Lateral Control for an Aircraft of Folding Wing

Transcription

1 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 Latal Contol fo an Aicaft of Folding Wing ZHENG JIE WANG, WEI LI, SHIJUN GUO 3. School of Aoac and Scinc Engining Bijing Intitut of chnology Bijing, 8 CHINA. Rach Intitut of Elctic Scinc and chnology Univity of Elctic Scinc and chnology of China Chngdu, Sichuan, 64 CHINA 3. Datmnt of Aoac Engining Canfild Univity Canfild, Bdfod, MK43 AL, UK Abtact: hi a nt th dign of a latal contol ytm fo a loiting aicaft of ailon-l folding wing. h contoll dign wa focud on bank-to-tun by diffntial movmnt of lvato and kid-to-tun by udd dflction. A nonlina modl of th aicaft wa tablihd, and thn linaizd by mall ditubanc mthod. h LQR tat fdback contol mthod wa ud to dign th at daming and tabilizing loo in od to achiv diabl dynamic chaactitic. h flight ath tack loo wa dignd bad on th lf-oganizing fuzzy contol algoithm fo th aicaft to fly in a did ath. wo ty of cou contol lan dnding uon th tuctu tait of th aicaft w invtigatd and vifid. h ult how that th contol lan a faibl and th contol ytm i adquatly obut to mt th quimnt of th cou contol Ky-wod: loiting aicaft, LQR, fuzzy contol, bank-to-tun (B), kid-to-tun (S) Nomnclatu A Stat matix b Wing an C Outut matix D Dict matix C y Latal foc cofficint C l Rolling momnt cofficint I x Momnt of intia in oll I xz Poduct of intia about ox and oz ax K Fdback gain matix L Lift: Rolling momnt m Ma N Yawing momnt Roll at Yaw at R Radiu of tun S Wing fnc aa u Inut vcto v Latal vlocity V otal vlocity x Stat vcto Y Latal foc y Outut vcto ζ Rudd angl η Elvato angl β Sidli angl Ф Roll angl ISSN: ISBN:

2 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 Intoduction A light wight mall loiting aicaft of ailon-l folding back wing a hown in Fig. ha bn conidd in thi a. It i dignd to b caid by a lag aicaft and cat ov th tagt aa. It could loit autonomouly in low d a a mall UAV whn th wing and th tail a unfoldd[]. h aicaft loit in an anticiatd cou which i indicatd by lin btwn th contiguou navigation wayoint in th loiting tag a illutatd in Fig.. h contol ytm will gnat th contol command bad on th aicaft oition and navigation dflction ignal fom an onboad navigation ytm. h idal contol command will mak th actual flight cou idntical to th diabl. Noth( dg) LOP Hading WP(n) Baing ack Contol Statgy Dign o mak u th aicaft fly though th chduld navigation wayoint a hown in Fig., an onboad navigation ytm dtct th tack angl dflction = ack-hading. h tak of flight tack contol i to minimiz th dflction, and mak th aicaft fly though th chduld navigation wayoint along th hott ath.. Bank-to-tun Contol Statgy Bank-to-tun contol man that th lift vcto i alway towad th diction of tagt by banking th fulag duing flight a hown in Fig. 3. h itch angl and oll angl chang togth to mak ncay manuv and acclation quickly in th diabl diction. In th am tim, th idli angl hould b ducd to zo[]. L Lco Y Eat(9 dg) y WP(n-) Lin Fig. A loiting aicaft Fig. Navigation wayoint h challng fo th contol ytm dign i how to atify th quimnt of latal manuvability in od to accomlih th chduld flight miion. Du to light wight, mall iz and low flight vlocity, th aicaft i on to ditubanc aiflow. h lift cofficint vai with th angl of attack affctd by th wing dfomation. h facto mak it difficult to achiv a atifid contoll dign by claical contol thoy. It i thfo ncay to utiliz flight contol algoithm uch a fuzzy logic, nual ntwok, gntic algoithm o oth knowldg-bad ytm to dign th contol ytm. hi cunt invtigation fitly focud on dicuing th latal contol tatgy and tablihing th nonlina modl. Attntion wa thn aid to th dign of th contol ytm by utilizing th LQR tat fdback mthod and lf-oganizing fuzzy contol algoithm. Finally, numical imulation and analyi w caid out in Matlab/Simulink nvionmnt. Fig.3 Foc comonnt duing bank-to-tun In Fig.3, th foc quilibium quation in th diction Oz b and Oy b a xd by: mv Fy Y co Lin R F Lco Y in W Z Whn no idli angl i gnatd duing band-to-tun, th id foc Y= and th latal manuvabl foc i balancd by th hoizontal comonnt of th lifting foc: mv Lin mv R h lationhi btwn th tuning angl at and oll angl i wittn a: Lin g g Lcov v z W Duing th aicaft tuning, qual to. hough Lalac tanfomation, th flight cou angl i xd by: ISSN: ISBN:

3 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 Whn th flying diction nd to b altd o th aicaft i hoving to tun, th autoilot maniulat th olling channl to mak th manuv. hn th imay lifting ufac i maniulatd towad th tagt in od to oduc th acclation in nomal diction a gat a oibl; th autoilot alo maniulat th yawing channl to nu th latal acclation and th idli angl to b zo. o achiv th aicaft olling without ailon, thi a nt a mthod of contol by diffntial movmnt of th lvato indndntly. h contol tatgy i hown in Fig. 4. Navigation Sytm g v Did ack - Cunt ack ack Contoll GPS Did Roll Angl Roll Contoll - - Roll Rat Roll Angl Elvato Actuato Elvato Actuato Fig.4 h bank-to-tun contol tatgy Du to th maniulation oc of th aicaft in th bank-to-tun, om chaactitic a notd: a ignificant couling in th channl of itch, yaw and oll; a idli angl clo to zo and a tong manuvability [].. Skid-to-tun Contol Statgy Fo an axi ymmtic aicaft in aodynamic configuation, S contol mthod i gnally adatd to alt idli angl and adjut th hoizontal navigation tack by maniulating th udd. h aicaft uing S ha a tabl oll channl and minimum couling btwn itch, yaw and oll channl. Fo a lan-ymmtic aicaft conidd in thi a, it i ood to adat a kid-to-tun tatgy a hown in Fig. to ov th contol caability. h diffntial lvato contol mak th olling angl zo; th udd contol th hoizontal manuv of th aicaft. Whn th aicaft fli at a lag angl of attack in th S mod, a gat idli angl gnat vly aymmtic ddy. hi would oduc a hamful oll and yaw momnt, which might xcd th allowd limit of th contol ytm. Whn th angl of attack i gtting gat gadually, an incaing dynamic couling and intial couling would b gnatd in itch and yaw IMU channl. Accodingly, th manuv ability i undmind. Fig. h kid-to-tun contol tatgy 3 h Equation of Motion Fo a vat majoity of aicaft und mall tubation tanint motion, longitudinal-latal couling i uually ngligibl. Conquntly it i convnint to imlify th quation by auming dcould longitudinal and latal motion. 3. h Latal-dictional Equation of Motion h dimnional dcould quation of latal-dictional motion i futh imlify a Y Y ( Y mu ) mg Y Y L I L I L L L x xz N Ixz N I z N N N () Wh, Y Cy V Sb, L Cl, V Sb Y Cy V S a latal aodynamic contol. Fo a mall tubation, th olling at i latd to th attitud at by. h motion of th ytm i xd in tat ac: x Ax Bu y y y y y y l l l l l = n n () n n n Wh A and B nt th aodynamic tability divativ and contol divativ matix ctivly, and y Y m, y Y m, l ( I L I N ) ( I I I ) z xz x z xz a futh dtaild in th fnc [3]. h flight d i Mach.3 and th altitud i m. abl nt om tchnical data of th aicaft. ISSN: ISBN:

4 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 abl Aicaft vaiabl m S I x I z I xz b V kg m kgm kgm kgm m m/ Subtituting th dimnionl latal divativ into th latal tat quation (), th lina dcould tat quation i: x x u Wh, x,,, u, 4 Contol Sytm Dign h contol ytm dign mainly includ a fw contol loo: th at daming and tabilizing loo; th flight ath tack loo[4]. 4. Rat daming and Stabilizing Loo Dign Bad on LQR Contol Mthod h tanf function of olling angl at coonding to th diffntial lvato dflction could b obtaind fom latal tat quation (): ( ) ( ) h a th mod of latal movmnt [3]: th olling convg mod, th ial mod and th dutch oll mod. In th ign-olution of th abov quation, th i a oitiv chaactitic oot, which indicat th intability of aicaft. Fig. 6 how th t on of fou tat coonding to two contol vaiabl whn th i no contol inut. h Lina quadatic gulato (LQR) mthodology i adatd in th dign of tat fdback contol to imov th dynamic chaactitic and mt th dfind fomanc indx of th aicaft. h contol objct i th lina ytm in th fom of tat ac, and th cot function i a quadatic function of tat with contol inut: t J (u) [x ( ) ( )x( ) u ( ) ( )u( )] t Q t t t R t t dt t Wh Q(t) and R(t) a wight matix fo diffnt objctiv of tuning to th quilibium oint and minimum contol ow dmand []. h tat fdback contol law i u= -K * x, wh K i th gain matix which can b dignd by uing th LQR function in MALAB. h wight matix i Q(t) = diag[,q,,q] otimal tat fdback gain matix i: with q=, q=3. h K h tat function though tat fdback i x (ABK)x Bu. h t on of th clod loo ytm with a tat fdback i hown in Fig.7. Obviouly, aft th configuation of ol w accomlihd though tat fdback, th daming tait had bn imovd, and th on of attitud had bcom tabl. hi mak th aicaft quickly ond to th guidanc command ovidd by th fight ath tack loo. Amlitud Sidli Amlitud Sidli Rolling Rat Yaw Rat Rolling Angl Roll Rat Rolling Angl Fig.6 St on of vaiou tat (no contol) Yaw Rat u im (c) u St Ron St Ron im (c) Fig.7 St on though tat fdback 4. Path ack Loo Dign Bad on Slf-oganizing Fuzzy Contol Mthod Fo th cunt comlicatd ytm of multil vaiabl, high-od, nonlinaity, a lf-oganizing fuzzy u u ISSN: ISBN:

5 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 contoll caabl of auto-adjuting and nhancing th fuzzy contol law i diabl. o dign uch a lf-oganizing fuzzy contoll, th main tak a to adjut th caling facto and tuning facto to mlioat th contol fomanc [6]. 4..Scaling facto Lt k and k c dnot th caling facto of th dflction and it chang at ctivly. Whn th dflction i lag, a mall k hould b chon to mak th ytm ond quickly but not ult in too much ovhoot; a it duc, k hould b gadually incad to imov th tady-tat accuacy. Lt k dnot th incmnt of k, it fom a lationhi with th incmnt of dflction x. Whn k i incad u to k max, th lationhi btwn k and x i uly lina. In thi ca, k can b xd a: K K kx K max and k x c K max K K max Wh c i an intgal contant. Whn th dflction bcom ngligibl, kx+c= and k i qual to k max. By auming c=, w obtain K K max k x K max Whn k i affimd, k c =βk. k max, k and β can b facto, th lf-adjuting tuning facto can b dducd by t k x k f. Similaly, by tting J t x t dt t a th cot function, k and k could b otimizd to dtmin th function of lf-adjuting tuning facto. Fom th baic thoy of fuzzy contol, fuzzy contol ha no intgal oc comad to th claical PID contol [7]. hby, it i diabl to blnd th intgal into th fuzzy contoll dign can imov th tady-tat accuacy of contol. Fig.8 how th contol loo diagam bad on tat fdback and lf-oganizing fuzzy contol mthodology. K i K E ( ) E c Kc Simulation k k u x=ax+bu y=cx+du Fig.8 Diagam of contol loo A nonlina imulation modl of th mall aicaft with ix dg of fdom i catd in th MALAB/Simulink utilizing C-languag and MALAB mx-function tool a hown in Fig.9 and Fig.. o account fo th atuation of th actuato and dynamic on chaactitic, all of th actuato a modld a fit-od lag with a gain and limit on dflction and at. otimizd by a imlx mthod, wh th cot function t f i J t x t dt. Accodingly, a a concutiv t function of th dflction, th lf-adjuting function of k and k c can b dtmind. fcn UE fuzzy contoll fcn UE contoll fcn UE hi contoll MALAB Function K3 m - K K K Aicaft Mod Flight dynamic v q m hi thta i 4.. uning facto In th fuzzy contol modl with tuning facto, th contol ignal could b t a: U x x, Wh, i tuning facto; x and x a th dflction and it chang at ctivly. uning th a magnitud could alt th wighting of th dflction and it chang at. Simila to th dducd oc of lf-adjuting caling hi i _oll Fig.9 Bank-to-tun imulation modul fcn contoll _yaw UE_R fcn UE_Y fuzzy contoll K3 mu - K K K Aicaft Modl Flight dynamic Fig. Slid-to-tun imulation modul h imulation i in flight condition H =3m and v q m hi thta i ISSN: ISBN:

6 8th WSEAS Intnational Confnc on SIMULAION, MODELLING and OPIMIZAION (SMO '8) Santand, Cantabia, Sain, Stmb 3-, 8 i/dg V =8 m/; th yaw, itch and oll a initializd at o. h tim of imulation lat 3. Givn th contol 4 3 command: hading angl χ=, th contol ult a obtaind and hown in Fig. and Fig.. bta/ad dign and fomanc imulation. h natu of th mall aicaft uch a nonlinaity and tim-vaiation atly du to non-modulaity in th aodynamic chaactitic and andom ffct in th flight nvionmnt mak th contol mo comlicatd. h ult how that th contol ytm will b th nc of challng fo th mall aicaft. Futu wok hould focu on th ach of advancd contol algoithm to achiv otimal contol. -.8 i/dg t/ - 3 t/ (a) Hading angl (b) Sidli angl Fig. B imulation ult t/ t/ (a) Hading angl (b) Roll angl Fig. S imulation ult A hown in th ult, th bank-to-tun by a diffntial movmnt of th lvato aa to b tadi. Du to mall olling momnt howv, th hading angl ond lowly to th command, a hown in Fig.; th kid-to-tun by th dflction of udd ond to th command aidly and could achiv tady tat quickly. In th tuning oc howv, th aicaft fli in an untabl tat, and th hading angl ha a lag ovhoot, a hown in Fig.. hotically, bank-to-tun could ovid gat manuv caability and fat on d. Fo thi aticula aicaft howv, it i inffctiv to accomlih bank-to-tun by uing th diffntial movmnt of th lvato having a mall contol ufac aa. Manwhil, it i ay to oduc ignificant couling among th th contol channl and affct th contol oc and ffctivn. If th manuvability dmand i not too high, it i diabl to adat th lativly iml S contol mthod. hi/dg Rfnc []Wu G.H., Wang Z.J. and Fan N.J., Contol Mthod of Dynamic Invion with Nual Ntwok Ud fo MAV, Jounal of Atonautic, Vol., 8. []ong, C.X., Wang, Z.J. and Zhang,.Q., Dcouling Sytm Dign Bad on Vaiabl Stuctu Sytm fo B Miil, J. of Atonautic, Vol., 6. [3]Cook, M.V., Flight Dynamic Pincil, Buttwoth-Hinmann, [4]Kulczycki, E. A., Johi,S. S., and H,R. A., owad Contoll Dign fo Autonomou Aihi Uing SLC and LQR Mthod. AIAA Guidanc, Navigation, and Contol Confnc and Exhibit, AIAA , -4 Aug. 6, Kyton, Coloado. []Na,S.,Libcu, L., Kim,M.H.,tc.,Robut aolatic contol of flad wing ytm uing a liding mod obv, Aoac Scinc and chnology,vol., 6,.-6. [6]H,., Wang, H.X., Fuzzy Contoll Dign and allication, Scinc P, 997. [7]Zhang,.Q., Luo, X.S. and Zhan L., Slf-oganizing Fuzzy Dcouling Contol fo Nonlina Sytm, Comut Simulation,Vol.,4 (in China). 6 Concluion In thi a, a lina and a nonlina aicaft modl without ailon hav bn built fo th aim of contoll ISSN: ISBN: