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1、Chapter2ModelingtheQuad-RotorMini-RotorcraftThecompletedynamicsofanaircraft,takingintoaccountaero-elasticeffects,flex-ibilityofthewings,internaldynamicsoftheengineandthewholesetofchangingvariablesarequitecomplexandsomewhatunmanageableforthepurposesofcon-trol.Therefore,itisinterestin
2、gtoconsiderasimplifiedmodelofanaircraftformedbyaminimumnumberofstatesandinputs,butretainingthemainfeaturesthatmustbeconsideredwhendesigningcontrollawsforarealaircraft.Thischapterdealswiththemodelingofaquad-rotorrotorcraft,andisorganizedasfollows.Section2.1givesageneraloverviewoftheq
3、uad-rotoraerialvehicleanditsoperationprinciple.Next,Sect.2.2dealswiththequad-rotormodeling,present-ingtwodifferentapproaches:Euler–LagrangeinSect.2.2.1andNewton–EulerinSect.2.2.2.Subsequently,itisshowninSect.2.2.3howtoderiveLagrange’sequa-tionsfromNewton’sequations.Section2.2.4pres
4、entsaNewton–Eulermodelingforan“X-Flyer”quad-rotorconfiguration.Finally,someconcludingremarksarepresentedinSect.2.3.2.1TheQuad-RotorMini-RotorcraftThequad-rotormini-rotorcraftiscontrolledbytheangularspeedsoffourelectricmotorsasshowninFig.2.1.Eachmotorproducesathrustandatorque,whoseco
5、mbinationgeneratesthemainthrust,theyawtorque,thepitchtorque,andtherolltorqueactingonthequad-rotor.Conventionalhelicoptersmodifytheliftforcebyvaryingthecollectivepitch.Suchaerialvehiclesuseamechanicaldeviceknownasswashplate.Thissysteminterconnectsservomechanismsandbladepitchlinksino
6、rdertochangetherotorbladespitchangleinacyclicmanner,soastoobtainthepitchandrollcontroltorquesofthevehicle.Incontrast,thequad-rotordoesnothaveaswashplateandhasconstantpitchblades.Therefore,inaquad-rotorwecanonlyvarytheangularspeedofeachoneofthefourrotorstoobtainthepitchandrollcontro
7、ltorques.FromFig.2.1itcanbeobservedthatthemotorMi(fori=1,...,4)producestheforcefi,whichisproportionaltothesquareoftheangularspeed,thatis,fi=kw2.iL.R.GarcíaCarrilloetal.,QuadRotorcraftControl,AdvancesinIndustrialControl,23DOI10.1007/978-1-4471-4399-4_2,©Springer-VerlagLondon2013242M
8、odelingtheQuad-RotorMini-R
