Near Space Hypersonic Unmanned Aerial Vehicle Dynamic Surface Backstepping Control Design

Transcription

1 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp Snsos & ansducs 4 by IFSA Publishing S. L. Na Spac Hypsonic Unmannd Aial Vhicl Dynamic Sufac Backstpping Contol Dsign inyong YU i CHEN Chao WANG Shigai LI Dpatmnt of Contol Engining Naval Aonautical and Astonautical Univsity Shandong Yantai 64 China Dpatmnt of aining Naval Aonautical and Astonautical Univsity Shandong Yantai 64 China l.: hjhychnji@63.com Rcivd: 8 Apil 4 /Accptd: 3 un 4 /Publishd: 3 uly 4 Abstact: Compad with taditional aicaft th na spac hypsonic unmannd aial vhicl contol systm dsign must dal with th ta pominnt dynamics chaacts which a diff fom th taditional aicafts contol systm dsign. A nw obust adaptiv contol dsign mthod is poposd fo on hypsonic unmannd aial vhicl HSUAV unctain MIMO nonaffin block contol systm by using multilay nual ntwoks fdback linaiation tchnology and dynamic sufac backstpping. Multilay nual ntwoks a usd to compnsat th influnc fom th unctain which dsigns th obust tms to solv th poblm fom appoach o. Adaptiv backstpping is adoptd dsignd to nsu contol law th dynamic sufac contol statgy to liminat th plosion of tms by intoducing a sis of fist od filts to obtain th diffntiation of th vitual contol inputs. Finally nonlina si-dg-of-fdom 6-DOF numical simulation sults fo a HSUAV modl a psntd to dmonstat th ffctivnss of th poposd mthod. Copyight 4 IFSA Publishing S. L. Kywods: Hypsonic ummannd aial vhicl Nual ntwoks Dynamic sufac Backstpping.. Intoduction Hypsonic ummannd aial vhicl contol tchnology has attactd a lot of attntion in cnt yas bcaus of highly nonlina dynamics and high Mach vlocity [-3]. Wang [4] adoptd adaptiv sliding contoll to analy th longitudinal dynamics of a gnic hypsonic ai vhicl. Shtssl [5] dsignd inn and out sliding mod contoll loop to invstigat th nty of hypsonic vhicls Austin [6] us fuy logic contol to compnsat th unknown nonlinaitis gntic algoithm to optimi th scaling paamts of fuy contoll. A kind of nual adaptiv contoll fo hypsonic ummannd aial vhicl is poposd by Xu Mimiani and Ioannou [7]. A fw cnt contibutions hav also attmptd dsign dictly on nonlina modls [8-]. Most sach sults w stictd to linaly paamtid and stat fdback linaiabl. Diffnt fom abov wok th pap invstigat a MIMO nonaffin nonlina hypsonic unmannd aial Vhicl modl with gnal st of unctaintis. Dynamic sufac backstpping contoll is dsignd basd on Radial-Basis- Function RBF nual ntwoks appoach. Stability analysis is also shown by th Lyapunov stability thoy. Finally a numical simulation of a 6-DOF 9

2 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp HSUAV modl is pfomd to vify th ffctivnss of th poposd algoithm and th conclusions a givn.. Nonlina HSUAV Modl Wingd-con [] is on of th main invstigat objcts with its hypsonic mach numb and opn aodynamic paamts but most sach is basd on its longitudinal channl modl. In this pap w finishd Wingd-con s th-as highly nonlina modl with gnal st of unctaintis. h nonlina dynamic quations a givn as follows = f = f + b + h u 3 = f + bu W assum that f b h f f 3 and b a unknown and f= f+δ f b = b+ Δb f3 = f3+ Δf 3 b = b + Δb h = h + Δh wh f b h f b a nominal systm paamts th oths a unctaintis. = [ V θψ c ] = [ β μ] 3 = [ p q ] u = [ ] a. h task of th contoll is to tack th commands signals whn aodynamic modl unctaintis ist. Assumption : Ignoing th ffct of th fin dflction on th aodynamic foc and viwing it as a pat of th unctaintis namly h. 3. Contoll Dsign 3.. RBF Nual Ntwok = In th contoll dsign RBF NN is usd to appoimat th unknown function φ. In a compact st RBF NN can b pssd as ˆ φ = WS ˆ 4 wh p Wˆ R is th tuning wight mati and φ is th vcto composd of Gauss functions. Givn a smooth function φ wh Ω is th compact subst of R m and > th ist a Gauss m p function vcto S : R R and an optimal wight mati W such that φ W S Ω. Dfin Δ Δ h WS = h 5 as NN constuction o. h optimal wight mati W is only usd in th analysis. Assumption : Givn a smooth function φ and NN stimato 6 th ists a optimal wight mati ε > is W such that Δφ εh wh h m Ω R a constant and m is th dimnsion of th input spac. Assumption 3: h ists constant giu > gi > to mak < g < g : = f g < Ω i=... n iu i i i i+ i i i+ i+ n 3.. Dynamic Sufac Backstpping Contoll Dsign Stp Dfin o sufac = d V θ ψ [ ] d= d d cd is th systm anticipant tack divativ is = f d. 6 Dfining v= d + k k >. By using Assumption and v = w can gt th following inquality f + v > g > Fom litatu [] w can gt that th has an = v so idal vitual contol function d d f + v = 7 d λ d f = f + g 8 = + d g λ : g λ λ λ λ < λ < Accoding to function 6 7 so that = = k + g 9 λ d 93

3 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp = + W S V X + ε d d wh d is th ctain pat of d Multilay NN W S V X + ε can b usd to appoach th unctain pat of d wh X is th input of abov NN ε ε u s th NN appoaching o and ε u >. Considing d is had to b acquid in th factual contoll dsign. Intoduc a nw stat vaiabl d which can b obtaind by th following fist-od filt d + d = d d = d = l + d d hn w choos dsid vitual contol valu as follow = l + + W ˆ S V ˆ X + d d wh c > is th dsignd paamt is th inductd obust itm and will b mbodid as follow. Dfin o stat valu as = d thn th dynamic function of o stat valu thn λ d d λ ˆ ε u = k + g + = k + g c 3 + g W S SV X + W SV X + d + λ V = + W Γ W + t V Γ V 4 { V } W g λ wh Γ W=Γ W> Γ V=Γ V> a th paamts to b dsignd. aking th tim divativ of V w hav ' ' = XW S SV X ˆ ˆ + ˆˆ + η F / 5 Wˆ =Γ S SVˆ X σ Wˆ W W η > Vˆ =Γ XWˆ Sˆ ' σ Vˆ V V 6 Stp By th o sufacs = d. So w hav d = f + b + Δ f +Δb = f + b Δ 3 d with Δ= Δ f +Δ b 3 is th unctain tm. By mploying th nual appoimato to appoimat Δ. Stp 3 Dfin th o sufacs 3 = 3 3d. In this stp w consid th thid quation of 8 to dsign th actual contol input fo th hypsonic aicaft. Lt 3 d pass though a fist-od filt a nw stat vaiabl 3 d can b obtaind 3 3d + 3d = 3d 3d = 3d = l + 3d d 8 Aft diffntiating th o sufac 3 w gt = c f + bu d W popos an idal contol input u = b k + f + b + k d 3 Such that d = f + bu + bu bu = l + b k + b + b u u 3 3 wh k k > a th dsign paamts. H u is not availabl. Assum d ˆ u = b l + f b k W S V X ε and choos th contol input d ˆ u = b l + f + b k + Wˆ S V X + v Choos th following adaptiv laws and th obust tm ' ˆ Wˆ =Γ S SVˆ Z σ Wˆ 3 W W3 3 Vˆ =Γ Z SWˆ σ Vˆ 3 V V3 3 v = WS X SV X ˆ' ˆ + η 3 3 F / F

4 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp V3= 3b 3 + t W Γ W + t V Γ V i= Slcting { i Wi i} { i Vi i} k > bd thn 5 V 3 l + l3b 3 σ Wi σvi 6 + W i V i + ci i= 4. Numical Simulation Rsults In od to validat th ffctivnss and validity of th poposd mthod nonlina 6-DOF simulation sults fo a HSUAV modl a psntd. h contoll dsign paamts a chosn as follows l = l = 3 σw = σ. i V = η i = η3=. Simulation sults a shown in th following figus fom Fig. to Fig. 7. Fom th simulation sults it can b shown that th contol systm has good stability pfomanc and obustnss vn if th lag modl unctaintis ist. 5. Conclusions his pap psntd a nonlindaptiv contoll fo a HSUAV with a gnal st of unctaintis. h nonlindaptiv contoll is dsignd using dynamic sufac backstpping contol tchniqus and fully tund RBF nual ntwoks. Lyapunov stability thoy is usd to pov th stability of th systm and div th tuning uls fo updating all paamts of th RBF nual ntwoks. Finally a nonlina 6-DOF numical simulation of a HSUAV modl is pfomd to dmonstat th good pfomanc of th poposd mthod. Fig.. acking cuv of θ. Fig.. acking cuv of p. Fig. 3. acking cuv of. Fig. 4. acking cuv of β. 95

5 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp Fig. 5. acking cuv of q. Fig. 6. acking cuv of. Appndi Fig. 7. W 3 tuning wight. h wingd-con dynamics modl V = [ P cos cos β + qs CD m + CD ] sin + CD + CD g θ θ= [sin P cos μ+ cos sin β sin μ mv + qs CL + CL cos + CL μ g qs CY ββ+ CY sin ] cos + CY + CY μ θ V ψ c = [ Psin sinμ mv cosθ cossin βcos μ + qs CL + CL sin + CL μ + qs C β + C + C + C cos μ] Y β Y Y Y = [ qs CL + CL + CL + Psin ] pcostan β + qsintan β + β = [ qs CY ββ+ CY + CY + CY mv Pcos sin β] + psin+ qcos μ = p tg ϑ qcos μ sin μ qsb p = Cl ββ + Cl + Cl + Cl b b + C p+ C q + q l p l q y V V qs q = [ bc n β+ Xcg CY β β+ bc n + X cg CY + bc + X C + bc + X C ] n a cg Y n cg Y qsb qsb + Cnp p+ Cnq q+ p V y V y y qs = [ c Cm + XcgCD sin+ XcgCL cos + cc + X C sin+ X C cos m cg D cg L + c C + X C sin+ X C cos m a cg D cg L a + c C + X C sin+ X C cos ] m cg D cg L qsc + C + pq V f m y [ qs CL + CL + CL + Psin [ qs C β + C + C + C Y β Y Y Y = mv Pcossin β] 96

6 Snsos & ansducs Vol. 74 Issu 7 uly 4 pp costgβ sintgβ b = sin cos tgϑ cosγ tgϑ sinγ qscl qsc L a qscy qsc Y qsc Y a h = mv mv mv y qbs ωω y + C l ββ qb S + C l ωω + C lωω y y V qs ωω + bc n β + cg C Y β β y y f = qb S + C n ωω + C nωω y y V y y qs ωω y+ cc ma + C cg Da sin qc S + C cg L a cos + Cm qω V Acknowldgmnts h pap is suppotd by National Natu Scinc Foundation of China 6743 Aviation Scinc Foundation of China 384. Rfncs [].. D. Shaughnssy S. Z. Pinckny. D. Mcminn C. I. Cu and M. L. Klly Hypsonic vhicl Simulation Modl: Wingd-Con Configuation NASA M-6 National Aonautics and Spac Administation 99. []. I. M. Ggoy R. S. Chowdhy. D. McMinn and. D. Shaughnssy Hypsonic vhicl modl and contol law dvlopmnt using H and μ-synthsis NASA M-456 National Aonautics and Spac Administation 994. [3]. H. Bushck and A.. Calis Unctainty modling and fid-od contoll dsign fo a hypsonic vhicl modl AIAA ounal of Guidanc Contol and Dynamics Vol. No. 997 pp [4]. Q. Wang and R. F. Stngl Robust nonlina contol of a hypsonic aicaft ounal of Guidanc Contol and Dynamics Vol. 3 No. 4 pp [5]. Y. Shtssl and. McDuffi Sliding mod contol of th X-33 vhicl in launch and -nty mods in Pocdings of th AIAA Guidanc Navigation and Contol Confnc and Ehibit 998 pp [6]. K.. Austin and P. A. acobs Application of gntic algoithms to hypsonic flight contol in Pocdings of th IFSA Wold Congss and th NAFIPS Intnational Confnc Vancouv BC Canada uly pp [7]. H. Xu M. Mimiani and P. Ioannou Adaptiv sliding mod contol dsign fo a hypsonic flight vhicl ounal of Guidanc Contol and Dynamics Vol. 7 No. 5 4 pp [8]. C. ouns D. B. Landum Y. Shtssl and C. W. Hawk Ramjt-powd usabl launch vhicl contol by sliding mods ounal of Guidanc Contol and Dynamics Vol. No pp [9]... Pak A. Sani S. Yukovich M. A. Bolnd and D. B. Doman Contol-ointd modling of an aibathing hypsonic vhicl ounal of Guidanc Contol and Dynamics Vol. 3 No. 3 7 pp []. L. Fiontini A. Sani M. Bolnd and D. Doman Nonlina obust/adaptiv contoll dsign fo an aibathing hypsonic vhicl modl in Pocdings of th AIAA Guidanc Navigation and Contol Confnc and Ehibit -3 August 7 Hilton Had South Caolina 7 AIAA Pap pp. -6. []. S. S. G and C. Wang Adaptiv NN contol of unctain nonlina pu-fdback systms Automatica Vol. 38 Issu 4 pp []. Michal A. Bolnd David B. Doman A non-lina modl fo th longitudinal dynamics of a hypsonic ai-bathing vhicl in Pocdings of th AIAA Guidanc Navigation and Contol Confnc and Ehibit San Fancisco Califonia 5-8 August 5 AIAA [3]. D. Swaoop. K. Hdick P. P. Yip and. C. Gds Dynamic sufac contol fo a class of nonlina systms IEEE ansactions on Automatic Contol Vol. 45 Issu pp [4]. P. P. Yip and. K. Hdick Adaptiv dynamic sufac contol: a simplifid algoithm fo adaptiv backstpping contol of nonlina systms Intnational ounal of Contol Vol. 7 No pp Copyight Intnational Fquncy Snso Association IFSA Publishing S. L. All ights svd. 97