Modeling and Stabilizing Control of an UAV for Easy Taking-off and Hovering.

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1 Moeling n Sbilizing Conrol of n UAV for Esy Tking-off n Hovering. NASR Slh CEM-Lb ENIS Sfx, Nionl Engineering School of Sousse, Universiy of Sousse, Tunisi. nsrslh.oc@gil.co BOUALLEGUE Kis Depren of Elecricl Engineering, Higher Insiue of Applie Sciences n Technology of Sousse, Universiy of Sousse, Tunisi. kis_boullegue@yhoo.fr MEKKI Hssen CEM-Lb ENIS Sfx, Nionl Engineering School of Sousse, Universiy of Sousse, Tunisi. ekki.hssen@gil.co Absrc A synhesis robus sbilision of sll unnne eril vehicle ype quroor wih vericl kingoff n hovering oion is propose for conrol he posiion n liue rcking. Anlyicl relions for ynic oeling, physicl phenoen n conrol of he cions on four roors h ensure quroor oion over prescribe rjecory wih esire vlues of posiion n liue is presene. The quroor is conrolle wih clssicl proporionl inegrl erivive conroller in hree se of syse: posiion conrol, ngle conrol n inpus conrol. Nuericl siulion resuls re provie o show he goo perfornces of sbilision n conrol sregy. Keywors PID conroller, Quroor UAV, Hovering, oel, siulion. I. INTRODUCTION The subjec of unnne eril vehicle (UAV) for iliry, inusril n in urbn environen sks cquire keen ineres in recen yers where he UAV will hve o opere in enclose spces. A nuber of iporn pplicions will require his, e.g. fire n nurl isser serch n rescue, police n securiy services, inspecion n surveillnce ngerous sks h pu hun inegriy risk [-3]. In civilin secors, UAV cn be use for ny pplicions such s low enforceen, rffic repor, eril phoogrphy n ore [4]. Mny reserch es re working on he conrol n sbilizion for he surveillnce of ln, explorion groun for explosives or hzrous erils n sving hun vicis he scene of he isser. UAV re known o be inherenly unsble, nonliner n couple. Differen ehos for oel-bse uonoous UAV conrol hve been presene in lierure. Dynic oeling n configurion of quroor were propose by Mc Kerrow [5] n Hel e l. [6]. Nonliner conrol probles for hovering quroor such s feebck linerizion conrol n bck-sepping conrol lws were suie by Alug e l. [7] n Misler e l. [8]. Therefore, bse on he ynic oel of PVTOL ircrf, Csillo e l. [9], Hel n l. [] esigne conrollers for Yw ngulr isplceen, Pich n Roll oveens of hovering quroor. In [], Xiong n Zheng re propose novel robus erinl sliing oe conrol lgorih. In his work, our pproch is o use siple nese proporionl inegrl erivive (PID) conroller o rck esire rjecory for ke-off n hovering oion. The res of his pper is orgnize s follows: The ynic oel of quroor is inrouce in he nex secion. Then, he propose eho of conrol is given in secion III. In secion IV, siulion resuls re presene. Our concluing rerks re conine in he finl secion. II. DYNAMIC OF QUADROTOR The quroor hve four roors s shown in Fig., he wo pir of oors (,3) re running in he se irecion, wheres he ohers (,4) in he opposie irecion o eliine he ni-orque. By incresing/ecresing he n 4 roor s spee conversely prouces he Roll ngle llows o ove he quroor in lerl irecion x. Pich ngle prouce by vrying he n 3 roor s spee llows he quroor o ove in lerl irecion y, n by vrying ll roor s spee ogeher wih he se vlues, cn chnge he lif force, ffecing he liue z of quroor hen Yw ngle prouce n enble he oion o ke-off. The forces n oens of conrol he liue n posiion of he syse provies by he Euler ngle orienion (,, ),uner he coniions (- ) for Yw ngle, ( / / ) for Pich ngle, n ( / / ) for Roll ngle. To escribe he oion of 6 egree of freeo (DOF) rigi boy i is usul o efine wo reference fres s shown in Fig.. he erh ineril fre E(,X,Y,Z), n

2 he boy-fixe fre Q(,x,y,z). The equions of oion re ore convenienly forule in he Q-fre becuse of he following resons: Fig. The quroor UAV. he ineri rix is ie-invrin; vnge of boy syery cn be ken o siplify he equions; esureens ken on-bor re esily convere o boyfixe fre; conrol forces re los lwys given in boy-fixe fre. Where c n s inice he rigonoericlly funcions cos n sin respecively. Le he vecorp, q, r, enoes he quroor s ngulr velociy in he Q-fre. The corresponing rnsforion rix fro,, o p, q, r is given by:. p sin. q cos sin cos. r sin cos cos J is syeric posiive efinie consn ineri rix of he quroor. I x J I y I z For he force, we noe he grviy force resuln of lif i 4 i F g T cree by he four roors: () (3) n he F 4 F g T i i (4) Fig. Generl coorine syse The liner posiion of he quroor (X, Y, Z) is eerine by he coorines of he vecor beween he origin of he Q- fre n he origin of he E-fre ccoring o he equion of oion. The ngulr posiion (or iue) of he quroor (, θ,ψ ) is efine by he orienion of he Q-fre wih respec o he E-fre. This is given by hree consecuive roions bou he in xes which ke he E-fre ino he Q-fre. The roion rix beween he E n Q fres hs he following for [] : c c s s c s c c s c s s R s c s s s c c c s s s c s s c c c () Where, F g g T i i x x An T T lb i i y i y (6) Ti z i z i is he ngulr spee of roor i, b enoes he lif coefficien, enoes he ol ss, g represens he ccelerion of grviy n l is he isnce beween he quroor cener of ss n he roion xis of propeller. For he oen, M is he oens evelope by he quroor ccoring o he Q-fre. I is escribe by he following rix: (5)

3 [ ] (7) Where is he rg coefficien. We cn finlly erive he equions governing he ynics oel of quroor s escribe by he following equions [3-6]: ( I y Iz) Ir Kx = - Ω r - l + u = ( I z I x) Ir Ky + Ω r - l + I u 3 y ( I x ) Kz = - + Iz Iz z = - Kx = - Ky (8) I u 4 (9) + ( )u + ( )u Kz cos( )cos( ) = - -g+ u Where kx, k y n kz re he rnslion rg coefficiens n kx, k y n k z re fricions eroynics coefficiens. The syse s inpus re pose u, u, u 3, u 4 n Ω is isurbnce, obine s: u = b ( ) u = b ( ) u 3 = b ( ) () u 4 = ( ) Ω = The roors re riven by DC oors wih he well-known equions [7]: V=Ri + L + () = + + III. STABILIZING AND CONTROL STRATEGY The objecive of his pr of sbilizion n conrol is o evelop eho h clcules he volges of four oors fro he wo in enrnces. These re he esire yw ngle ), spil esire posiion ( x, y, z ) n rel vlues ( h re provie by he sensors (cceleroeer, gyro n lieer). Our sbilizion sregy n conrol is ivie ino hree blocks of conrollers ( C, C n C 3 ) s shown in Fig.3. The firs block conroller C conins hree conrollers PID: conrol of x posiion, conrol of y posiion n conrol of z liue wih invoking Eqs. (3), Eqs.(4) n Eqs.(5). The secon block conroller C use o conrol of Yw ( ), Roll ( ) n Pich ( ) (genere fro he se block) by using Eqs. ( 6), Eqs.(7) n Eqs. (8). The ls block C3 conrollers inclue he conrol inpus of syse genere by he force n orque block (illusre by Eqs.(9). The force n orque block inclue ll copue n rnsforion of he force n orque injece s inpus syse wih invoking he rix (), () n (8). The se block iscloses using o genere he Euler ngles n efine s follows: ( xsin ycos ) rcsin( ) x y z () ( xcos ysin ) rcn( ) z The ynic of quroor block presen he globl ynics of quroor s escribe in secion II. The generl pproch o sbilize our syse is s follows: The conrol lgorihs for he posiion n ngle, roll, pich An yw, of he UAV re esigne bse on PID conrollers s shown in Fig. 3. We clcule he ifference beween he esire vlue n he cul vlue n PID conroller is use o iniize his error. The conrol inpu u o conrolling he posiion n ngle of he UAV respecing o he reference inpu esigne s follows: u() = K p e () Ki e( ) + K e () (3) Where, v is he oor inpu,, : re respecively he elecricl n echnicl orque consn, : is he soli fricion n, is he lo orque consn.

4 Z[] Y[] X[] IV. SIMULATION RESULTS The heicl oel escribe by equion (9) n () ws siule on MATLAB / Siulink, wih oor spee n bsic syse preers (lise in TABLE I) s inpus. The esire/reference vlue of Yw ngle n liue use in siulion ess re s follows: / 6. 8r n z 5. TABLE I. MODEL PARAMETER Fig. 3 Synopic schee of conrol sregy. This principle is pplie in our oel o conrol he spil posiion (x, y n z) s follows: u k ( x x ) k ( x x ) k x p i ( x x ) (4) ( y y ) u k ( y y ) k ( y y ) k (5) y p i ( z z ) u k ( z z ) k ( z z ) k (6) z p i Where kp, ki, k re PID conroller gins for he posiion conrol. The ngles (, n ) re conrolle s escribe: u kp ( ) ki ( ) k ( ) (7) u kp e ( ) ki ( ) k ( ) (8) u kp ( ) ki ( ) k ( ) Wih kp, ki, (9) k re preers of PID conroller for he conrol of Roll ngle, Pich ngle n Yw ngle. An he four inpus roors re conrolle s follows [7]: i ( ) ui ( ) ui ( ) ui ( ) () u kpe ki e k e The esire behviour consiss of wo phses: king off n hovering. Iz Ir b l g Preer Vlue Uni 8.e-3 8.e-3 4.e-3 4e-6 54.e e-6 Kg N/r/s / s N./r/s The PID preers cn be se s{kp=6, ki=, k = 9} for he posiion x,y n z esire vlue rel vlue Tie[s] Fig. 4 Trcking Siulion resuls of rjecories long (X,Y,Z). The PID preers for he Roll, Pich n Yw Angle re he se becuse of he syery of ynics quroor

5 Z[] Z[] Yw Angle[r] Pich Angle[r] Z[] Roll Angle[r] Tie[s] Fig. 5 Siulion resuls of rjecories long he Roll( ), Pich ( ) n Yw ngle ( )., i cn be se s { kp =, Y[] - ki =, esire rjecory X[] k =5}. Fig. 6 Siulion resul of esire rjecory in 3D Y[] - esire rjecory rel rjecory X[] Fig. 8 Trcking Siulion resuls of globl rjecories in 3D. Fig. 4 represens he quroor posiions. We cn see well,fro his figure, very goo rcking of he esire rjecories. Fig. 5 shows roll, pich, n yw ngles uring he oion. Fig. 6 represens he rjecory of he esire oveens for quriroor. I escribes perfecly he oveen of keoff n hover. As shown in he Fig. 7, he perfornce of he rel rjecory conrol is very sisfcory. Fig. 8 escribes he 3D posiion of quroor uring he fligh. This figure shows goo robusness owrs sbiliy n rcking for esire rjecory. Which explins he efficiency of sbilizing n conrol sregy evelope in his pper. Siulion resuls presene he en, confir h he propose sbilision n conrol sregy coul be succefully use UAV. The PID conroller prove o be well pe o he quroor when flying n hovering. V. CONCLUSIONS This presene work suies he sbilizion n conrol for esy king-off n hovering of sll quroor UAV using he propose conrol sregy bse on hree se PID conrol eho, his PID conroller is bse on nese loops. The resul of siulion proves h he ope eho of conrol is siple, fs n effecive for king-off n hovering. The ke-off n hovering sks is sill chllenging while he cover re vrie fro n environen o ohers. Nex we will focus on new n ore effecive conrol ehos for UAV [8], n how o ipleen conrol lgorihs in ore coplice environens is noher chllenging issue in our fuure work. -5 rel rjecory - - Y[] - - X[] Fig. 7 Siulion resul of rel rjecory in 3D. REFERENCES [] Rffo GV, Oreg MG, Rubio FR. An inegrl preicive/nonliner H conrol srucure for quroor helicoper. Auoic ;46:9 39. [] Derf L, Benllegue A, Frin L. Super wising conrol lgorih for he iue rcking of four roors UAV. J Frnkl Ins ;349: [3] Grci-Delgo L, Dzul A, Snibáñez V, Ll M. Quroors forion bnse on poenil funcions wih obscle voince. IET Conrol Theory Appl ;6():787 8.

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