COMPARATIVE ANALYSIS OF TUNING MISSILE AUTOPILOTS USING INTELLIGENT METHODS

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SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 COPRTVE NLYSS OF TUNNG SSLE UTOPLOTS USNG NTELLGENT ETHODS Rumn GEORGEV, olyo OLEV NU, viation Faculty, Dolna itropolia, Bulgaria gorgivrg@gmail.

1 SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 COPRTVE NLYSS OF TUNNG SSLE UTOPLOTS USNG NTELLGENT ETHODS Rumn GEORGEV, olyo OLEV NU, viation Faculty, Dolna itropolia, Bulgaria gorgivrg@gmail.com, kolv_7@abv.bg DO:.96/ btract: Thi articl xplor baic tchnical and dign challng aociatd with th miil flight control ytm, including it rol in th ovrall miil ytm, it ubytm, typ of flight control ytm, dign objctiv, and dign challng. yword: miil homing loop, fdback control, ynthi tchniu for homing guidanc.. NTRODUCTON TO SSLE UTOPLOTS Bfor w go on to dicu any particular typ of guidanc ytm, it i ncary to conidr firt th ovrall opration of an ntir miil guidanc and control ytm; to divid it into convnint group of unit; and to indicat th gnral function of ach major group o that th opration of th particular unit may b undrtood in rlation to th opration of th guidanc and control ytm a a whol []. a Traditional GNC topology b Guidanc intrcpt tchniu FG.. Th figur how traditional GNC topology and diffrnt guidanc intrcpt tchniu indicatd in Fig.. a, th traditional architctur for all fildd guidd miil ytm ar particular xampl of th fdback concpt. Th GNC topology for a guidd miil compri guidanc filtr, guidanc law, autopilot, and inrtial navigation componnt. Th inrtial navigation ytm NS provid th poition, vlocity, acclration, angular orintation, and angular vlocity of th vhicl by mauring th inrtial linar acclration and inrtial angular vlocity applid to th ytm. Th information from th NS i ud throughout miil flight to upport guidanc and flight control function. Th guidanc filtr rciv noiy targt maurmnt data from th homing nor and timat th rlvant targt tat. Th guidanc law tak th intantanou targt-tat timat a input and dtrmin what th intrcptor dirction of travl hould b to intrcpt th targt. t typically i an anticipatory function in that it gnrat guidanc command to put th miil on a colliion cour with th targt. 5

2 ELECTRCL ND ELECTRONCL ENGNEERNG RENEWBLE ENERGY ND ENVRONENT Th problm i to dign a pitch plan autopilot to track th normal acclration commandd from th guidanc ytm. Th autopilot gnrat fin angl command which ar nt to th tail urfac rvo. By dflcting th tail fin, thy gnrat arodynamic forc and momnt that manuvr th miil. Rat gyro and acclromtr maurmnt ar procd by th flight control ytm to clo th fdback control loop. Th principal function of th guidanc ytm ar to dtct th prnc of th targt and track it; to dtrmin th dird cour to th targt; and to produc lctrical tring ignal which indicat th poition of th miil with rpct to th ruird cour. Thrfor, you can ay that th output of th guidanc and control ytm i th actual miil flight path. f thr i a diffrnc btwn th dird flight path input and th on th miil i actually on output, thn th control ytm oprat to chang th poition of th miil in pac to rduc th rror. a Tim rpon charactritic b Bod plot opn-loop fruncy rpon of an acclration autopilot FG.. Traditional approach for dvloping GNC ytm -tim and fruncy charactritic Th purpo of an autopilot i to produc latral miil acclration a in rpon to commandd acclration a c a hown in Fig.. n autopilot tim contant th approximat tim it tak for th miil to achiv commandd acclration. Th miil motion in pac i compltly dfind by th acclration normal to th vlocity vctor and th rat of chang of th vlocity magnitud. Th commandd normal acclration i th input to a combination of limitr and tranfr function that imulat th autopilot, control ytm, and arodynamic, yilding ralid acclration a th output. Spcifically, th commandd acclration i pad to th autopilot in a body fram n.. THE COON UTOPLOT ND SSLE ODEL Th dynamic of th airfram ar govrnd by fundamntal uation of motion, with thir pcific charactritic dtrmind by th miil arodynamic rpon, propulion, and ma proprti. uming that miil motion i rtrictd to th vrtical plan typical for arly concpt dvlopmnt, th uation of motion that govrn th miil dynamic can b dvlopd in traightforward fahion. Th uation ar ufficint to obtain rough timat of th impact point. Variation in wind condition and motor burn a wll a hading and attitud control rror would affct actual prformanc. dding impl trim arodynamic with a tranfr function rprntation of th autopilot and a proportional navigation guidanc law produc a imulation modl. 5

3 Th gain in th autopilot ar chduld a a function of flight condition to achiv miil tability and command following. Th actuator command pa through a cond-ordr tranfr function with angl and rat limitr. a utopilot block diagram b Simpl tranfr function modl for th actuator with angl and rat limiting FG. 3. Th autopilot acclration command from th guidanc law and th maurd acclration and body rat a input to obtain th actuator command. thr-loop autopilot and impl tranfr function modl for th actuator with angl and rat limiting ud to dcrib th dynamic a in [5] ar: a a a a c ξ Th application of th longitudinal vrtical plan flight control ytm for a bank to turn miil form a ingl input multioutput dign modl. Th plant output ar normal acclration ft/, and pitch rat rad/, and th plant tat ar T x ] [ angl of attack, pitch rat, fin dflction, and fin rat rpctivly. Th nominal longitudinal airfram dynamic i rprntd by G. Th dfrntial uation ud to dcrib th opn loop dynamic a in [5] ar: V V uming that th actuator i cond ordr ytm a: c ξ 3 n th tat pac form, th airfram dynamic ar rprntd by th following tat pac tripl, B, C: Du Cx y Bu x x, ξ, B, V V C 4 Th tranfr function matrix i B C G. Th longitudinal miil dynamic form a ingl input multioutput dign modl from uation -5, th tranfr function matrix from th lvon fin dflction command c to th normal acclration and pitch rat i S S S V G c c ζ ζ 5 SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 53

4 whr,,, and ar th arodynamic tability drivativ. Th maurmnt that ar availabl ar normal acclration V V ft/, pitch rat rad/. Th calar control input u rad i th fin angl command. lthough th diffrntial uation can b olvd numrically, an analytical approach oftn i dirabl to fully undrtand th miil dynamic. Thrfor, th uation of motion ar linarid around an oprating condition o that linar ytm thory can b applid. Th abov arodynamic hav bn linarid and rprntd a trim angl of attack of 6 dgr, ach numbr.8, V ft/, an altitud of 4 ft., actuator damping ζ.6, and actuator natural fruncy 3 rad/. Th following paramtr ar th nominal valu of th dimnional arodynamic tability drivativ;.346 /;.4/; ±47.79 / which wr takn from [4]. ELECTRCL ND ELECTRONCL ENGNEERNG RENEWBLE ENERGY ND ENVRONENT Th ign of dtrmin th tability of th opn loop airfram. Whn th i ngativ th airfram i tabl, and whn it i poitiv th airfram i untabl, which occur whn th arodynamic cntr of prur i forward of th cntr of gravity [5]. 3. EXPLORE THREE-LOOP UTOPLOT Th thr loop pitch/yaw autopilot i ud to mot guidd tactical miil today a hown in Fig. 4. t ha four gain,, R and which ar ud to control th third ordr dynamic of th autopilot. Th dynamic ar du to cond ordr dynamic and an intgrator that allow th flight control ytm to control untabl airfram. Th longitudinal autopilot dign proc i automatd to vary th acclration fdback loop and th pitch rat loop gain and valuat longitudinal autopilot prformanc and robutn proprti. Th prformanc valu xamind ar th normal acclration command ttling tim, th prcnt undrhoot, th prcnt ovrhoot and th tady tat rror. FG. 4. Standard thr-loop autopilot block diagram Th thr loop autopilot, it includ an intgrator for body rat in ordr to rduc th tady tat rror. t hould b clar from Fig. 4 that th acclration fdback loop i a proportional controllr acting on th acclration rror. Th innr loop form a proportional plu intgral P for pitch rat to tabili th miil body. Th outr loop rlationhip i givn by c whr i th maurd output acclration and i th input acclration command. c Convntional thr-loop autopilot and impl tranfr function modl for th actuator controllr do not giv accptabl prformanc for ytm with uncrtain dynamic, tim dlay and non-linarity []. Hnc it i ncary to automatically tun th paramtr for obtaining atifactory rpon. Th automatic tuning gain of 54

SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 controllr ha bn don uing fuy logic. Bad on xprt knowldg a fuy logic ytm tranform a linguitic control tratgy into an automatic control tratgy [3].

USNG NTELLGENT FUY CONTROLER Th fuy controllr ud in th implmntation of Fuy longitudinal autopilot dign proc hav fixd rul ba and mmbrhip function.

Th input to th controllr ar th rror c whr i th maurd output acclration and c i th input acclration command. and th rat of chang of rror θ whil th output ar controllr gain, and.

5 SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 controllr ha bn don uing fuy logic. Bad on xprt knowldg a fuy logic ytm tranform a linguitic control tratgy into an automatic control tratgy [3]. Figur 6 how th block diagram of a fuy controllr. Th fuy controllr ha bn implmntd uing fuy logic toolbox in TLB. 4. USNG NTELLGENT FUY CONTROLER Th fuy controllr ud in th implmntation of Fuy longitudinal autopilot dign proc hav fixd rul ba and mmbrhip function. Th fuy controllr ha baically thr main componnt: caling factor, mmbrhip function and th rul. Th fuy controllr i formd by th rul ba hown a in th figur 5. Th input to th controllr ar th rror c whr i th maurd output acclration and c i th input acclration command. and th rat of chang of rror θ whil th output ar controllr gain, and. a Th tructur of fuy controllr b Two input thr output FLC tructur FG. 5. mplmntation of Fuy longitudinal autopilot dign proc Th tructur of fuy controllr i a two input rror innr loop and outr loop - thr output controllr gain, and. From thr th rang of th input a wll a output mmbrhip function hav bn found. Th mmbrhip function of th input fuy t ar hown in Figur 6. Th linguitic variabl lvl ar aignd a: ngativ big NB, ngativ mall NS, ro, poitiv mall PS and poitiv big PB. Similarly, th fuy t for rror chang θ i prntd a NB, NS,, PS, PB. a Fuification of th Output; b Common Rul Ba FG. 6. Baic infrnc mchanim For th output fuy t th caling of rang ha bn don corrponding to th formula: max min min ; max min min ; max min min. Th infrnc mchanim ha two baic tak [7]: Dtrmining th xtnt to which ach rul i rlvant to th currnt ituation a charactrid by th two input rror - innr loop and outr loop. Thi tak i calld matching ; Drawing concluion uing th currnt input aid th information in th rul- ba, thi tak i calld infrnc tp. Th dfuification pha i ndd to nd th rul which ar valuatd in th infrnc pha a an uniu control gain, and to th longitudinal autopilot. 6 55

ELECTRCL ND ELECTRONCL ENGNEERNG RENEWBLE ENERGY ND ENVRONENT 5. SULTON RESULTS ND CONCLUSONS Simulation rult for tracking ytm how that th fuy controllr provid th bttr noi rjction a xpctd.

6 ELECTRCL ND ELECTRONCL ENGNEERNG RENEWBLE ENERGY ND ENVRONENT 5. SULTON RESULTS ND CONCLUSONS Simulation rult for tracking ytm how that th fuy controllr provid th bttr noi rjction a xpctd. Stp rpon of th ytm for fuy application i mor dampd than P and P control and control variabl variation hav mallr amplitud du to th adoptd dfuification mthod. Sytm tting tim to rfrnc input ha an accptabl valu approximatly 3.3. Th rult obtaind from thi tudy ha ld to th furthr dvlopmnt in th implmntation of Fuy longitudinal autopilot dign proc. a pitch rat b normal acclration FG. 7. Comparion among diffrnt mthod for tuning longitudinal autopilot prformanc Th comparion among diffrnt tuning mthod in trm of variou prformanc pcification uch a ri tim, ttling tim, ovrhoot, undrhoot and tady tat rror uing th intllignt and convntional tuning mthod ha bn hown in Tabl. aur of th fficincy i how uickly th miil will rpond to a chang in guidanc command and alo th dviation of th achivd miil motion rlativ to th command t i tim contant, p i pak magnitud, t p i tim to fit pak, t r i ri tim, and t i tting tim. Paramtr Tuning thod Convntional tuning mthod Fuy controllr Ri tim t c Stting tim t c Ovrhoot P %.35.9 Undrhoot u % Stady tat rror a Tim domain baic objctiv b Tabl FG. 8. Comparion among diffrnt tuning mthod in trm of variou prformanc pcification Th variou prformanc pcification hav bn improvd uing th intllignt mthod xcpt th ri tim which i l in ca of convntional tuning mthod. Th tady tat rror rmain ro in all th tuning mthod. GNC algorithm ar divr in typ and complxity. Th tuning proc, whrby optimum valu for th adjutabl paramtr ar dtrmind. REFERENCES [] Nil F. Palumbo, Homing iil Guidanc and Control, John Hopkin PL tchnical digt, Volum 9, numbr ; [] T. J. Ro, Fuy Logic with Enginring pplication, Wily ndia Edition 9; [3]. S. Tang,. F. an, G. Chn, and S. wong: n Optimal Fuy PD Controllr, EEE Tranaction On ndutrial Elctronic, Vol. 48, No. 4, ugut, pp ; 56

7 SCENTFC RESERCH ND EDUCTON N THE R FORCE-FSES 6 [4] Fan, L. F., Chn, Y., & Lin, P. 4. Control analyi for a non-minimum pha tatic untably miil. Procding of th 4th ntrnational Confrnc on Control, utomation and Sytm pp [5] Wi,.., & Ebrhardt, R. 99. utomatd gain chdul for miil autopilot uing robutn thory. Procding of th Firt EEE Confrnc on Control pplication pp [6] Nlin, F. W., & Nlin,. L How autopilot ruirmnt contrain th arodynamic dign of homing miil. Procding of th Confrnc on mrican Control. [7] Paino.., Yurkovich S., Fuy Control, ddion Wly Longman, nc., California,

8 ELECTRCL ND ELECTRONCL ENGNEERNG RENEWBLE ENERGY ND ENVRONENT ELECTRCL ND ELECTRONCL ENGNEERNG / RENEWBLE ENERGY ND ENVRONENT 58

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd