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外文翻译--倒立摆的控制最合适的算法 英文版.pdf

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外文翻译--倒立摆的控制最合适的算法 英文版.pdf

52ACTAELECTROTECHNICAETINFORMATICA,VOL11,NO2,2011,52–57,DOI102478/V1019801100196ISSN13358243PRINT2011FEITUKEISSN13383957ONLINEWWWAEITUKESKWWWVERSITACOM/AEITHEMOSTSUITABLEALGORITHMFORINVERTEDPENDULUMCONTROLPETERPSTORDEPARTMENTOFAVIONICS,FACULTYOFAERONAUTICS,TECHNICALUNIVERSITYOFKOŠICE,RAMPOV7,04121KOŠICE,SLOVAKREPUBLIC,EMAILPASTOR_PETOYAHOOCOMABSTRACTTHEAIMOFTHEPAPERISTOSHOWCOMPARISONBETWEENTHREEPOSSIBLEREALIZATIONSOFTHEPIDREGULATORCONNECTIONINTHISCASETHEREGULATEDPARAMETERISDEVIATIONFROMDESIREDVERTICALPOSITIONTHESTRUCTUREOFTHEREGULATORISSAMELIKESTRUCTUREOFAUTOPILOTUSEDINAIRCRAFTFORPITCHANGLESTABILIZATIONTHREEDIFFERENTSTRUCTURESOFALGORITHMSAREDESCRIBEDANDTHESESTRUCTURESDIFFERBYPROPORTIONAL,INTEGRATIONANDDERIVATEGAINCONNECTIONTHEGOALISTOFINDTHEMOSTSUITABLESTRUCTUREFORPENDULUMSTABILIZATIONTHECRITERIAFORTHEBESTSYSTEMSELECTIONARESYSTEM’SSTABILITY,WIDERANGEOFSTABILIZEDANGLE,UNCOMPLICATEDFINALSTRUCTUREANDNOOVERSHOOTINGOFINPUT’SLIMITATIONSKEYWORDSINVERTEDPENDULUM,THRUSTVECTORINGNOZZLE,PIDREGULATOR,AUTOPILOT1INTRODUCTIONINVERTEDPENDULUMISATYPICALEXAMPLEOFTHEINHERENTLYUNSTABLESYSTEMANDISWIDELYUSEDASBENCHMARKFORTESTINGCONTROLALGORITHMSPIDCONTROLLERS,NEURALNETWORKS,FUZZYLOGIC,ETCTHISSYSTEMAPPROXIMATESTHEDYNAMICSOFAROCKETIMMEDIATELYAFTERLIFTOFF,ORDYNAMICSOFATHRUSTVECTOREDAIRCRAFTINUNSTABLEFLIGHTREGIMESINLOWDYNAMICPRESSURECONDITIONSTHEOBJECTIVEOFTHEROCKETCONTROLPROBLEMISTOMAINTAINTHEROCKETINAVERTICALATTITUDEWHILEITACCELERATES1ANGULARPOSITIONOFTHEINVERTEDPENDULUMISCONTROLLEDBYINPUTFORCEINTHISCASETHECONTROLLINGFORCEISGENERATEDBYSYSTEMOFVECTOREDNOZZLES,WHEREFORCEISDIRECTLYPROPORTIONALTONOZZLEDEFLECTIONPOSITIONLIMITATION20DEG,RATELIMITATION60DEG/SECANDNOZZLEDYNAMICREPRESENTINGBY2NDORDERTRANSFERFUNCTIONAREALSOCONSIDEREDTHEMODELOFTHESYSTEMOFTHEVECTOREDNOZZLESWILLBEBRIEFLYDESCRIBEDLATERTHISMODELISCONNECTEDWITHTHENONLINEARMODELOFTHEINVERTEDPENDULUMGIVENBYFOLLOWINGEQUATIONS22222COSDXDDMMMLMLFDTDTDTΘΘΘ−⎛⎞⎜⎟⎝⎠122222COSSINDDXJMLMLMGLDTDTΘΘΘ−2WHEREM–MASSOFTHECART,M–MASSOFTHEPENDULUM,L–LENGTHTOPENDULUMCENTREOFMASS,J–INERTIAOFTHEPENDULUM,Θ–DEVIATIONFROMVERTICALPOSITION,X–CARTPOSITIONCOORDINATE,G–ACCELERATIONOFGRAVITY,F–INPUTFORCETHECONSTRUCTIONOFTHEMODELISDESCRIBEDINMOREDETAILSINPUBLICATION2THISSYSTEMWILLBEAPPLIEDFORFINALNONLINEARANALYSESOFTHESELECTEDCONTROLLINGSYSTEMTRANSFERFUNCTION,GIVENBYEQUATION3WILLBEUTILIZEDFORCONTROLLERDESIGNANDREGULATOR’SPARAMETERSSETTING5222201,2815101,90836LSKJMLUSSSSGJΘΩ−−−⋅−−3WHEREK–GAINOFTHESYSTEM,Ω0–NATURALFREQUENCYOFTHESYSTEMTHISFUNCTIONISEASYTOANALYSEANDTHEPIDREGULATORDESIGNISALSONOTCOMPLICATED21STALGORITHMTHEFIRSTALGORITHMSTRUCTUREISDESCRIBEDBYFOLLOWINGCONTROLLAW3ZFSPSSSDSΘΘΘ−4WHEREFS–FORCEAPPLIEDTOTHEPENDULUM;ΘZS–DESIREDVALUEOFΘANGLE;P,D–COEFFICIENTSOFTHEREGULATORTHESTRUCTUREOFTHISAUTOPILOTCONSISTSOFTWOLOOPS–OUTERANDINNERANDISDEPICTEDINFIG1FIG1STRUCTUREOFTHE1STALGORITHMTHETRANSFERFUNCTIONOFTHEINNERLOOPIS2202202201KSSKSKDSSKDSSΩΩΩ5ANDTRANSFERFUNCTIONOFTHEWHOLESYSTEM220ZSKPSSKDSKPΘΘΩ6THEP,DPARAMETERSCOULDBECALCULATEDBYCOMPARINGTHEDENOMINATOROFEQUATION6WITHDESIREDDENOMINATORSHAPE222SPSPSPSΞΩΩ7ACTAELECTROTECHNICAETINFORMATICA,VOL11,NO2,201153ISSN13358243PRINT2011FEITUKEISSN13383957ONLINEWWWAEITUKESKWWWVERSITACOM/AEIFROMPREVIOUSFORMULAYOUCANFINDTHESIMILARITYWITHAIRCRAFTSHORTPERIODMODEANDTHESAMECRITERIAFORSHORTPERIODDAMPINGΞSPANDFREQUENCYΩSPAREUSEABLEFORTHISPURPOSETHECRITERIAFORSHORTPERIODDAMPINGANDFREQUENCYACCORDING4,5,6ARE0,351,3;1/SECSPSPRADΞΩ≤≤≥COMPAREDENOMINATOROFEQUATION6WITHEXPRESSION7222202SPSPSPSKDSKPSΩΞΩΩCOEFFICIENTDCANBECALCULATED12SPSPJDKGMSLΞΩ−−⎡⎤⎣⎦8ANDCOEFFICIENTP22SPJPMGKGMSLΩ−−⎛⎞⎡⎤⎜⎟⎣⎦⎝⎠9FIG2SHOWSTHESTEPRESPONSE,WHENINPUTSIGNALISSTEPFUNCTIONWITHFINALVALUEΠ/10THISVALUEWASAPPROXIMATELYCALCULATEDFROMEQUATIONS1AND2VALUEOFPCOEFFICIENTISP461049ANDDCOEFFICIENTD312133FIG2ΘANGLETIMERESPONSEYOUCANSEEFROMFIG3,THATTHEINPUTFORCEINT0EXCEEDSTHELIMITATIONANDTHISSTRUCTURECANNOTBEUSEDFORFURTHERDESIGNFIG3INPUTFORCETIMERESPONSE32NDALGORITHMTHESECONDALGORITHMISGIVENBYFOLLOWINGCONTROLLAW3ZPSIFSSDSSSSΘΘΘ−10WHEREI–INTEGRATIONCOEFFICIENTOFTHEPIDREGULATORANDMEANINGOFOTHERPARAMETERSISSAMELIKEINEQUATION4THESTRUCTUREOFTHEAUTOPILOTISDEPICTEDINFIG4FIG4STRUCTUREOFTHE2NDALGORITHMTHEMODELCONSISTSALSOFROM2LOOPS–INNERANDOUTERANDTHETRANSFERFUNCTIONVALIDFORINNERLOOPISGIVENBYEQUATION5INCLUDINGOUTERLOOP,THEFINALTRANSFERFUNCTIONIS3220ZSKPSKISSKDSKPSKIΘΘΩ11BINOMIALSTANDARDFORMFOR3RDORDERSYSTEMDESCRIBESDESIREDTIMERESPONSE3322333ZZZSSSΩΩΩ,WHEREΩZISDESIREDVALUEOFNATURALFREQUENCYTHEP,I,DCOEFFICIENTSARE223ZJPMGKGMSLΩ−−⎛⎞⎡⎤⎜⎟⎣⎦⎝⎠1233ZJIKGMSLΩ−−⎡⎤⎣⎦1313ZJDKGMSLΩ−−⎡⎤⎣⎦14THETIMEOFREGULATIONCANBEAPPROXIMATELYCALCULATEDBYUSINGFORMULA7SECRZTΩ≈15THESTEPRESPONSEISSHOWNINFIG5ANDTHEPIDREGULATORCOEFFICIENTSAREP1085315,8;I624267;D468200ITCANBEOBSERVEDINFIG5THEUNDESIRABLEOVERSHOOTTRYTOADJUSTP,IANDDCOEFFICIENTSTOELIMINATETHEOVERSHOOTTHECOEFFICIENTSFORDIFFERENTΩZVALUEARESHOWNINTABLE1TABLE1COEFFICIENTSFORDIFFERENTΩZVALUEΩZPID1383015,87303323410021085315,862426746820043894515,8499413393640054THEMOSTSUITABLEALGORITHMFORINVERTEDPENDULUMCONTROLISSN13358243PRINT2011FEITUKEISSN13383957ONLINEWWWAEITUKESKWWWVERSITACOM/AEIFIG5ΘANGLETIMERESPONSEITISPOSSIBLETODETERMINEFROMFIG6THERELATIONSHIPBETWEENOVERSHOOTANDΩZVALUEIFTHEΩZVALUEISINCREASING,THEOVERSHOOTISDECREASINGANDVICEVERSAFIG6ΘANGLETIMERESPONSEYOUCANSEEINFIG7THATINPUTFORCEEXCEEDSLIMITATIONAGAINFORALLCOEFFICIENTSVALUESETTINGFIG7INPUTFORCETIMERESPONSE43RDALGORITHMTHEFOLLOWINGCONTROLLAWISVALIDFORTHIRDALGORITHM32ZSFSSDSSPSISSΘΘΘΘ−LET’SDIVIDETHEPREVIOUSEXPRESSIONBY1/SZIFSSDSPSSSSΘΘΘΘ−16THESTRUCTUREOFTHEAUTOPILOTISSHOWNINFIG8FIG8STRUCTUREOFTHE3RDALGORITHMTHESTRUCTURECONSISTSOFTHETHREELOOPS–INNER,MIDDLEANDOUTERTHEFORMOFTHEINNERLOOPISTHESAMELIKEINPREVIOUSEXAMPLESANDISGIVENBYEQUATION5THETRANSFERFUNCTIONINCLUDINGMIDDLELOOPHASFORM220KSKDSKPΩANDTHETRANSFERFUNCTIONOFTHEWHOLESYSTEM3220KISKDSKPSKIΩ17THEDENOMINATOROFEQUATION17HASTHESAMEFORMLIKEDENOMINATOROFEQUATION11,SOTHESAMEVALUEOFP,I,DCOEFFICIENTAREVALIDFIG9SHOWSTIMERESPONSETOINPUTSTEPFUNCTIONWITHFINALVALUEΠ/10FIG9ΘANGLETIMERESPONSEFIG10INPUTFORCETIMERESPONSEACTAELECTROTECHNICAETINFORMATICA,VOL11,NO2,201155ISSN13358243PRINT2011FEITUKEISSN13383957ONLINEWWWAEITUKESKWWWVERSITACOM/AEIYOUCANOBSERVEINFIG10THATINPUTFORCEDOESNOTEXCEEDTHELIMITATION,WHICHISDEPICTEDASREDLIMITINGLINETHISSTRUCTUREISTHEMOSTSUITABLEFORΘANGLECONTROL,BECAUSEINPREVIOUSEXAMPLESTHEINPUTFORCEEXCEEDSLIMITEDVALUETHEBODECHARACTERISTICOFTRANSFERFUNCTIONGIVENBYEQUATION17ISSHOWNINTHEFOLLOWINGFIGUREFIG11BODECHARACTERISTIC5NONLINEARANALYSESTHESTRUCTUREFORNONLINEARANALYSESCONSISTSOFTWONONLINEARMODELS–MODELOFINVERTEDPENDULUMDESCRIBEDBYEQUATIONS12ANDMODELOFTHRUSTVECTORINGSYSTEMOFAIRCRAFT’SENGINEINCLUDINGDYNAMICOFNOZZLESGIVENBY2NDORDERTRANSFERFUNCTIONSIMILARLIKEINPUBLICATION4240040400SSITSDEFLECTIONISLIMITED20DEGINPOSITIONAND60DEG/SECINRATE1MODELPROVIDESCALCULATION7OFTHESUMMARYFORCESANDMOMENTSGENERATEDBYTHRUSTSYSTEMINTHISEXAMPLEONLYFORCEINPITCHCONTROLISCONSIDEREDSINFSTSΦ⋅18WHERETISTHETHRUSTPRODUCEDBYNOZZLEANDITSVALUEISCONSTANTDURINGSIMULATION;Φ–ANGLEBETWEENVECTOREDNOZZLEDEFLECTIONANDLONGITUDINALAXESSUBSTITUTEEQUATION18INTOCONTROLLAW16SINZITSSDSPSSSSΦΘΘΘΘ−19LET’SASSUMETHESIMPLIFICATION–FORSMALLANGLEOFNOZZLEDEFLECTIONAPPROXIMATELYUPTO20DEGISVALIDSINΦSΦSDIVIDEEQUATION19BYTHRUSTT1ZDPISSSSSSTTTSΦΘΘΘΘ⋅−20EQUATION20REPRESENTSCONTROLLAWFORSYSTEMMENTIONABOVEANDSHOWNINFIG12FIG12SYSTEMFORNONLINEARANALYSESNEWP,I,DVALUESCANBECALCULATEDBYAPPLYINGEQUATION20ANDASSUMINGTHATNOZZLESGENERATEDTHRUST148916NITISNECESSARYTOEMPHASISE,THATTHESEPARAMETERSARECONSTANTONLYIFTHETHRUSTOFTHEAIRCRAFTISCONSTANTINCASETHETHRUSTVARIESDURINGSIMULATION,THESEPARAMETERSHAVETOBEADJUSTEDACCORDINGACTUALTHRUSTVALUENOTETHEP,I,DVALUESAREGIVENASRATIOTHISISVERYIMPORTANTFACTFORPRACTICALREALIZATIONOFTHESIMILARSYSTEMWITHSAMEPROPERTIESLIKEMENTIONABOVESYSTEMTHESYSTEMDEPICTEDINFIG12WASANALYSEDFIG13SHOWSSTEPRESPONSEWHENΘZ18,8DEGANDTHISISTHEMAXIMUMVALUE,WHENPENDULUMCANBESTABILIZEDTHISLIMITATIONCANBEALSOCALCULATEDFROMEQUATIONS2AND1FORCONSTANTΘVALUETHEMOTIONOFTHEPENDULUMABOVETHISLIMITATIONISUNSTABLEFIG13ΘANGLETIMERESPONSEIFTHEINPUTISIMPULSEFUNCTIONWITHPERIOD20SANDPULSEWIDTH50THENTHEMAXIMUMΘZISLIMITEDTO16,1DEGTHETIMERESPONSEOFANGLEANDANGULARVELOCITYISDEPICTEDINTHEFOLLOWINGFIGURESFIG14ΘANGLETIMERESPONSE

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