Modeling and nonlinear tracking control of novel multi-rotor UAV

Transcription

1 mme.modares.ac.ir 3 * mmahjoob@ut.ac.ir * : : : Modelingandnonlineartrackingcontrolofnovelmulti-rotorUAV MohamadAliTofigh,MohamadMahjoob*, MoosaAyati DepartmentofMechanicalEngineering,CollegeofEngineering,UniversityofTehran,Tehran,Iran P.O.B Tehran,Iran,mmahjoob@ut.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper Received17January2015 Accepted09June2015 AvailableOnline04July2015 Keywords: UnmannedAerialVehicle Five-rotorAircraft ModifiedQuadrotor Input-OutputFeedbackLinearization Inthispaper,modelinganddesignoftrajectorytrackingcontrolsystemfornovelmulti-rotor UAV(UnmannedAerialVehicle)isdeveloped.TheUAVissimilartoquadrotorwithanextrano feedbackpropellerwhichisaddedtocenterofvehicle.theadditionalrotorimprovestheability of lifting heavier payloads, and anti-crosswind capability for quadrotor. For validation, the dynamic model is obtained via both Newton Euler and Lagrange approaches. The dynamical model is under actuated, nonlinear, and has strongly coupled terms. Therefore, an appropriate controlsystemisnecessarytoachievedesiredperformance.theproposednonlinearcontrollerof thispaperisaninput-outputfeedbacklinearizationcompanionedwithanoptimallqrcontroller forthelinearizedsystem.thecontrollerinvolveshigh-orderderivativetermsandturnsouttobe quite sensitive to un-modeled dynamics. Therefore, precise model of UAV is derived by consideringactuator sdynamics.tocompensatethe actuator s dynamicandmoreover,toavoid complexityinthecontroller,secondcontrolloopisutilized.theobtainedsimulationresults confirmthat the proposedcontrolsystem has promising performancein termsofstabilization andpositiontrackingeveninpresenceofexternaldisturbances UAV Pleasecitethisarticleusing: : M.A.Tofigh,M.Mahjoob, M.Ayati, Modelingandnonlineartrackingcontrolofnovelmulti-rotorUAV,ModaresMechanicalEngineeringVol.15,No.8,pp ,2015 (InPersian)

2 . 1 x. y. () x. ) y. y ( () z. x () () = =.[2] (2) (1) D (1) (2) T.. 2 (6) (3) = ( ) + (3) = ( ) (4) = ( ) = ( + ) + z F y x (5) (6) z. [1].. [2].[4,3] [5] [7,6] ). (.[8]

3 . (10). = = 1 (ss + csc) (ssc cs) (10) cc. (11) - = ( (11) + + ) G. (6-4) (11). (12) ( + )/ = ( )/ (12) ( + )/ : = 4 2 = ( 13) = + = + (9) (14) = s c = c s + s c s s + c c = s c + c c s c (14) + s c (12) (14) (9) PE=mgZ (15) = (1/2)[ sin + cos + sin cos coscossin [( cossin ) + ( coscossin ) coscos sin +( cos cos sin ) ] + ( cos cos sin + ) (15) (7). 2 ( + ) + = (7) 2 ( ) + = mg (7) (2) (8) (,, ) = (, ). (, ). (, ) = cc sc s sc + css cc + sss cs ss + csc cs + ssc cc (8). sin cos s. (8) c.[9] (9) 1 0 s = = 0 c cs (9) 0 s cc

4 x 5 y. y Z F 4.. x y - 4..[10] (9).. -3 = + = = (18) L=KE-PE (16). = = + = ( ) sin cos + ( sin2(cos ) sin2 + 2 cos2 cos )) + cos + sin cos + cos + sin cos = (cos ) + (sin ) ( sin2 cos sin2cos2cos cos sin 2 (sin) (cos) cos sin cos sin sin( + )= (sin ) +(cos ) ( (cos ) + (sin ) sin+ 1 2 cos (sin 2+ cos 2 sincos 1 2 sinsin + cos + sin 2 (sin ) (cos ) + = ( 16) = (sin sin + cos sin cos ) = (sinsincos cossin) = coscos = = cos sin = sincos + cossin sin (17). sin cos. sin cos - sin sincos (12) (10). 200 rad/s. 40. x y

5 (23) = ( + ) tan / cos (23) = ( + ) tan -..[11] -2-3 X Y Z - (20). () = sin + 2 cos sin + cos () = + + sin cos sin sin (2 + ) cos cos + 2 cos sin () = cos cos 2 + sin cos (2 + )sin cos + 2 sin sin (24). (18) =[,,, ]. (25). X= [,,,,,,,,,,,,, ] z- y- x [ (), (), () ] =[][,, ] +[] (25) (26) = [] ([] + ) () = () = () =. (26) (25) (27).. =(,,) = () = LQR = 1 2 ( + ) (28). [,,, ] =,,,.. (,, ) = (, ). (, ). (, ) = cc + css ss csc sc cc sss cs + ssc (19) s cs cc. = sin = sin cos (20) = cos cos (20) (10) (20) (18) [,,,,, ] -. =[,,, ]. =,,,,,, = = (1/ )( + ) = = (1/ )( ) = = (1/ )( + ) = = (1/)( sin ) = = (1/)( sin cos ) = = (1/)( cos cos ) (21),,,,, (21) -1-3 Z 12 [,,, ] = /(cos cos )( + ) = ( ) = ( + ) = ( ). (22). (21) = PD - =,,,

6 () () sin 0 = cos sin () cos cos cos cos sin cos cos sin sin cos sin + 2 cos sin + cos cos sin sin sin 2 + cos cos + + sin cos 2 sin sin + cos cos ( ) cos sin (2 + ( ) sin cos. -. (31 26)...[8] (32) = (33) = = 1 ( + ) (33) = (33).. 5 (31 26). = = (34) = = (33) (34) (6-3) (25) ( ). + + =0 (1 1) B A (4 4) = = () + = () = = ( 29) (30) = () + (18). PD = = ( 31) -3-3 (31) (26) (32) = + = +,.[12] = (32)

7 5 6 (111) 7. 0 < (t) = + (1 + ( )) ( ) > (1 + ( )) ( ) (35) = Z (m) Y (m) (18) ) t 80s. 3 1 ( 0 X: 0 Y: 0 Z: X (m) X: 1 Y: 1 Z: rad/s = 500 y x. Z. = ( =1, = ) ( = 0, =0, = 0). (-2,0,2) (-2,-2,2) (0,-2,2) (0,0,0) (0,0,2) (0,0,2) = = = = m IX=IY IZ J J 1 4/082 9/842 9/822 4/ /0081 0/0142 0/0001 0/0005 kg NmS /rad NmS /rad NmS /rad NmS /rad / /0002 0/ / /103 15/ NS /rad NS /rad NmS /rad NmS /rad

8 /9 1 1/5 1/4 1 1/ ( = 2cos ) = 2 sin = 0.1 = 0 (0) (0)(0)(0)(0)(0)= RMS( )= RMS( )= RMS( )=0.011 RMS( )= RMS(rootmeansquare)

9 d(t)=0.04(sin(0.8t)+cos(0.2t)+sin(0.4t)).[13] Y X

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