哈工大惯性技术导航原理大作业.docx
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哈工大惯性技术导航原理大作业.docx
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哈工大惯性技术导航原理大作业
Assignmentof
InertialTechnology
《惯性技术》作业
MyChineseName
MyStudentID
15S004001
Autumn2015
Assignment1:
2-DOFresponsesimulation
A2-DOFgyroissubjectedtoasinusoidaltorquewithamplitudeof4g.cmandfrequencyof10Hzalongitsouterringaxis.Theangularmomentofitsrotoris10000g.cm/s,andtheangularinertiasinitsequatorialplaneareboth4g.cm/s2.Pleasesimulatetheresponseofthegyrowithin1second,andpresentwhateveryoucandiscoverorconfirmfromtheresult.
Inthissimulation,wearegoingtodiscusstheresponseofa2-DOFgyrotosinusoidaltorqueinput.Accordingtothetransferfunctionofthe2-DOFgyro,theoutputscanbeexpressedas:
Theoriginalsystemtransferfunctionisa2-input,2-outputcouplingsystem.Butthegiveninputonlyexistsoneinput,wecantreatthesystemas2separateFIFOsystem
Asaconsequence,wecanestablishtheblockdiagramofthesysteminsimulinkinFig1.1.
Substitutetheparametersintothesystemandinput,thenwehavetheinputsignalsasfollow:
ThentheinverseLaplacetransformoftheoutputequalstheresponseofthegyrointimedomainasfollows:
Fig1.1Theblockdiagramofthesysteminsimulink
Andthesimulationresultsintimedomainwithin1secondareshowninthefollwingpictures.Fig1.2isthetheoutputofouterring.Fig1.3istheoutputofinnerring.Fig1.4isthetrajectoryof2-DOFgyro’sresponsetosinusoidalinput.AswecanseefromtheFig1.3,thereareobvioussawtoothwaveintheoutputoftheinnerring.It’saunexpectedphenomenoninmyoriginaltheoreticalanalysis.
Fig1.2Theoutputofinnerring
Fig1.3Theoutputofouterring
Ibelievethesawtoothwaveiscausedbythenutation.Forthefrequencyofthenutationisobtainedas,whichisfarhigherthanthefrequencyoftheappliedsinusoidaltorque,namely.
Fig1.4Trajectoryof2-DOFgyro’sresponsetosinusoidalinput
Thetrajectoryof2-DOFgyro’sresponsetosinusoidalinputareshowninFig1.4.Aswecansee,it’scouplingofXandYchannelscopeoutput.Theoverallshapeisanellipse,whichisnotperfectfortherearesomanysawteethonthetopofit.
Notethatthemajoraxisofellipseisinthedirectionoftheforcedprocession,amplitudeofwhichis,whereastheminoraxisisinthedirectionofthetorsionspringeffects,withamplitude.
Thenutationcomponentsaremuchsmallerthanthatoftheforcedvibration,whichcanbeeliminatedtogettheclearstaticresponse.
Toproveit,weeliminatetheeffectsofthenutationnamelythequadraticterminthedenominatorandgetFig1.5,whichisaperfectellipse.Wecanconcludethatwheninputtothe2-DOFgyroissinusoidaltorque,thegyrowilldoanellipseconicalpendulumasastaticresponse,includingprocessionandthetorsionspringeffects,togetherwithahigh-frequencyvibrationasthedynamicresponse.
Fig1.5Trajectoryofthegyro’sresponsewithoutnutation
Assignment2:
Single-axisINSsimulation
2.1descriptionoftheproblem
Amagneticlevitationtrainisbeingtestedalongatrackrunningnorth-south.Itfirstacceleratesandthencruisesataconstantspeed.Onboardisasingle-axisplatformINS,workinginthewaydescribedbythecoursewareofUnit5:
BasicproblemsofINS.ThemotioninformationandEarthparametersareshownintable2-1,andthepossibleerrorsourcesareshowninTable2-2.
Fig2.1Thesketchmapofthesingle-axisINSproblem
YouareaskedtosimulatetheoperationoftheINSwithin10,000seconds,andinvestigate,firstonebyoneandthenaltogether,theimpactoftheseerrorsourcesontheperformanceoftheINS.Theblockdiagraminthecoursewaremightbeofsomehelp.However,therelurksaninconspicuouserror,whichyouhavetocorrectbeforeyoucanobtainreasonableresults.
Thereareonecorerelevantformula,togetthespecificformofitssolution,weshouldsubstitutetheunknownparameters.
Firstly,theinputsignalisaccelerometeroftheplatform,andthevelocityoftheplatformistheintegrationoftheacceleration.
TheaccelerationalongYpmaycontainstwoparts:
Whenaccelerometererrorsareconcerned,theoutputofaccelerometerwillbe:
Whengyroerrorsconcerned:
Onlyisunknown:
AndthereferenceblockdiagramandsimulinkblockdiagramareasfollowsinFig2.2,Fig2.3.Thereisasmallfaultinthereferenceblock,whichisthatthesignofthemarkedaddoperationshouldbepositiveinsteadofnegative.
TheresultsofthesimulationareshowninFig2.4toFig2.13.
Fig2.2Thereferenceblockdiagraminthecourseware(unrectified)
Fig2.3ThesimulinkblockdiagramforAssignment2
2.2resultsandanalysisoftheproblem
Fig.2.4realacceleration,velocityanddisplacementoutputwithouterrorsources
Fig2.5positionbiasw
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