CONTROL SYSTEM DESIGN FOR AN AUTONOMOUS HELICOPTER USING PARTICLE SWARM OPTIMIZATION

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1 5 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES CONTROL SYSTEM DESIGN FOR AN AUTONOMOUS HELICOPTER USING PARTICLE SWARM OPTIMIZATION Byoung-Mun Mn*, Hyo-Sang Shn*, and Mn-Ja Tahk* *ora Advancd Insttut of Scnc and Tchnology (AIST) ywords: control systm dsgn, autonomous hlcotr, nonlnar dynamcs, artcl swarm otmzaton (PSO), squntal quadratc rogrammng (SQP) Abstract Ths ar rsnts a control systm dsgn mthod for an autonomous hlcotr usng th Partcl Swarm Otmzaton (PSO) mthod. In ths ar, th nonlnar dynamc modl of a mnatur hlcotr s drctly usd to dsgn a control systm wthout lnarzaton rocss. Th nonlnar dynamcs of modl hlcotr s rrsntd by sxtn stat varabls ncludng flang dynamcs, ngn dynamcs, and rotor sd dynamcs. PSO algorthm s adotd as an otmzaton solvr. In th roosd mthod, controllr gans ar slctd to mnmz th rror btwn th dsrd rsons and th actual rsons of hlcotr control systm. To mrov th convrgnc sd, squntal quadratc rogrammng (SQP) s ntgratd to th basc PSO algorthm. Th rformanc of th dsgnd control systm for an autonomous hlcotr s valuatd through fully nonlnar smulaton. Introducton Th hlcotr systm s a vrsatl flght machn bcaus of ts hovrng caablty, vrtcal tak-off and landng, and aggrssv manuvrablty. Rcntly, th ntrst n unmannd hlcotr systm has bn abrutly ncrasd for survllanc and rconnassanc. For succssful alcaton to ths mssons, control systm for an autonomous flght should b dsgnd and mlmntd. Thrfor, som rsarchs for an autonomous flght usng unmannd hlcotr wr rformd. In ths rvous rsarchs, YAMAHA RMAX systm s th most succssful on. Th autonomous flght control systm of RMAX was comltd usng lnar PD controllr []. Th flght control systm dsgn basd on convntonal aroach [] can b rformd n such a way of yldng lnar modls at svral rfrnc flght condtons, dsgnng lnar controllr for ach condton, and blndng ths dsgn onts wth gan schdulng schm. Howvr t s vry dffcult to dvlo an autonomous flght control systm of unmannd hlcotr basd on th convntonal mthod bcaus th dynamcs of hlcotr s usually hghly nonlnar and many uncrtants. In ordr to ovrcom ths dffculty, varous knds of nonlnar control tchnqus hav bn studd. Among thm, adatv control usng nural ntwork was gracfully mloyd for unmannd hlcotr systm [3-5]. Though th nonlnar control tchnqus hav som advantags n comarson to th convntonal aroach, th roortonal-ntgral-drvatv (PID) controllr has bn wdly usd n th ral flght control systm bcaus of ts sml structur and robust rformanc. Unfortunatly, t s qut tdous and tm-consumng to tun rorly th gans of PID controllr. In ths ar, a hurstc mthod for th gan tunng of PID controllr s roosd and ald to flght control systm dsgn for an autonomous hlcotr. Th roosd mthod dtrmns th controllr gans from numrcal otmzaton aroach. Fg. shows th man rocss of th nw mthod. In th nw aroach, th controllr gans ar slctd to mnmz th rror btwn th dsrd rsons and th actual rsons of flght control systm usng artcl swarm otmzaton (PSO) mthod [6,7]. Morovr, a hybrd PSO mthod ntgratd wth squntal

2 BYOUNG-MUN MIN*, HYO-SANG SHIN*, AND MIN-JEA TAH quadratc rogrammng (SQP) algorthm [8,9] s dvlod to mrov th convrgnc sd. Th ar s organzd as follows. Scton rsnts th nonlnar dynamcs of unmannd hlcotr. In Scton 3, a hybrd PSO algorthm s roosd. Scton 4 outlns a hlcotr alcaton of th nw aroach dvlod n Scton 3. Conclusons ar gvn n Scton 5.. Rgd Body Dynamcs Rfrrng to Gavrlts [0], f th cross roducts of nrta ar nglctd, th rgd body quatons of moton for a hlcotr ar gvn by ( mr fus ) θ ( mr fus tr vf ) θ ( mr fus ht ) u = vr wq gsn θ + X + X / m v = w ur + gsnφcos + Y + Y + Y + Y / m w = uq v + gcosφcos + Z + Z + Z / m () Nonlnar or Lnar Dynamc Modl Dtrmn Control Systm Structur Control Systm Rqurmnt Formulat Otmal Control Problm Otmzaton Solvr 3 4 Prformanc Evaluaton Fg.. Th man rocss of roosd control systm dsgn mthod Nonlnar Hlcotr Modl In mlmntng th dsgnd controllr to th ral systm, modlng fdlty s an mortant factor to guarant th rformanc of flght control systm. Th unmannd hlcotr modl for control systm dsgn s a Voyagr GRS 60 dvlod by JR PROP. As shown n Fg., ths mnatur hlcotr faturs a convntonal ty: two-blads, clockws rotatng man rotor, stablzr bar, and tal rotor. Also, th hyscal aramtrs of our mnatur hlcotr ar summarzd n Tabl. = qr( Izz Iyy) / Ixx + ( Lmr + Lvf + Ltr) / Ixx q = r( Ixx Izz )/ Iyy + ( Mmr + Mht )/ Iyy () r = q( Iyy Ixx )/ Izz + ( Q + Nvf + Ntr )/ Izz whr th subscrt mr, fus, tr, vf, and ht ndcat man rotor, fuslag, tal rotor, vrtcal fn, and horzontal stablzr, rsctvly. In Eq. (), Q s th torqu roducd by th ngn to countract th arodynamc torqu on th man rotor blads. Snc th hlcotr blads rotat clockws, Q s always ostv (Q > 0).. Flang Dynamcs From th rvous rsarch on modlng of a small-scal unmannd hlcotr [], flang dynamcs of th man rotor and stablzr bar can b lumd and rrsntd by a ar of frstordr t-ath lan dynamcs. Th latral and longtudnal flang dynamcs ar b b v v w lat b δ = + δlat τ τ µ v ΩR τ (3) B Fg.. Voyagr GRS 60 mnatur hlcotr Tabl. Paramtrs of Voyagr GRS 60 hlcotr Engn 3cc Gasoln Engn, 3HP Fuslag Lngth 570 mm Man/Tal Rotor Da. 770 mm / 89 mm Emty Wght 6.6 kg Max. Payload 5.0 kg a a u u a w w w w δlon a = q δlon τ τ µ ΩR µ z ΩR τ (4) whr B δ and A lon δ ar ffctv stady-stat lon latral and longtudnal gans from th cyclc nuts to th man rotor fla angls, δ lat and δ long ar th latral and longtudnal cyclc control nuts, and τ s th ffctv rotor tm constant for a rotor wth th stablzr bar. Th control momnts roducd by th flang moton s th domnant rollng and tchng momnts of man rotor..3 Engn and Rotor Sd Dynamcs Th rotor sd dynamcs and th ngn dynamcs to th commandd torqu ar A

3 CONTROL SYSTEM DESIGN FOR AN AUTONOMOUS HELICOPTER USING PARTICLE SWARM OPTIMIZATION Ω = + I r ( Q Qmr ntr Qtr) (5) rot Q = Q + Q + gov Qc Ω τ τ ng ng 0 ( ( )) (6) In Eq. (5), Q s th ngn torqu, whch s ostv whn th man rotor rotats clockws, and Q mr s th man rotor torqu, whch has an oost sgn to th ngn torqu. Q tr and n tr rrsnt th tal rotor torqu and th gar rato btwn th man rotor and tal rotor, rsctvly. In th ngn dynamcs modld as a frst ordr lag systm, τ ng s an ngn tm 0 constant, Q s th man rotor torqu at hovr, and Ω s th rotor sd. gov s a govrnor gan of th ngn. Govrnor lays a rol of mantanng a constant ngn rotatonal sd. Th nonlnar dynamcs rrsntd n ths scton s avalabl n low advanc rato flght nvlo: from hovr to 0m/sc (quvalnt advanc rato s 0.5) [0]. 3 A Hybrd Partcl Swarm Otmzaton Th artcl swarm otmzaton (PSO) mthod s on of th volutonary comutaton tchnqus. It was ntroducd by nndy and Ebrhart basd on obsrvatons of th socal bhavor of anmals such as brd flockng, fsh schoolng, and swarm thory. PSO s dffrnt from volutonary algorthm (EA) n that t dos not nd rroducton or mutaton for roducng th nxt gnraton. In ths ar, a hybrd PSO algorthm s dvlod to mrov th comutaton tm and th convrgnc sd. Th roosd hybrd PSO algorthm changs th otmzaton solvr to squntal quadratc rogrammng (SQP) algorthm whn th gvn convrgnc crtron s mt. 3. Th Basc PSO Algorthm Th basc fatur of PSO mthod s that ach artcl n th swarm s sarchng for th otmum wth ts oston and vlocty. In ths rocss, ach artcl rmmbrs th oston t was n whr, t had ts bst rsult so far. Also, th artcls n th swarm co-orat ach othr n th way of xchangng th nformaton whr thy hav dscovrd th bst oston n th sarchng sac. Th basc PSO algorthm can b summarzd as follows; PSO algorthm. Randomly, ntalz th oston and th vlocty of th artcls. ( ) ( ) x = x + rand x x v v rand v v 0 mn max mn 0 = mn + max mn (7). For ach artcl, valuat th ftnss valu wth th gvn cost functon. 3. Comar a artcl s ftnss valuaton wth artcl s bst ( k ). Exchang th artcl s ftnss valu and locaton wth bst, f t s bttr. 4. Comar a artcl s ftnss valuaton wth th oulaton s ovrall rvous bst, g gbst ( k ). Exchang th artcl s ftnss valu and locaton wth gbst, f t s bttr. 5. Udat th vlocty and th oston of th artcl accordng to th followng quatons. ( ) ( ) v wv c r x c r x g k k k k k k + = + + (8) x x v = + (9) k+ k k+ 6. Loo to st untl a crtron s mt. In th vlocty udat quaton of Eq. (8), w, c, and c man nrta wght, slf and swarm confdnc factors, rsctvly. r and r ar random numbrs on th ntrval [0, ]. 3. Intgraton of SQP Algorthm Th trmnaton crtron of th basc PSO algorthm s chosn as th ftnss valu dos not vary durng fv gnratons. Howvr, th amount of udat rats n oston and vlocty s gradually dcrasd as all artcls ar gathrd around th otmal soluton. Snc th convrgnc sd s dcrasd as wll as th comutaton tm s ncrasd n th small 3

4 BYOUNG-MUN MIN*, HYO-SANG SHIN*, AND MIN-JEA TAH rgon contanng an otmal soluton. To avod ths roblm, an otmzaton solvr s changd from PSO algorthm to SQP algorthm whn all artcls ar convrgd wthn 0% of an ntal sarch ara. Hr, th fnal ostons of all artcls oston dtrmnd by PSO algorthm ar usd as th ntal valus of SQP algorthm. Th flow chart of th roosd hybrd PSO algorthm s shown n Fg. 3. Intalz th artcl oulaton Evaluat th ftnss for ach artcl channls,.. vrtcal, longtudnal, latral, and yaw channls, for alttud control, longtudnal vlocty control, latral vlocty control, and hadng angl control wth man rotor collctv tch, longtudnal cyclc, latral cyclc, and tal rotor collctv tch as control nuts. Th outr-loo controllrs hav PI controllr xct for th alttud controllr. Both th longtudnal and th latral channls hav an nnr-loo controllr formd by tch/roll angular rat and tch/roll atttud angl fd-back. All actuator dynamcs ar modld as frst ordr systm wth th tm constant of 0.05sc. ftnss < bst? ys Rnw bst no ftnss_bst < gbst? ys Rnw gbst no Udat artcl vlocty Udat artcl oston no Mt convrgnc crtron? ys Fg. 4. Block dagram of autonomous flght control systm for unmannd hlcotr SQP Algorthm Mt trmnaton crtron? ys Sto Fg. 3. Th flow chart of a hybrd PSO algorthm 4 Control Systm Dsgn for an Autonomous Hlcotr It s mortant to dsgn flght control systm for an autonomous or sm-autonomous flght of unmannd hlcotr. Th autonomous flght control systm of our unmannd hlcotr s shown n Fg. 4. Consdrng th msson that ths unmannd hlcotr has to accomlsh, th outr-loo flght control systm nvolvs four 4. Dsrd Rsons and Cost Functon As mntond n Introducton, controllr gans ar slctd to mnmz th rror btwn th dsrd rsons and th actual rsons of flght control systm. Th dsrd rsons of autonomous flght control systm s chosn that th outut shows a scond ordr systm s rsons: y ω y s s n = c + ξ ωn + ωn (0) Paramtrs of th dsrd rsons for four control channls ar summarzd n Tabl. Natural frquncs of vrtcal channl and yaw channl ar fastr than thos of longtudnal and latral channls. Th rason s that, n a mnatur hlcotr charactrstcs, man rotor collctv and tal rotor collctv drctly rsons to th control stck nuts, whl 4

5 CONTROL SYSTEM DESIGN FOR AN AUTONOMOUS HELICOPTER USING PARTICLE SWARM OPTIMIZATION longtudnal cyclc and latral cyclc rsonss hav som tm dlay causd by th 90 dg. gyroscoc has lag btwn th man rotor and a stablzr bar. Tabl. Paramtrs of th dsrd rsonss Vrtcal Longtudnal and Latral Yaw Channl Channls Channl ξ ω n Th otmzaton rsults ar snstvly affctd by th cost functon n an otmzaton systm. In ths ar, w us th followng cost functon ar dffrnt bcaus of th randomly ntalzd artcls, th convrgnc sds to rach a crtan cost valu ar sam. Howvr, th roosd hybrd PSO algorthm can radly rduc th cost wth a fw numbr of ftnss valuaton. Morovr, cost calculatd by th roosd mthod s smallr than that of ur PSO algorthm. Ths mls that th controllr gan st dtrmnd by th roosd mthod rrsnts a suror otmalty. Th avrag comutaton tm of th ur PSO algorthm and th roosd hybrd PSO algorthm ar, rsctvly, 508 sc. and 59 sc. J = wt t + dt t f u() t () ( ()) t0 u() t () () wt w, t0 t t = w, ttr t t tr f () whr t 0 s th ntal tm, t tr s th transnt tm, t f s th fnal tm. t () s th rror btwn th dsrd rsons and th actual rsons of flght control systm and u() t s th control nut. In ths cost functon, dffrnt wghtngs can b gvn from th ntal to transnt tm rod and transnt to fnal tm rod. 4. Otmal Controllr Gans In ths ar, th otmal controllr gans for ach control channl ar slctd by drctly usng th nonlnar dynamc modl dscrbd n Scton. In th roosd hybrd PSO algorthm, th numbr of artcls for ach aramtr s 30 and th slf and swarm confdnc factor s c = c =.5. Th otmal controllr gans ar calculatd 0 tms by usng ur PSO algorthm and th roosd hybrd PSO algorthm to comarson of convrgnt ffcncy. Fg. 5 shows th varatons of th cost n th cas that th ur PSO algorthm and th roosd hybrd PSO algorthm ar ald to vrtcal control channl. Though ntal costs Fg. 5. Th cost varatons of th ur PSO algorthm and th hybrd PSO algorthm Th otmal gan st obtand by th roosd mthod ar rsntd n Tabl 3. Tabl 3. Th otmal gan st of four control channls Vrtcal Channl Longtudnal Channl Latral Channl Yaw Channl w h h h d q θ 3.80 u u φ v v.770 r.488 ψ ψ

6 BYOUNG-MUN MIN*, HYO-SANG SHIN*, AND MIN-JEA TAH To analyz th rformanc of our flght control systm, w obsrv th tm rsonss of ach control channl to st nut and llustratd th rsults n Fg. 6. Hr, th longtudnal and latral vlocty commands ar lmtd to 5 m/sc. From th rsults shown n Fg. 6, w conclud that th dsgnd control systm mght b adotd as a ossbl autonomous flght control systm for an unmannd hlcotr. Fg. 7. Flght trajctory durng routt manuvr Fg. 6. Rsonss of four control channls to st nut 4.3 Nonlnar Smulaton Rsults Th routt manuvr rqurs that a hlcotr onts ts nos toward a ont dfnng th cntr of a crcl wth a scfd radus and thn manuvrs around th crcl holdng a constant alttud. To satsfy ths rqurmnts, vn though an xcllnt lot, routt manuvr s a dffcult flght. In ths ar, to vrfy a otntal caablty of th dsgnd autonomous flght control systm, w rform a nonlnar smulaton for routt manuvr. For ths smulaton, m/sc latral vlocty command, 6 dg. hadng angl command r scond, and 0 m alttud command ar ngagd. Th smulaton rsults ar shown n Fg. 7 ~ Fg. 0. From ths smulaton rsults, th autonomous flght control systm of our unmannd hlcotr succssfully achvs a routt manuvr. Also, th alttud control rformanc and trackng rformancs of longtudnal vlocty command and hadng angl command ar rfct. Fg. 8. Rsonss of longtudnal vlocty, latral vlocty, and alttud Fg. 9. Tm hstors of atttud angls 6

7 CONTROL SYSTEM DESIGN FOR AN AUTONOMOUS HELICOPTER USING PARTICLE SWARM OPTIMIZATION Fg. 0. Control stck nuts durng routt manuvr 5 Conclusons Th ar suggsts a control systm dsgn mthod for autonomous hlcotr usng a hybrd PSO algorthm. Th roosd hybrd PSO algorthm combns th basc PSO algorthm and SQP algorthm to mrov th convrgnc sd. Th roosd mthod s succssfully ald to th roblm of otmal gan slcton for unmannd hlcotr systm. Th rformanc of th dsgnd autonomous flght control systm for unmannd hlcotr s valuatd through fully nonlnar smulaton on routt manuvr. Imlmntaton th roosd autonomous flght control systm on th ral systm and flght tst ar rmand for futur work. Acknowldgmnt Ths ar was rformd for Smart UAV Dvlomnt Program, on of th st Cntury Frontr R&D Programs fundd by th Mnstry of Commrc, Industry, and Enrgy of ora. Rfrncs [] Sato A. Rsarch and Dvlomnt and Cvl Alcaton of an Autonomous, Unmannd Hlcotr. Procdngs of AHS Intrnatonal Forum 57, 00. [] Stvns B. L. and Lws F. L. Arcraft Control and Smulaton, John Wly & Sons, Inc., 99. [3] Cals A. J., m B. S., Ltnr J., and Prasad J. V. R. Hlcotr Adatv Flght Control Usng Nural Ntworks. Procdngs of th 33 rd Confrnc on Dcson and Control, Lak Buna Vsta, FL, , 994. [4] Ltnr J., Cals A. J., and Prasad J. V. R. Analyss of Adatv Nural Ntworks for Hlcotr Flght Control. Journal of Gudanc, Control, and Dynamcs. Vol. 0, No. 5, , 997. [5] Nakansh H. and Inou. Dvlomnt of Autonomous Flght Control Systms for Unmannd Hlcotr by Us of Nural Ntworks. Procdngs of th 00 Intrnatonal Jont Confrnc on Nural Ntworks , 00. [6] nndy J. and Ebrhart R. Partcl Swarm Otmzaton. Procdngs of th IEEE Intrnatonal Confrnc on Nural Ntwork. Prth, Australa, , 995 [7] nndy J. and Ebrhart R. Swarm Intllgnc. st dton, Acadmc Prss, 00. [8] Gll P. E., Murray W., and Wrght M. H. Practcal otmzaton. Acadmc Prss, 98. [9] Bryson Jr. A. E. Dynamc Otmzaton. Addson- Wsly, 999. [0] Gavrlts V., Mttlr B., and Fron E. Nonlnar modl for a small-sz acrobatc hlcotr. Procdngs of th AIAA Gudanc, Navgaton, and Control Confrnc. Montral, Canada, AIAA , 00. [] Mttlr B., Tschlr M., and anad T. Systm dntfcaton modlng of a small-scald unmannd rotorcraft for flght control dsgn. Journal of th Amrcan Hlcotr Socty, Vol. 47, No., 50-63, 00. 7