英文文献建模和MicroRadian精密指向一个更灵活文档格式.docx

英文文献建模和MicroRadian精密指向一个更灵活文档格式.docx

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Abstract—Controllingflexiblestructureshasbeenconsideredasawell-developedtopicinthecontrolfield.Inthistopic,vibrationsuppressionandline-of-sight（LOS）potingareintwoofthemainresearchissues.Unfortunately,amongallworksreported,onlyafewhavereallyachievedhighlevelsofpointingprecision.Thisismainlybecausefriction,especiallystaticfriction,ishardtodealwith.Inthisresearch,theLOScontroloftheflexiblebeamofastandardhub-beamsystemisstudied.Theprecisionrequiredisinsteadoftreatingfrictionasanexternalnoiseandtryingtocompensateforit,thefrictionphenomenonisrepresentedbyalinearspringandisincludedaspartofthesystemmodelwhenthehubsticks.Thisis,infact,agoodapproximationofthehystereticfrictionbehaviorinthepreslidingphaseifthespringstiffnessisap-propriatelychosen.Thismodificationgreatlyenhancesthefidelity.

Ofthesystemmodel.Whatismoreimportantisthatitmakesac-tivecontrolsstillavailableinthestickphasetofacilitatethefinetuningofthepointingerror.Basedonthismodifiedmodel,itisthennothardtosynthesizetraditionalproportional–integral–derivativeandlinearquadraticGaussiancontrolstogetLOSpointingwithmicroradianprecision.

IndexTerms—Disturbanceisolation,flexiblestructurecontrol（FSC）,line-of-sight（LOS）control,precisionpositioning,staticfric-tion,vibrationsuppression.

I.INTRODUCTION

F

LEXIBLEstructurecontrol（FSC）hasgainedalotofatten-tioninthespaceindustryaswellasinacademicresearch.

Ithasalsobeenanimportantresearchissueforroboticmanipu-lators.ThetopicsinducedbyFSCarequitevaried.Forexample,systemmodeling,largestructureidentification,model/controllerreduction,sensor/actuatorlocationanalysis,controltheoryde-velopment,experimentalverification,andsoonhaveallbeenwidelystudiedsincethe1970s.Athoroughreviewonthisissuecanbefoundin[1].Themaingoaloftheseresearchworksistogetastable,fast,andprecisemotionplatformwhichisessentiallysoftduetoitssizeorduetostringentperformancerequirements.Whenitcomestocontrollersynthesis,majoreffortshavebeenfocusedonsuppressingthevibrationofthesystemcausedbylargedistancemaneuverorexternalnoises.Alotofcontrolalgorithmshavebeenputforward,suchasthetraditionalpropor-tional–integral–derivative（PID）control,observer-basedlinearquadraticGaussian（LQG）control,Lyapunovefunction-basedalgorithm,fuzzycontrol,

control,adaptivecontrol,sliding

ManuscriptreceivedApril27,2006;

revisedOctober19,2006.Manu-scriptreceivedinfinalformFebruary7,2007.RecommendedbyAssociateEditorK.Kozlowski.ThisworkwassupportedinpartbytheMinistryofEconomicAffairsandNationalScienceCouncil,R.O.C.underGrant

92-EC-17-A-05-S1–0014andGrantNSC93–2218-E-006–018.

TheauthorsarewiththeDepartmentofAeronauticsandAstronautics,Na-tionalChengKungUniversity,Tainan,Taiwan,R.O.C.（e-mail:

chsieh@mail.

ncku.edu.tw;

p4894106@ccmail.ncku.edu.tw）.

Colorversionsofoneormoreofthefiguresinthisbriefareavailableonlineathttp:

//ieeexplore.ieee.org.

DigitalObjectIdentifier10.1109/TCST.2007.903093

modecontrol,pulsewidthmodulation（PWM）control,andsoon[2]–[12].Smartstructuresthatapplyembeddedactivemembershavealsoplayedanimportant

roleinimprovingthevibrationproblem.Theapplicationofsmartstructurescaneventakecareofthemicrovibrationseffectively,whichisusuallyconsideredimpossibleusingtraditionalactuators[12]–[15].Thesestrate-giesdoprovidesignificantimprovementonsuppressingsystemvibrationascomparedwiththosecaseswherenothingisdone.However,thoughoneofthemainmotivationstodothesere-searchworksistoobtainhighaccuracypointingwhichisre-quiredbysystems,suchasspaceobservationequipment,flex-iblerobotarms,andotherprecisioninstruments,fewworkshaveseriouslyexaminedhowpreciseisthepointingthattheyhavereallyachieved.Furthermore,inmostofthereportspublished,theplotsthatshowtheclosed-loopresponsesareusuallydrawnusingascaleofdegreeorradian.Thismakesitdifficultforthereadertoseetherealsteady-stateerrorwhenitcomestoare-allyhighprecisionpointingproblem.TableIlistssomeresearchworkswherethesteady-stateerrorcanbeidentifiedorestimatedbasedontheplotsordatashowninthecorrespondingreports[6],[7],[12].Thesystemsusedintheseresearchhavesimilarstructuresasthatusedinthisstudy.Obviously,theprecisionachievedbytheseworksisintheorderofmilliradian.

Itisthusthemaincontributionofthisbrieftoshowhowtomaketheline-of-sight（LOS）pointingofastandardflex-iblesystemachievemicroradianprecision.Thereisnoactivememberembeddedintheflexiblepartofthesystem.Inaddition,ithassignificantfrictioninit.ThesystemdiscussedinthisbriefisshowninFig.1,whichisastandardhub-beamsystem.Ithasabrushtypepermanentmagnet（PM）dctorquemotorrotatinghorizontally,whichistheonlyactuatorinthissystem.Thebear-ingsusedinthissystemareballbearingswiththeexistenceof

friction.Twoflexiblefiberglassbeamsareclampedtothehub.Eachbeamis1000mmlong,100mmhigh,and1.64mmthick,andalaserdiodeismountednearthetipofoneofthebeams.Aphotosensorislocated10.13mawayfromthishub-beamsystemtomeasurethepositionofthelaserspotemittedbythediode.Thediameteroftheeffectivemeasuringrangeofthissensoris20mm.Inadditiontothephotosensor,anencoderwitharesolutionof15s/countismountedonthemotorandastraingaugeisadheredtoeachbeamneartheroot.Theanalog-to-dig-ital（A/D）converterusedtomeasuretheoutputvoltagesofthestraingaugeandphotosensorhasaresolutionof12bits.Thegoalthenofthisresearchistodesignacontrolsystemthatcanmaneuverthelaserbeamfromitsarbitraryinitialpositiontothecenterofthephotosensorwithanerroroflessthan

50m.Thisaccuracyisequivalenttosayingthattheerrorofthehubangleplusthedeflectionangleatthetipofthebeamshouldbelessthan5rad.

Obviously,thewholecontrolprocesswillbedividedintotwosets.Thefirstsetinvolvesthemovementofthelaserbeamintotheeffectiverangeofthephotosensorsothatfinepositioningcanbestarted.Thisrequirestheerrorofthehubangletobelessthan0.057ifthebeamiscompletelystraight,orthedeflectionatthetipofthebeamtobesmallerthan0.72mmifthehubispointingexactlyatthetarget.Inthisset,bothencoderandstraingaugesareavailableforfeedback.Thesecondsetinvolvesthefinetuningofthehubpositionandthesuppressionoftheresiduevibrationofthebeamsothattheerrorofthehubangleislessthan5rad（0.00028）,andthetipdeflectionislessthan3.6m.Onlythephotosensorisavailableforfeedbackinthisset.

Asmentionedearlier,similarsystemshavebeenwidelystudiedintheliterature,butafewofthemhaveachievedthisaccuracy.Forexample,noneofthesystemslistedinTableIhaveachievedtheaccuracythatisgoodenoughtomovethelaserbeamintotheeffectiverangeofthephotosensortostartthefinetuning.Atfirstglance,themaindifficultiesinachievingthestringentLOSaccuracyarecopingwiththevibrationofthebeam,theinducementofthenonlinearbehaviorofthelargedeflectionofthebeams,andthepossiblespilloverproblem.Asamatterof

fact,theseissueshavebeenstudiedquitethoroughly.However,itturnsoutthatitisthefrictionembeddedintherollerbearingsandmotorthatshouldbeovercomeasitcomestoprecision.Thisis,infact,thecriticalfactorthatinfluencesthesteady-stateerror.Inarealsituation,thehubusuallysticksatsomepositionotherthanthedesignatedangleasitgetsclosetoit.Ifthishappens,accordingtotheAmonton–Coulombfrictionmodel,allcontroleffortswillbecounterbalancedbythestaticfrictionforceandfromthenon,thebeamjustbehaveslikeacantileveredbeam.Nocontrolisvalidanymore.TheLOSofthebeamishencestickingatawrongangle,andthisiswhypeopleusuallygetasteady-stateerrorevenifthebeamvibrationiscompletelyset-tled.Tosortoutthisproblem,peopleusetheCoulombmodel,theLuGremodel[16],orotherfrictionmodelstoestimatethefrictionforceandthencompensateforitusingfeedforwardcon-trols[7]–[9],[12].However,duetothevaryingpropertiesoffriction,modelswithconstantfrictionparameterscanneverpre-dicttheexactfrictionforce.Thedeviationsfromthetruefric-tionforcecausesdetrimentaldisturbancetosystemswherehighin-positionstabilityisdemanded,letalonethefactthatthosemodelsusedareusuallyonlyanapproximationforsomelim-itedcases.

Inthisresearch,frictionisnotconsideredasanexternalnoisetobecompensatedatall.Instead,itisconsideredaspartofthesystem.Moreprecisely,itistreatedasalinearspringandin-cludedinthemodelasthehubsticks.Thissimplemodificationis,infact,anappropriateapproximationofthehystereticfric-tionbehaviorasfarasprecisionpositioningisconcerned.Thisgivesamuchmoreaccuraterepresentationofthesystem.Furthermore,itallowscontroltobeavailableinthestickphasetokeepsuppressingtheresiduevibrationofthebeamandim-provingtheLOSofthewholesystem.

InSectionII,thestaticfrictionbehaviorisbrieflyreviewed,andboththetraditional