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357Vol.35,No.720097ACTAAUTOMATICASINICAJuly,2009111222,,.,,,.,,,,.,,,TP271.31DisturbanceRejectionControlofIndustrialHeavy-loadHydraulicForceServoSystemYANGBo1LIWan-Zhou1JIANGZhao-Fang1SHITong-Gang2WUGuan-Yuan2SUNYong-Jun2AbstractBecausetheloadofheavy-loadroughgrindingmachinehaslargeinertiaandlowdamping,acoupleofvirtualzerosexistintheopen-looptransferfunction,andtheopen-loopbandwidthisalsoa®ectedbythecharacteristicsofload.High-speedrotatingwheelwillgenerateeccentricinterferenceofhighfrequencyandlargemagnitude,andasimpleoutputfeedbackmethodcannotsuppresstheinterferencebecauseofthelowfrequencyresponseofthesystem.Inthispaper,byadoptingnonlineartrackingdi®erentiatortopickupthestatevariableandintroducingnonlinearfeedforwardcoe±cient,virtualzerosandtheimpactonopen-loopbandwidthbytheloadareeliminated,andtheoutsidedisplacementdisturbanceandeccentricdisturbancearesigni¯cantlyrejected.KeywordsRoughgrindingmachine,disturbancerejection,nonlineartrackingdi®erentiator,modeling,,.,..,,,;,,,.,PID[1],,.[2],.,,[3¡4]2008-04-252008-06-15ReceivedApril25,2008;inrevisedformJune15,20081.1000842.0540251.DepartmentofAutomation,TsinghuaUniversity,Beijing1000842.SinosteelXingtaiMechineryandMillRollCO.,LTD.,Xingtai054025DOI:10.3724/SP.J.1004.2009.00926[5][6](Particleswarmoptimization,PSO)[7][8][9][10][11].,,,,,,,,.,.,,,,.,.,,,,,(Trackingdi®erentiator,TD)[12]7:927..1.,,,,,.,,,,.100,250,80m/s,12000N.1Fig.1Heavyrollbeforemachining12..,,,.O,xy,,,,Fn=GLGcosµ+GwxA¡FhLCsin±¡Jd2µd2t+FOsin!tLn(1),FnFhFO,GGw(),LGLCLnO,xAA,J,BO(,B,),!,µ±2.3().QL(s)=KqXV(s)¡KcP1(s)(2)XV(s)=KuU(s)(3),QL,xV,p1(),KqKc{,u.QL+Cip(p2¡p1)=¡A1d¢xpdt+V1¯edp1dt(4)Fh=p2A2¡p1A1(5),Cip,p1A1V1,p2A2,p22Fig.2Mechanicalstructureandforceanalysisofroughgrindingmachine928353Fig.3Hydraulicsystemofroughgrindingmachine,¯e(),xp.,(5)¢QL(s)=¡A1s¢Xp(s)+Cip¢P1(s)+V1¯es¢P1(s)(6),2¢xp=¡LB¢µ(7)(1)(5),¢P1(s)A1LCsin±=¢Fn(s)Ln+Js2¢µ(s)+Td(s)(8),Td,Fh,FO.,Fn=0,Kce=Kc+Cip,Td=0,(2),(3),(6)»(8)V(s)=¡KqKuA1U(s)JV1¯eA21LBLCsin±s2+JKceA21LBLCsin±s+1(9)(9)KqKuKce¯e,.xp=0:6,§0.5V§1.0V,T=0:008s.[13¡14],,Matlab\Systemidenti¯cationtool(9),8:µKqKuA1¶xp=0:6=(2:9438£10¡2;u03:1295£10¡2;u0µJV1¯eA21LBLCsin±¶xp=0:6=7:5169£10¡4µJKceA21LBLCsin±¶xp=0:6=7:6027£10¡3(10),4,.(10)Kq¢KuKce¯e,.4Fig.4Comparisonbetweentherealoutputandtheoutputofmodelforvelocityofthepiston,Fhxp5(),¢Fh¢xp.(1)¢Fn=¡¢FhLCsin±=Ln,¢Fn¢xp.¢Fn¢xpKs,¢Fn=¡Ks¢xp(11),1,Xd,(7)¢xp=¡LB¢µ+Xd(12)(2),(3),(5),(6),(8),(11),(12)¢QL¢P1¢Xp,7:929¢Fn(s)=KqKuA1LCsin±KceLnµs2!2m+1¶¢U(s)+A21~KsKceLnsTd(s)+A31LCsin±KceLnµs3!2m+s¶Xd(s)µs!r+1¶µs2!20+2»0s!0+1¶(13)~Ks,~Ks=KsLnLCsin±;!m,!m=vuuut~KsJLBLCsin±;Kh,Kh=¯eA21V1;!h,!h=vuuutKhJLBLCsin±=s¯eA21LBLCsin±JV1,!r=1A21Kce~Ks+A21KceKh,!0=!hs1+~KsKh,»0=KhKce2!0A21Ã1+~KsKh!.5FhxpFig.5RelationshipbetweenFhandxpunderstaticconditions22.1(13)uFn.!0!h,!r!0,!h,!r.,!r;,,!r.,,,.,,.,,,5,,,,,.(13).Xd,,,.TdFO.900mm100mm80m/s,FO28.3Hz,2mm,104N,,2mm.,.,6(),3Hz,.2.2,.,\,[12](TD).:v(t),z1z2,z1v(t),z2=_z1,z2v(t).,93035,TD8:_z1=z2_z2=¡R¢satµ_z1¡v+jz2jz22R;¸¶(14)sat(A;¸)=8:sgn(A);jAj¸¸A;jAj·¸;¸0(15)2.37,Fnset.,,,.(10),Kq¢Ku,EKvar,Kq¢Ku,E¢Kvar=¡A1KqKu(16)Gp(s)=¢Fn(s)¢U0(s)=KqKuA1LCsin±KceLn1+s!p(17),!p=KceKh=A21.,,,,.7,,,XdTd,.7,xpPI.6,,,,.6Fig.6Frequencyresponsecurvesofopen-loopforce-loadingsystem36,.8(),750,,,12000N.,7FnFig.7Closed-loopcontrolofloadforceFn7:931,,80%,,10%.9.8FnFig.8RealloadingforceFnbeforeandaftertheproposedmethodisapplied9Fig.9Thesceneofroughgrinding1011,,,,,.4,,,,.,,,,.10Fig.10Performanceofroughgrindingmachineinthispaper11Fig.11Performanceoftheforeigners0roughgrindingmachineReferences1MerritHE.HydraulicControlSystems.NewYork:WileyandSons,19672DetiekE,KikerE.Anadaptiveforcecontrolofhydraulicdrivesoffacilityfortestingmechanicalconstructions.Ex-perimentalTechniques,2001,25(1):35¡393LiG,KhajepourA.Robustcontrolofahydraulicallydriven93235°exiblearmusingbacksteppingtechnique.JournalofSoundandVibration,2005,280(3-5):759¡7754NamvarM,AghiliF.Acombinedschemeforidenti¯ca-tionandrobusttorquecontrolofhydraulicactuators.Jour-nalofDynamicSystems,Measurement,andControl,2003,125(4):595¡6065YouSH,HahnJO,YoungMC,KyoIL.Modelingandcontrolofahydraulicunitfordirectyawmomentcontrolinanautomobile.ControlEngineeringPractice,2006,14(9):1011¡10226SekhavatP,SepehriN,WuQ.Impactstabilizingcon-trollerforhydraulicactuatorswithfriction:theoryandexperiments.ControlEngineeringPractice,2006,14(12):1423¡14337ZouJ,FuX,YangHY,ZhangJM.Aparticleswarmop-timizationapproachforPIDparametersinhydraulicservocontrolsystem.In:Proceedingsofthe6thWorldCongressonIntelligentControlandAutomation.WashingtonD.C.,USA:IEEE,2006.7725¡77298SchlacherK,ZehetleitnerK.AnalysisandDesignofNon-linearControlSystems.Berlin:Springer,2008.207¡2219ZouJ,FuX,YangHY.Activedisturbancerejectioncontrolforhydraulicwidthcontrolsystemforroughmill.JournalofZhejiangUniversity(ScienceA),2007,8(9):1429¡143410ChengG,PanSX.Adaptiveslidingmodecontrolofelectro-hydraulicsystemwithnonlinearunknownparameters.Con-trolEngineeringPractice,2008,16(11):1275¡128411GhazyMA.Variablestructurecontrolforelectro