哈工大惯性技术(导航原理)大作业

AssignmentofInertialTechnology《惯性技术》作业MyChineseNameMyStudentID15S004001Autumn2015Assignment1:2-DOFresponsesimulationA2-DOFgyroissubjectedtoasinusoidaltorquewithamplitudeof4g.cmandfrequencyof10Hzalongitsouterringaxis.Theangularmomentofitsrotoris10000g.cm/s,andtheangularinertiasinitsequatorialplaneareboth4g.cm/s2.Pleasesimulatetheresponseofthegyrowithin1second,andpresentwhateveryoucandiscoverorconfirmfromtheresult.Inthissimulation,wearegoingtodiscusstheresponseofa2-DOFgyrotosinusoidaltorqueinput.Accordingtothetransferfunctionofthe2-DOFgyro,theoutputscanbeexpressedas:12222()()()()yxyxyxyJHsMsMsJJsHsJJsH12222()()()()xyxxyxyJHsMsMsJJsHsJJsHTheoriginalsystemtransferfunctionisa2-input,2-outputcouplingsystem.Butthegiveninputonlyexistsoneinput,wecantreatthesystemas2separateFIFOsystemAsaconsequence,wecanestablishtheblockdiagramofthesysteminsimulinkinFig1.1.Substitutetheparametersintothesystemandinput,thenwehavetheinputsignalsasfollow:0,4sin(20)yoxMMtThentheinverseLaplacetransformoftheoutputequalstheresponseofthegyrointimedomainasfollows:02222000200222200()sinsin()()()coscos()()oxaoxaxaxaoxoxaoxaaaaaMMtttJJMMMtttHHHFig1.1TheblockdiagramofthesysteminsimulinkAndthesimulationresultsintimedomainwithin1secondareshowninthefollwingpictures.Fig1.2isthetheoutputofouterring()t.Fig1.3istheoutputofinnerring()t.Fig1.4isthetrajectoryof2-DOFgyro’sresponsetosinusoidalinput.AswecanseefromtheFig1.3,thereareobvioussawtoothwaveintheoutputoftheinnerring.It’saunexpectedphenomenoninmyoriginaltheoreticalanalysis.Fig1.2Theoutputofinnerring()tFig1.3Theoutputofouterring()tIbelievethesawtoothwaveiscausedbythenutation.Forthefrequencyofthenutationisobtainedas0100002500/3974eHradsHzJ,whichisfarhigherthanthefrequencyoftheappliedsinusoidaltorque,namely0a.Fig1.4Trajectoryof2-DOFgyro’sresponsetosinusoidalinputThetrajectoryof2-DOFgyro’sresponsetosinusoidalinputareshowninFig1.4.Aswecansee,it’scouplingofXandYchannelscopeoutput.Theoverallshapeisanellipse,whichisnotperfectfortherearesomanysawteethonthetopofit.Notethatthemajoraxisofellipseisinthedirectionoftheforcedprocession,amplitudeofwhichis0oxMH,whereastheminoraxisisinthedirectionofthetorsionspringeffects,withamplitudeoxaMH.Thenutationcomponentsaremuchsmallerthanthatoftheforcedvibration,whichcanbeeliminatedtogettheclearstaticresponse.220020220()sinsin()cos(1cos)()oxoxaaxaoxoxoxaaaaaaMMtttJHMMMtttHHHToproveit,weeliminatetheeffectsofthenutationnamelythequadraticterminthedenominatorandgetFig1.5,whichisaperfectellipse.Wecanconcludethatwheninputtothe2-DOFgyroissinusoidaltorque,thegyrowilldoanellipseconicalpendulumasastaticresponse,includingprocessionandthetorsionspringeffects,togetherwithahigh-frequencyvibrationasthedynamicresponse.Fig1.5Trajectoryofthegyro’sresponsewithoutnutationAssignment2:Single-axisINSsimulation2.1descriptionoftheproblemAmagneticlevitationtrainisbeingtestedalongatrackrunningnorth-south.Itfirstacceleratesandthencruisesataconstantspeed.Onboardisasingle-axisplatformINS,workinginthewaydescribedbythecoursewareofUnit5:BasicproblemsofINS.ThemotioninformationandEarthparametersareshownintable2-1,andthepossibleerrorsourcesareshowninTable2-2.Fig2.1Thesketchmapofthesingle-axisINSproblemYouareaskedtosimulatetheoperationoftheINSwithin10,000seconds,andinvestigate,firstonebyoneandthenaltogether,theimpactoftheseerrorsourcesontheperformanceoftheINS.Theblockdiagraminthecoursewaremightbeofsomehelp.However,therelurksaninconspicuouserror,whichyouhavetocorrectbeforeyoucanobtainreasonableresults.Thereareonecorerelevantformula,togetthespecificformofitssolution,weshouldsubstitutetheunknownparameters.(1)()cNayAKygaFirstly,theinputsignalisaccelerometeroftheplatform,andthevelocityoftheplatformistheintegrationoftheacceleration.0/pyyydtyRTheaccelerationalongYpmaycontainstwoparts:cosgsingypfyyWhenaccelerometererrorsareconcerned,theoutputofaccelerometerwillbe:(1)NaypNaKfAWhengyroerrorsconcerned:'(1)pgpKOnlyisunknown:000[(1)]tgpttptKdtdtAndthereferenceblockdiagramandsimulinkblockdiagramareasfollowsinFig2.2,Fig2.3.Thereisasmallfaultinthereferenceblock,whichisthatthesignofthemarkedaddoperationshouldbepositiveinsteadofnegative.TheresultsofthesimulationareshowninFig2.4toFig2.13.Fig2.2Thereferenceblockdiagraminthecourseware(unrectified)Fig2.3ThesimulinkblockdiagramforAssignment22.2resultsandanalysisoftheproblemFig.2.4realacceleration,velocityanddisplacementoutputwithouterrorsourcesFig2.5positionbiaswhenonlyaccelerometerscalefactorerrorexists0.0001aKFig2.6positionbiasoutputwhenonlygyroscalefactorerrorexists0.0001gKFig2.7positionbiaswhenonlyaccelerometebiaserrorexists20.0002/NAmsFig2.8positionbiasoutputwhenonlyinitialvelocityerrorexists200.01/ymsFig2.9positionbiasoutputwhenonlyinitialpositionerrorexists010ymFig2.10positionbiasoutputbiaswhenonlygyrobiaserrorexists0.000000024240.00681/3/hradsFig2.11positionbiasoutputwhenonlyinitialplatformmisalignmentangleexists00.000012120''345radFig2.12outpu