哈工大惯性技术导航原理大作业.docx

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