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《》2007264ControlTheoryandAPPlieatiosn,(,410083):。,。。:;;;:Tp273::10037241(2(lO7)04000405UPswingandSatbili8tZionContorlofaSingleInvertedPendulumSystemBasedontheLagarngianModelingXIAOLilong,PENGH(SehoolofnIfomrationSeienee&igneeirng,CenterSohutUinvesrity,Changsha,410083,China)Abstract:InthisPaPel`,theInathematiealmodelofasingleinVertedPendulum15establishedbyusingtheLagrangeeguation.Thenethodofenergyfeedback15introdueedtocontroltheuPswingandthePolePlacementmethod15usedforhtestabill-zationoftheinvertedPendultrn.Thedesign15ProvedbysimulationalldexPeriment.Keywords:invertedPendulunsyste`n;Lagrangjanxnodeling:energyfeedbaek:PolePiaeement1、、,I’-4]。、、、,。。,5】iLe,LQR;6[]BangBangLQR。「7]LQR。。,。:20060809,,。,,。4IeTJ&`《》2007264CorltrolTheoryandAPPJieatons(6)01341lselllwsssssleeeeeeeeJweloJnO00,10nO03941OO00(7)UǐlesJeseewese00l..es.L+..........,...................·X.el|||tweesweesesesesesllJ-esLIJlleslL2,,,1。,F,M,m,l,x,e。:L(q,=T(q,V(q,,L,q,T,V。「1。:}`I-}{L」「xy=】~】LSJ〔{00O)0」__,_.d`、aL“￡L:{`,,。,=11,2,.3n,,,x,。。:T=+,TM,Tm,。::==?!(x,)’·:`Z,)·/”2,.,m,,3:T=2+2m`cose+m,223:V=mcoso::2,m`cos。、。;22`2m、zcose223e,:、。dtae)ao3,。、,。。,0,ElefZm·:E+mgleoso(8)(l)(2)____4.。yJJ:,nlcosml`mglsln=Ujj、..4ù、ùl.J、、,1,《1,:“:=“()(3)eos=l,sins=,。。4141、·x[,*,。,,Zmgl,,,,。:v=k(Eefr)E(9)k,k=2。,:l)o,o;2)oo,o;3)o,Jo;4)00,0。::,,,l,3;:,,。0,,2,4;:,0O,。,。,。,,(9),,v,,,。,。ehniquesofAuotmion&APPIsCtions15《》2007264ControlTheoryandAPPileations4,。,。:M1.kIgm0,109kgl0.25mg9.8m/S“l、g(6),(7):ù=B=D00029.4100CU1weJ=l0ìAC,,,2。+2++)s,+)s“++》+20kZ)。+k,+bk。=+++。kZ=)。kl=,2,,=22j,9,--9a=29.4,b=3k,=44·osl6kZ=20·8163k380.8272=14.2721u:u==44.0816x+20.816380.827214.2721,,3。,2,。lseessef000,.ù00(AB)K{sI(AB)K0:{{·{。{!”!O0O)10({{…·1;!2*34(“0」Lb」1300001nU0000Oree,,lIlesesweLes,.1`l.esesesweweIJ0000JO500s,s`+(k2+bk4》,+--(a+k,+bk3》’akZsakl=0k,,kZ,k3,k4。,:,,4,5,,3,,4,。。。35。,350〕。6}JA&《》2070264IndustryControlandAlPPieations6,。,,,,,,。5,:004160.0198=XIOO%=52.6%O,0416,6.04。,,,,,,。:【1].M[〕,:,2005【21.[M],:,199313]KATSUGIROKOUDAKoudaete.GustLoadAIleviaitonDeslgnforMUPSLExrinlerltaliAcrrBasedonthePanelMethodEstationiA}.SCIEAIlualCoxlfereneeinFukui【C〕.Japan:FukulUlllveristy,2003.P924:(1982),,,,:、。(7):11」J.A.K,SUYKENS,J.VANDEWALLE,B.DeMOOR,OPtimaleofltrolbyastsquaressuPPortveCtormaenes【J」.NeuralNetworks.2001,(14):2335.【2」PETERJ.GAWTHROP,LIUPNIGWANG.1lltemitelltPreideitveeontrolofaninvertedePndu}ulllIJ】CofltrolEngueeirngParetieel(111))11111:19.【3」DEBASISHCHAFERJEE,AMITPATRA,HARISHK.JOGLEKAR.Swingupandstabzationofaeartpendulumsystelnunderrestrietedearttraekleth,【J】Sysms&ControlLdters2002(47):355364.【4」JIANGQIANGYI,NAOYOSHIYUBAZAKI,KaourHiroatUwlllgalldatSl〕iilaznContr01ofIvertdeltdltIJn〕Steln3」ontlleSIRMsdax】lycolceti。I,encemdoe{,[J]FLZyeStsandSystellls20()1(122)139152.5[],,.l[J.,2003,(1):3537.【6],,BagnBagn.2004(8):1618.171,..200423(10):2326.72:(1979),,,,:、、、。36}.J1&