU High-isio st-ow iti vigtos 56