Lateral Dynamic Modeling of Hezarfen Unmanned Aerial Vehicle (UAV) and H Loop Shaping Robust Control System Design

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Candace Terry
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1 Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7) tel Dynmic Modeling of Hezfen Unmnned eil Vehicle (UV) nd H oo Shing obut ontol Sytem Deign KMU TUKOGU EOUS M. JFOV Detment of eonutic nd tonutic tnbul Technicl Univeity tnbul Teknik Univeitei, Uck-Uzy ilimlei Fkultei, Mlk 69 Siye, tnbul TUKE btct: - n dily life, thee e evel liction e of Unmnned eil Vehicle (UV tting fom gicultue u to defene elted iue. n tht ene, dynmicl modeling nd contol ytem deign in UV e tking n imotnt ole in tem of inceing the functionlity nd miion ccucy of UV. egding ll of thee fct, in thi e, the tbility deivtive nd evel chcteitic of Hezfen UV e obtined fo the fit time nd dynmicl model h been contucted uing tte ce och, whee Hezfen UV ototye i being deigned nd going to be oduced in collbotion with tnbul Technicl Univeity. Secondly, time domin chcteitic nd oen loo eone hve been nlyzed nd eult hve been given. thid, in the following ection, in ode to tify obut efomnce fo the given ytem, oo Shing obut contolle uing H ynthei h been develoed nd lied to the ytem. loed loo eult hve been given nd futhe te hve been uggeted t the end of the e. Key-Wod: - UV, tel dynmic, Stte Sce, obut ontol, H-infinity, oo hing. ntoduction UV hve wide nge of liction e. Even if in the eent ye they hve been ued in defene technologie, they hve lo been ued in obevtoy uoe uch detemining the dmge cued by ntul event o exlotion of ctic lce whee humn-being cnnot ech. n thi kind of event eciion, functionlity nd tbility of the vehicle i lying vitl ole in ccomlihment of the miion. n tht ene, it i in ll dynmic ytem, obtining n ccute dynmic model i vey imotnt. egding thee fct, in the fit t of the e, ltel dynmic model of the Hezfen UV h been contucted uing tte ce och. n the econd t, utomtic contol ytem of the UV h been tken into ccount nd H oo Shing obut contolle h been imlemented to the ytem. Obtined eult with evel nlye nd ome uggetion e eented fo futhe nlye in the lt t of the e. tel Dynmic Modeling Stte ce och h been efeed in dynmicl modeling of ltel flight of UV in ode to hve good fundmentl fo the utomtic contol ytem deign t. n tht ene, tte ce eqution ued in thi ection, hve been tken fom []. y uing the eenttion in [], the ltel dynmic tte ce eqution could be given with no touble nd coeonding Tnfe Function (TF could be obtined eily.. Stte Sce och Uing the fundmentl tte ce eeenttion hown in (), x x u y x Du () one i ble to contuct the tte ce fom of ltel motion fo Hezfen UV. Fo the ce, the mtching tte vecto i choen, whee x (), i the ide li ngle, i the oll te, i the yw te, i the oll ngle, i the yw ngle

2 The inut vecto i given, u () whee, i the ileon inut, i the udde inut The tte mtix- fo the given ytem i, v U g () whee imed tbility deivtive e, () zz xz xx xz (6) The contol mtix- could be hown * * U (7) The outut mtix- cn be eented, x y (8) fte obtining ll the tte ce mtixe, if they e going to be lced ll togethe in (), it i oible to hve the whole ytem eeenttion : U g x v * (9) y (). Stbility Deivtive nd TF The chcteitic oetie nd tbility deivtive with coeonding inut of Hezfen UV e given in Tble- nd Tble- eectively, m U g S wing S veticl til yy c [kg] 8 [mn] 9.87 [mn ]. [m ]. [m ].6 [kgm ]. [m ]. [m] Tble- hcteitic oetie of UV. y -.89 y.8 l -. l. l -. n -.8 l.68 y. y.87 l.6 y. n -. n -.7 xx.86 zz.86 xz. Tble- Stbility deivtive nd inut of UV. Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7)

3 Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7) With the hel of ecified vlue in Tble- nd Tble-, it i oible to contuct the tte ce mtixe. Stting fom (), tte mtix- i obtined uch, () fom (7), contol mtix- i found, () fom (8), outut mtix- i gined, nd D () Fom the clculted tte ce mtixe (,, nd D), it i oible to obtin ll necey TF, ( ( ( (,,,, ( ( ( ( ( fo given ileon nd udde inut, eectively. ut befoe obtining the TF, the eigenvlue of tte mtix- hould be nlyzed nd the ole of the oen loo ytem hould be obeved. Uing Mtlb, it i oible to obtin the ole of the ltel ytem uch, i i -. () One cn notice tht the oen loo ytem i tble but h ole lying t the oigin (,), which mke the ytem mginlly tble one. Such ytem with ole t the oigin (,), could eily become untble with little ditubnce. n ode to event ny intbility, utomtic contolle with good ditubnce ejection will be equied. f the ole of the ytem e going to be nmed ccoding to the mode of ltel flight, they e obtined, Dutch oll Dutch oll oll il.98.6i.98.6i () Fom () it i oible to ee the mode of the ytem well. y uing the elementy eeenttion in (6), ( ζ D nd nd )( )( ) τ τ (6) fo chcteitic eqution, one cn contuct the mode of the ytem, ( )( )(.) (7) whee ( ) (8) eeent the chcteitic eqution of Dutch oll Mode of the UV. The coeonding ntul fequency, dming fequency nd dming tio of Dutch oll Mode e, ζ nd D DD. [ d ].6 nd ζ D.6 [ d ] (9) Fom (9) it i likely to y tht the Dutch oll Mode of the UV h fequent nd lightly dmed ocilltion with eltively mll eiod T DM π.89 [ec] n D ()

4 Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7) chcteitic oety ignifying the efomnce of the UV, time contnt fo oll nd il mode could be offeed. f the time contnt of both oll nd il mode e clculted, it could be found τ il [ec] (). τ oll. [ec] () dditionlly, in Dutch oll Mode ( () ( ( ( tio cn tell u if the dutch oll mode i comoed of motly ywing motion, motly olling motion o oximtely equl contibution of ech. Vi (), the tio could be obtined l ( n zz xx ρu.8 () Fom (), it i likely to witne tht the ( ( tio i highe thn, which led to olly dutch oll mode nd i genelly becue of high degee of ltel tbility. fte uch nlye, it i time to get into time domin eone of the oen loo ytem. n ode to do tht it i eentil to contuct the TF fo ech contol ufce (ileonudde) deflection. (.9e ( nd the TF fo udde deflection, ( ( ( e - ( ( ( (6) e ( (.99e ( Fom both TF et, it i likely to ee tht in the numeto t, thee e zeo t the oigin (,), which might be cncelled with the ole t the oigin (,) in the denominto t. Due to the fct tht, the cncelltion of ole nd zeo will educe the ode of the ytem nd will led to light chnge in the chcteitic of the ytem; the elimintion hn`t been done nd the noml TF hve been ued. f time domin te eone of coeonding TF e lotted, they e obtined hown in Figue- nd Figue-. Uing Mtlb, it i likely to find ll the TF fo ileon deflection, (.e ( ( e - ( ( ( () -.e ( Figue- Oen loo time domin te eone fo given inut.

5 Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7) fte n itetive oce, the let but not lt, weighting function e elected o tht W i (..8).. W,, W, (7)..8. f the weighting election oce i cied on, fte n itetive oce, W i obtined W, W, W, W 6 6, W, (8) Figue- Oen loo time domin te eone fo given inut. it i oible to ee obeve fom the oen loo time domin eone, the flight contol ytem need n efficiently weighted contol ytem, which cn lo veify the obutne of the ytem. eult of thi need, H oo Shing obut ontolle will be deigned nd lied to the ytem nd obtined eult will be invetigted in the following ection. obut ontol Sytem Deign: H oo Shing fte evel nlye, it i oible to ee tht the icft ytem i vey enitive to the ditubnce nd noie ignl. n ode to ue the ditubnce nd obtin obutne in the ytem, obut contol och h been ued. n tht ene, H oo hing deign h been uggeted in the ubequent t. Fit of ll,uing ecommended method in [], Simulink block digm h been contucted in Figue-. y uing the choen weighting function nd ncfyn Mtlb commnd, the mximum tbility mgin, e mx, cn be etimted efomnce citeion, which i defined e γ (9) mx nd whee min h been decibed H otiml cot. Hee, the otion of hving n otiml contolle h been elected by chooing ncfyn fcto equl to. With thee elected vlue, the mximum tbility mgin i found e.776 mx () min whee the otiml vlue i uggeted. < e < mx. () fte obtining conideble tbility mgin nd ignificntly hed weighting function, it i time to ee the time domin eult of ou ytem. ut befoe inecting the oo hing eult, we hould hve look t the ignl without ny contol ction which e hown in Figue-. Figue- H oo hing block digm. fte contucting the block digm, weighting function election i coming next. t thi tge, one hould be vey ceful in election of weighting mtixe becue of dimenion of the ytem. Unfotuntely, in mot of the time, ytem mtix eeenttion of dynmicl ytem i being in tem of non-que mtixe (i.e. no. of inut nd outut nd due to thi fct, the dimenion election of weighting function equie imle dimenion nlyi. Figue- Oen loo time domin eone.

6 Poceeding of the th WSES ntentionl onfeence on SSTEMS, Vouligmeni, then, Geece, July -, 6 (69-7) The time domin eone in Figue- h been lotted fo te inut. it i ey to ee fom Figue-, the icft cn eily become untble fo ingle te inut; theefoe obut contolle deign neceity might be eily vlued. f the time domin eone of ugmented ytem with given H oo hing obut contolle i lotted, the cloed loo ytem-time domin eone i chieved hown in Figue-, Figue- Time domin eone of H oo hing otiml obut contolle in UV. n ddition, if the contol foce cting on the ctuto (i.e. ctuto ignl e lotted, they e obtined hown in Figue-6. Figue-6 Foce cting on the ctuto. Fom Figue-6, it i oible to ee tht the foce cting on the ctuto e between. nd.6 [], which men oximtely ~6 gm of weight; nd when it i conideed tht the UV i oximtely kg, the contol ignl cting on ileon nd udde i conidebly good. oncluion n the e, the min im w to how the oen loo dynmic efomnce ecifiction nd chcteitic oetie of n UV in ltel flight. dditionlly, in ode to u the ditubnce effect, H oo hing obut contolle h been deigned nd lied to UV. The eult of H ynthei e howing the tong chcteitic of loo hing nd the dvntge of weight ugmenttion. Fom the eult, it i lo oible to ee tht H obut contol lgoithm h hown it conideble efomnce of ditubnce ejection. futhe te, unde diffeent kind of ditubnce effect, the efomnce of the UV with H Mixed Senitivity o nlyi might be conideed. efeence: [] Mcen D., utomtic Flight ontol Sytem, Pentice Hll, 99. [] Skogetdt S. nd Potlethwite, Multivible Feedbck contol, Wiley, 996. [] Steven. nd ewi F.., icft ontol nd Simultion, Wiley,. [] Ogt, K., Moden ontol Engineeing, Pentice Hll, 997. [] lkelock, J. H., utomtic ontol of icft nd Miile, Wiley, 99. [6] uenbege, D., ntoduction to Dynmic Sytem, Wiley, 979. [7] Fnklin, G.F, Powell, J. D. nd Emmi-eini., Feedbck ontol of Dynmic Sytem, ddion Weley, 99. [8] echout, T.., ntoduction to icft Flight Mechnic, Eduction Seie,. [9] Etkin,., Dynmic of tmoheic Flight, Wiley, 97. [] Tukoglu, E., liction of obut ontol to oty Wing icft, PhD Thei in ntumenttion nd ontol Gou, Univeity of eicete, UK, 6. [] King, E. T., Ditibuted oodintion nd ontol Exeiment on Multi-UV Tetbed, MSc Thei in eontuic nd tonutic, MT. [] Knehige, J., ull, J. nd Toth, J. Geneic eul Flight ontol nd utoilot Sytem, - 8. [] Tukoglu, K., bdulhmitbill, E., Tekin,., Kle, S. nd Jfov, E. M., ongitudinl Dynmicl modeling of Hzefen UV nd PD ontolle Deign, 6 th tionl Symoium on eonutic, Kyei, Tukey, 6. [] Tukoglu, K., nvetigtion the mode of Hezfen UV nd utomtic ontol Sytem Deign,.Sc. Thei in Det. of eonuticl Eng., tnbul Technicl Univeity, tnbul, Tukey, 6.

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