TY - JOUR

T1 - Energy Control of Electric Machine

T2 - Inverse Stoker Problem.⁎

AU - Plotnikov, Sergei A.

AU - Shepeljavyi, Alexander I.

N1 - Funding Information: SergeiA.InPlotnversiekovS∗∗t,,∗∗∗o∗ kAlexer anPdrerobI.leSmhep.e★ljavyi∗∗∗∗∗∗ Sergei A. Plotnikov ∗,∗∗ Alexander I. Shepeljavyi ∗∗∗ ∗,∗∗ ∗∗∗ ∗∗Institute for Problems of M∗e,∗c∗hanical Enfiineerinfi, Russian A∗∗c∗ademy ∗InstiStuertegeiforA.ProPlotnblemsikofovMechaAlexnicalanEnfiiderneI.eriSnfi,hepReulsjsaivanyiAcademy Institute for Problems of Mechanical Enfiineerinfi, Russian Academy Institute for Problems of Mechanical Enfiineerinfi, Russian Academy ∗ of Sciences,∗∗StI.TPMeOterUsbnuivrfei,rsRituys,sSiat.(Pe-emtearislb: uwrafi,teRrwuasslfi@a fimail.com) oInfsStictiuetnecefos,rSPtr.oPbleetmerssboufrMfi,eRchuasnsiaca(leE-mnfaiiinl:eewraintefir,wRaulfs@sfiiamnaAil.caodmem) y ∗∗∗Saint Pet∗e∗rsIbTuMrfiOStUanteivUernsivteyr,sSitty.,PSett.ePrsebtuerrfsi,buRrufis,sRiaussia (e-mail: of Sciences, StI.TPMeOterUsbnuivrfei,rsRituys,sSiat.(Pe-emtearislb: uwrafi,teRrwuasslfi@a fimail.com) ∗∗∗ Saint Peter∗∗sburfi StataesU@naisv1e0r2s0it.ys,pbS.te.dPu)etersburfi, Russia (e-mail: ∗∗∗ Saint Petersburfi StataesU@naisv1e0r2s0it.ys,pbS.te.dPu)etersburfi, Russia (e-mail: Abstract: This paper formulates a neaws@inavse1r0s2e0S.stpobk.erdup)roblem: to Ωesign the control algorithm Abstract: This paper formulates a new inverse Stoker problem: to Ωesign the control algorithm Abstract: This paper formulates a new inverse Stoker problem: to Ωesign the control algorithm ftohre peorsfeoΩrmpirnogbltehme ΩtwesoirceoΩnnturoml baelgroorfitchymclsessuligpgpeisntgesΩ.unTΩheerfairrsbtitarlagroyriitnhimtitaisl bcoanseΩΩitoionnst.hTe ospseoelvΩe-the poseΩ problem two control algorithms suggesteΩ. The first algorithm is baseΩ on the speeΩ-tghraeΩpieonsetΩalpgroorbitlhemm,twhoilceonthtreosleaclognoΩriothnme isssaugsigmesptleeΩr.eTlahyeafligrostriathlgmor.iFthomr sims bualasteiΩononthtehpersopbeleeΩm-fohrepeorsfeoΩrmpirnogbltehme ΩtwesoirceoΩnnturoml baelgroorfitchymclsessuligpgpeisntgesΩ.unTΩherfairsbtitarlagroyriitnhimtitaisl bcoanseΩΩitoionnst.hTe ospseoelvΩe-gtorapΩeierfnotrmalgaorΩitehsimre,Ωwnhuilme bthere osefccoyncΩleosnleipipsiangssimapt ltehreelbaeygainlginogritahnmΩ.tFhoenr stiommulaktieonrotthoer posrcoiblllaetme thraeΩpieonsetΩalpgroorbitlhemm,twhoilceonthtreosleaclognoΩriothnme isssaugsigmesptleeΩr.eTlahyeafligrostriathlgmor.iFthomr siims bualasteiΩononthtehpersopbeleeΩm-twoitpherafocromnstaaΩnetsairmeΩplnitumΩebeisr pofosceyΩc.leTshlieprpeisnuglstsatofthsiembuelagtinioinngshaonwΩetΩhetnhetoe∆mcaieknecryotoofrporsocpiollsaetΩe with a constant amplituΩe is poseΩ. The results of simulation showeΩ the e∆ciency of proposeΩ waligtohriathcmonss.tant amplituΩe is poseΩ. The results of simulation showeΩ the e∆ciency of proposeΩ algorithms. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Electric Machine, Oscillation, SpeeΩ-GraΩient Algorithm, Excitability InΩices, alKeygorwiothrdms.s: Electric Machine, Oscillation, SpeeΩ-GraΩient Algorithm, Excitability InΩices, KteoykweorrPdsr:obElelemctric Machine, Oscillation, SpeeΩ-GraΩient Algorithm, Excitability InΩices, Stoker Problem SteoykweorrPdsr:obElelemctric Machine, Oscillation, SpeeΩ-GraΩient Algorithm, Excitability InΩices, 1. INTRODUCTION relatively simple moΩel of sycnhronous EM ΩeriveΩ on Stoker1.ProINbleTRmODUCTION relatively simple moΩel of sycnhronous EM ΩeriveΩ on 1. INTRODUCTION relatively simple moΩel of sycnhronous EM ΩeriveΩ on 1. INTRODUCTION relatively simple moΩel of sycnhronous EM ΩeriveΩ on The transformation of one kinΩ of energy to another t2h0e0b6a))s.is of the Lagrange-Maxwell equations (RoΩyukov The transformatio1.nIoNfToRnOeDkinΩUCTIOofNenergy to another t(2006)heleatbiva)es.liys osfimthpeleLmagorΩaenlgeo-fMsayxcwnhelrloneqouuastiEoMns (ΩReroiΩveyΩukonv Tplhaeystraanksefyormroaletioinn uosfinogneofkninaΩturoaflerneesorguyrcetso. Tanhoattheisr (2006)). The transformation of one kinΩ of energy to another thoer bsoalsvisinogf the pLoasgerΩanpgreo-bMleamxwwelel ecqhuoasetiotnhse (aRlgooΩryituhkmovs pwlhayyselaecktreiyc mroalechiinneuss(inEgMo),f wnhaticuhraalreretshouertcoeos.lsTfohratthies For solvingthe poseΩ problem we chose the algorithms(2006)). plhaeystraanksefyormroaletioinn uosfinogneofkninaΩturoafl erneesorguyrcetso. Tanhoattheisr F2ao0sr0e6Ωso)o)lv.ninthgetehneerpgoysecΩonptrroolb.lOemnewoef tchheocsoentshiΩeeraelΩgocroitnhtmrosl wenheyrgeyletcrtarnicsfmoramchatinioens,(aErMeu),sewΩhiinchalalrienΩthuesttroieosls(Gfoerrltinhge FbaseΩor soonlvingthetheenerpgyoseΩconprotrolble.Omnewofetchheoconse thsiΩeeraeΩlgocrithmontrols wlhayyselaecktreiyc mroalechiinneuss(inEgMo),f wnhaticuhraalreretshouertcoeos.lsTfohratthies blagsoerΩitohnmtshiesebnaesregΩy oconnthroel.spOeneeΩ-ogfrtahΩeiecnotnmsiΩeethreoΩ c(oFnrtarΩo-l e(2n0e1rg4y)).trTahnesfionrvmesattiigoant,ioanreofusEeMΩsininacllluiΩneΩausltortieosf(ΩGiffeerrleinngt bFlaseΩogrorsiotonlhvmintshgiestenhbeaerspegyoΩseocΩonnptthrroloeb.slpOemeneeΩw-ofgertachΩheioeconsnet tmsihΩeerthaeΩolgΩocr(oiFtnrhtamrΩols- w(2nh0ey1rg4ey)).letcrTtarhenicsfimonrvamecshatigtinioeanstio,(aEnrMeofu),sEMsewΩhiincihnclalaluΩerienΩthaueslottrtoieoosfls(ΩiffGfoeerreltinhnget alkogorv (i1979,thms2007,is baseΩ2017)on)t,hewhspileeeΩth-gre seconaΩienΩtonmetehisoΩa si(FmraΩple-(p2r0o1b4le)m).sTahneΩinitveistvigeraytiiomnpoofrEtaMntsfinorcltuhΩeeaaplpolticoaftiΩoinff.eOrennet alkoagorvse(Ωi1to9hn7ms9t,h2ies0e0bn7aseΩe,r2g0y1onc7o)n)t,therwolh.spiOleeeΩnteh-groefstaΩehceoiencnΩotnometsniΩeehriseoΩΩacs(oiFmnrtaΩprole-l epro2n0e1rbleg4y)m).tsrTaahnnΩesfionitrvmeissattviigeoryant,iimoanrepoofurtasEeMΩntsinfoinarcllltheuiΩneΩaaupplicsltortieoasftio(ΩGin.ffeerOnerleinngt kreolvay(1979,algorithm2007,. H2017)owev)e,r,whtheilecthhoeicsecone of theΩ ongeainis aΩesipmenΩsple pofrosbulcehmspraonbΩleimtissivsertyheimstpuoΩrytanoftftorranthsieenatpsp,lwichaticiohnh.aOsnae kreolglvaoyr(i1979,tahlgmosri2007,tishmba.sHe2017)Ωowoenv)et,rhwh,etshipleeeecthΩho-egicrseconeaΩoifentΩtheonmgeeathiinsoΩaΩesi(pFmernaplΩΩes- p2r0o1b4le)m).sTahneΩinitveistvigeraytiiomnpoofrEtaMnts finorcltuhΩeeaaplpolticoaftiΩoinff.eOrennet oenlatyheaelgxocrititahbmili.tyHionwΩeicvesr,anthΩeecnheorgicyecofnttrhoel tghaeinorΩye(pFernaΩΩs-ogfresautchrelpervoabnlceemisnisprtahcetiscteuΩanyΩofΩettrearnmsiiennetss,thwehiec∆hchieanscya reoonlvatyh(e1a9elg7x9oc,rithmit2a0b0il7i.t,yH2i0on1wΩ7ei)cv)ee,sr,wahntheiΩleecnthheoregicsyeeccooofnnttheΩroolntgehaeinisoraΩeys(piFmernΩsapΩle- ofrosbulcehmspraonbΩleimt iss ivsertyheimstpuoΩrytanoft ftorranthsieenatpsp, lwichaticiohnh. aOsnae oonvth(2e0e0x7c)i)t.aTbihlietsyeianlΩgiocreisthamnΩs ewneerregsyuccocnestsrfoulltlhyeaoprpyl(ieFΩrafoΩr-gorfetahterseylsetveamnc.eOinneporfatchteicmeoasntΩinΩfeotremrmatiinveescthhaeraec∆tecriiesnticcys orenlathey aelgxcorithmitabili.tyHinΩicoweveesr,anΩtheecnehorgicyecoofnttherol thgaeoinrΩey (pFernΩsaΩ-gresautchrelpervoabnlceemisnisprtahcetiscteuΩanyΩofΩettrearnmsiiennetss,thwehiec∆hchieanscya Ωoifvfe(r2e0n0t7p)r)o.bTlhemesse,aslugcohritahsmcosnwterorel soufcocsecsisllfautlliyonaspipnlieliΩnefoarr ofttrhaenssyiesntetmsi.sOthneenoufmthbeermofstcyinclfeorsmlipaptiivnegsc,hwarhaicchtertirsatcicess koonvthe(2007)excita). Thbiliesety inΩicalgoreisthamsnΩ ewneerrge suy cccessfontroullthlyeoaprpyl(ieΩFraforΩ- gorfetratahtensrseyielsentvetamsnisc.eOtheinnenpourfamtchbteiecrmeooafsntcΩycinΩlefeotrsemlippingrmatiinveessc,thhwaerhaiecc∆htecrtraiiesntciccesys ΩiffanΩerenonnlinet proabler smysste,msusch(Sahirias conevtroeltoafl.o(2sc0illa01tio); AnsnΩriin linevseakyr othfetroauntspieunttvsairsiathbelencuhmanbgeerso,fΩciyvcisliebslelipbpyinthgse,pwehriiochΩtorfatchees ΩiffkonvΩe(ren2o0nn0tl7ipron))e.ableTrhsmeyssset,eamslugscohr(iStahhsimrcoisanewvteroreeltsoaufl.coc(se2cs0illas0fu1tio)ll;yAnsanpΩinprliielineΩvseafkoyrr ofttrhaenssyiesntetmsi.sOthneenoufmthbeermofstcyinclfeorsmlipaptiivnegsc,hwarhaichtertirsatcices a2n0Ω05n)o;nPlinloetanriksoyvst,eamnsΩ(SAhnirΩiraieevvsektyal(.2(021030)1;)F;uArntaΩtrieevtsakly. tshysetoemutpnuotnlvianreiaarbiltey.changes,ΩivisiblebytheperioΩofthe aΩ2nΩif0f0er5noe)n;nlinetPplorotanbrilkesmoysvste,, amsunscΩh(SAahiriasnΩcorineevtvrsoekltyoafl.(2o(20sc10i3l0l)a1;t);iFouAnrsnΩritaint levseitneakyalr. thfetroauntspieunttvsairsiathbelencuhmanbgeerso,fΩciyvcisliebslelipbpyinthgse,pwehriiochΩ torfatchees (22001065)); PFrloatΩnkiokvove,tanaΩl. A(2n0Ω1r6i)e)vsaknyΩ(2in01a3Ω);apFtuivrteatcoenttraoll. systemnonlinearity. (2anΩ005no);nlinePlotnariksoysvte, amnΩs(SAhirianΩrieevvsekytal.(2(201030);1);FuArtnΩriatevset akyl. stJhys.eteSotmuotkpenourtnlinewvasriaatrbhilteey.fcihrsatngwehs,oΩifvoirsmibulleabteyΩthaenΩpesroiolvΩeoΩf the (2G0u1z6e)n;kForeatΩkaol.v(2e0t13a)l.; P(2lo0t1n6i)k)ovan(Ω201in5);aΩSaeplitviavneovcoenttraoll. J. Stoker was the first who formulateΩ anΩ solveΩ the (201065); PFrloatΩnkiokvove,tanaΩl. A(2n0Ω1r6i)e)vsaknyΩ(2in01a3Ω);apFtuivrteatcoenttraoll. Jspy.rsoStbetlmoemkenronfwlieanssetaitmrhiateyt.ifoirnstofwthhoefnourmmublearteoΩf acyncΩlesosllvipepΩintghse. (Guz(2015)en).ko et al. (2013); Plotnikov (2015); Selivanov et al. J. Stoker was the first who formulateΩ anΩ solveΩ the ((2016)2015);).FraΩkov et al. (2016)) anΩ in aΩaptive control pHreobcloenmsiΩoefreΩstimthaetisoynstoefmthwehnicuhmΩbeesrcroifbecsyctlheeslΩipapminpgesΩ. (2015)). p.roSbtloemkerofweastitmhaetifoirnstofwthhoefnourmmublearteoΩfacyncΩlesosllvipepΩintghse. TGhuezerensktooefttahle.(p2a0p1e3r);iPsloortgnaiknoizveΩ(20a1s5f)o;llSoewlisv:anSoevctieotnal2. HhaermcoonnsiciΩemreoΩtiotnhse osfysatempenwΩhuilcuhmΩ(eSsctorikbeers (t1h9e50Ω)a).mTpehΩe The restof the paper is organizeΩ as follows: Section 2(2015)). HreobcloenmsiΩoefreΩstimthaetisoynstoefmthwehnicuhmΩbeesrcroifbecsyctlheeslΩipapminpgesΩ. T2ehm0e1i5nr)Ωe)ss.tthoef tinhfeorpmaapteironisaobroguatntizheeΩmaosΩfeoll,loswpese:ΩS-gecratiΩoinen2t hparormbloemnicismtootiΩonetseromfinaeptehneΩurelugmion(Sotfotkheer i(n1i9t5ia0l))c.oTnΩhie- The rest of the paper is organizeΩ as follows: Section 2 HproaermblecoonmnsiciΩisemrtoeoΩtiΩeotnhtesermosfyinesatemptheenwΩhureilcughmioΩn(eSsoctforithekbeersinitia(t1h9e50Ωl)a)c.moTnΩi-pehΩe realgmoinΩsrithmtheanΩinfoexcrmitaatiobilnityabinΩicoutethes. InmSeoΩec.l,3swpeeeΩeΩ-gsiragnΩietwnot ptiroonbslefmoriwshtiochΩtehteerpmeinnΩeutluhme rpeegrifoonrmosf athΩeesinirietΩialnucmonbΩeir- reThmeinΩsresttheof tinfohermpapatioernisaorboganut theizeΩmasoΩefoll,loswpese:Ω-SgectraiΩieonn2t prorbmloemnicismtootiΩonetseromf inaeptehneΩurelugmion(Sotfotkheer i(n1i9t5ia0l))c.oTnΩhie-colgnotrriotlhamlgaonriΩthemxcsi,twabhiillietySeincΩ. i4cepse.rIfnorSmesc.th3ewseimΩueslaigtinontwoof toifontusrfnoorvwerhsicahrotuhneΩpetnhΩeupluivmotpperofionrtm. sFuathΩeersirweoΩrknsumwbereer arelgmoinΩsrithmtheanΩinfoexcrmitaatiobilnityabinΩicoutethes. InmSeoΩec.l,3swpeeeΩeΩ-gsiragnΩietwnot poifroontbuslrefnmoorviwesrshtiocahroΩteunΩhteerpmetheinnΩeupitluhvmeotrpepegroifoionnrtm.osfFuatthhΩeeersinirwietoΩiarkslnucmownbeΩreeir- cproonptroosleaΩlgaolgrithmorithms, ws.hFinaile Sellcy.,4wepecrfooncrmluΩes thewithsimSeulac.tio5.n of ofofctuusrenΩoovnerscoanrsoiΩuenrΩattihone pofivtohtispporinotb.leFmutfhoerrmwuolrtkiΩsimweenre- caolgnotrithmrol algaonΩrithmexcsita, wbhiilelitySeinΩicc. 4epse.rfoInrmSesc.the3 wseimΩeusilagtionntwoof oifontusrfnoorvwerhsicahrotuhneΩpetnhΩeupluivmotpperofionrtm. sFuathΩeersirweoΩrknsumwbereer proposeΩ algorithms. Finally, we concluΩe with Sec. 5. fsoiocnuasleΩcoonnticnounosuiΩs esryasttioemn sof(Ethrisshopvrao,blaenmΩ fLoreomnouvlti(Ω1i9m8e3n)-; control algorithms, while Sec. 4 performs the simulation of oofctuusrenΩoovnerscoanrsoiΩuenrΩattihone pofivtohtispporinotb.leFmutfhoerrmwuolrtkiΩsimwenre-2. PRELIMINARIES sSimoniranlocvoanteitnuaol.us(2s0y0s9t,em20s1(3E))rsahnoΩvam, aunltΩiΩLimeoensoivon(a1l98Ω3is)-; proposeΩ algorithms. Finally, we concluΩe with Sec. 5. soiocnuasleΩcoonnticnounosuiΩs esryasttioemn sof(Ethrisshopvrao,blaenmΩ fLoreomnouvlti(Ω1i9m8e3n)-; 2. PRELIMINARIES Scrmetirenpohvase tsyaslt.em(2s00(9U,ti2n0a13(2))00a3n)Ω; Umtiunlati,ΩainmΩenSshieopnealjaΩviys-i 2. PRELIMINARIES simoniranl ocvoanteitnuaol.us(2s0y0s9t,em20s1(3E))rsahnoΩvam, aunltΩiΩLimeoennsoivon(a1l98Ω3is)-; c(2re0t0e5)p)h.ase systems (Utina (2003); Utina, anΩ Shepeljavyi 2.1 Model Equation2. PRELIMINARIES S(2005)rmetirenpo)hv.aas etsyaslt.em(2s00(9U,ti2n0a13(2))00a3n)Ω; Umtiunlati,ΩainmΩenSshieopnealjaΩviys-i 2.1 Model Equation ((2005)2005))).. 2.1 Model Equation cTrheitse ppahpaesre fsoyrsmteumlast(eUs tnienwa (i2n0v0er3s)e; USttoinkae,r apnrΩobSlehmep,ewljahvicyhi ConsiΩer the mathematical moΩel This paper formulates new inverse Stoker problem, which 2.Cco1rnibsMeiΩoedbreylthEqutheematifoaltonlohweminagtiecqaulamtioonΩse:l TishisthepaΩepesrigfonromfuthelatesconnetwroilnvaelgrsoerithmStokefor pror pbleerfomrm, winghicha scribsieΩΩerbyththee matfollohwemating iecalquamotionsΩel: iΩsestihreeΩΩneusimgnbeorfotfhceyccolentsrloiplpainlggosriuthnmΩerfoarrbpietrraforrymiinnigtiaal scribeΩ by the following equations: ishtishepaΩpeesrigfnoromfutlahteesconnetwroilnvaelgrsoeriSthtomkefroprrpoberlefomrm,winhgicha χ˙=−aχ+sw+1, ΩcoensiΩrietΩionnus.mNboerteotfhcaytcltehisslippproinbglesmunisΩecronasribΩietrraeΩryailnsoitiianl χ˙ = −arχ + sw + 1, ΩsestihreeΩΩneusimgnbeorfotfhceycolentsrloiplpainlggosriuthnmΩerfoarrbpietrraforrymiinnigtiaalχ˙=−arrχ+sw+1, cthone Ωpiatipoenrs.PNlootnteikothvaett tahli.s(2p0r1o8b)le, mhowisevcoern,sihΩeerreeΩwealsstouΩiny w˙ = −arw − sχ, (1) coensiΩrietΩionnus.mNboerteotfhcaytcltehisslippproinbglesmunisΩecronasribΩietrraeΩryailnsoitiianl w˙˙ = −a w − sχ, tithempoarepeΩrePeplolytnaiknoΩvΩeetsiagln. (o2n0e18m),ohreowceovnetrr,olhearlgeowriethsmtuΩtyo wχρ˙˙˙ = s−,arrχ +−sswχ,+ 1, ((1)1) chone Ωpiatipoenrs.PNlootnteikothvaett tahli.s(2p0r1o8b)le, mhowisevcoern,sihΩeerreeΩwealsstouΩiny ρ = s, istolmveoriet.ΩTeehpelycoannsΩiΩΩeersaitginononoef mthoisrepcroonbtlreoml ailsgomriatΩhemftoor ws˙˙ == −pi(aarwbw−−sχu, sinρ + M). ithempoarepeΩrePeplolytnaiknoΩvΩeetsiagln. (o2n0e18m),ohreowceovnetrr,olhearlgeowriethsmtuΩtyo ρ = s, r f solve it. The consiΩeration of this problem is maΩe for s˙˙=pi(arbw−ufsinρ+M). (1) ★★stolmveoriet.ΩTeehpelycoannsΩiΩΩeersaitginononoef mthoisrepcroonbtlreoml ailsgomriatΩhemftoor where χ, w areρΩ=imse,nsrionlessfelectrical variables, ρ is a ★ ThisworkwascarriedoutinIPMERAS,undersupportofRussian where χ, w are Ωimensionless electrical variables, ρ is a SsociTlevnheciseiwtF.ooruTknwhdaaetsicoaonrnr(isgeirdΩaneotruat1ti4ni-o2In9P-M0o0Ef14Rt2h)A.isS,punrodberlesumppiosrtmofaRΩuessfiaonr whloaerΩeangχ,lewexprearesΩimsingensthioenleΩiffssereelenccetricbeatlwveaenriatheblesro,taρtioisna ScienceThis wFooruknwdaatsicoanrried(granoutt 14-29-00142).in IPME RAS, under support of Russian whloaerΩ eangχ,lewexpreare ssing the Ωifference between the rotation This work was carried out in IPME RAS, under support of Russian CScience2405-8963 opyrighFto© u©n2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 2d0a1ti8o nIFA(gCrant 14-29-00142). 28 loaΩ angle expressing the Ωifference between the rotation Copyright © 2018 IFAC 28 CPeer review under responsibility of International Federation of Automatic Control.opyright © 2018 IFAC 28 Copyright © 2018 IFAC 28 10.1016/j.ifacol.2018.12.079 Copyright © 2018 IFAC 28 Publisher Copyright: © 2018 Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This paper formulates a new inverse Stoker problem: to design the control algorithm for performing the desired number of cycle slippings under arbitrary initital conditions. To solve the posed problem two control algorithms suggested. The first algorithm is based on the speed-gradient algorithm, while the second one is a simple relay algorithm. For simulation the problem to perform a desired number of cycle slippings at the begining and then to make rotor oscillate with a constant amplitude is posed. The results of simulation showed the efficiency of proposed algorithms.

AB - This paper formulates a new inverse Stoker problem: to design the control algorithm for performing the desired number of cycle slippings under arbitrary initital conditions. To solve the posed problem two control algorithms suggested. The first algorithm is based on the speed-gradient algorithm, while the second one is a simple relay algorithm. For simulation the problem to perform a desired number of cycle slippings at the begining and then to make rotor oscillate with a constant amplitude is posed. The results of simulation showed the efficiency of proposed algorithms.

KW - Electric Machine

KW - Excitability Indices

KW - Oscillation

KW - Speed-Gradient Algorithm

KW - Stoker Problem

UR - http://www.scopus.com/inward/record.url?scp=85059196372&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2018.12.079

DO - 10.1016/j.ifacol.2018.12.079

M3 - Article

AN - SCOPUS:85059196372

VL - 51

SP - 22

EP - 26

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 33

ER -