热连轧液压活套系统非线性多变量建模及控制

3210201010JournalofUniversityofScienceandTechnologyBeijingVo.l32No.10Oct.2010李壮举1,2)石馨3)刘贺平1)杨卫东1)1),1000832),1000443),110034,,,,.,,(ESO).Lyapunov..;;;;;TP273ModellingandcontrolofhydraulicloopernonlinearmultivariablesystemsLIZhuangju1,2),SHIXin3),LIUHeping1),YANGWeidong1)1)SchoolofInformationEngineering,UniversityofScienceandTechnologyBeijing,Beijing100083,China2)SchoolofElectricandInformationEngineering,BeijingUniversityofCivilEngineeringandArchitecture,Beijing100044,China3)DepartmentofAvionicsEngineering,ShenyangAviationVocationalTechnicalCollege,Shenyang110034,ChinaABSTRACTInordertoimprovethecontrolaccuracyandqualityofautomaticgaugesinhottriprolling,anonlinearmultipleinputmultipleoutput(MIMO)modelofhydrauliclooperswasbuiltclosetotheworkingpointinconsiderationofstripweightandthenonlinearityofhydrauliccylindersandloopers,anditsvaliditywasverified.Adecouplingmethodbasedonbacksteppingandextendedstateobservers(ESO)wasproposedforthisnewmodeltakingallunmodelleddynamicsandvariousdisturbancesintoaccount.TherobuststabilityoftheclosedloopsystemwasprovedwiththeLyapunovstabilitytheory.Simulationresultsshowthattheproposedmodelanddecouplingcontrolmethodareavailable.KEYWORDShotrolling;hydrauliccontrolequipment;nonlinearsystems;modelling;decoupling;backstepping:20091117:(No.XK100080537):(1975),,;(1951),,,,Emai:[e-mail].,[1].,,[2].,,,.[23],,,,.,;,[1,45].,,,,,.,,,,32;,(ESO),;;,PID,.1,1.[2],,.,F33,.1Fig.1Schematicdiagramofloopersetandparametersbetweentheracks1:L;a;l1;l2;d;1;2;r;r;l;!;;∀;#;3;4.2212,Q.,[6].-10~10mA.,,.,,.2Fig.2Physicalmodelofhydraulicloopers[7](),,x!vT2/Ksp+xv/Ksp=i(1),T2,i,xv,Ksp.,,[8]dp1dt=∃gxvs(xv)ps-p1+s(-xv)p1-A1dydt-Cm(p1-p2)Vh1+A1ydp2dt=∃A2dydt+Cm(p1-p2)-gxvs(xv)p2+s(-xv)ps-p2Vh2+A2y(2),g=Cd%2&,s(x)=1,x∀00,x#0,Cm,∃,Cd,%1,&,A1A2,p1p2,ps,y,Vh1Vh2y=0().22#,[2],1M=Frcos∀,∀=!--#,y=2rsin(/2).,F,F=A1p1-A2p2(3),,,MMMWMD!1354!10::M=M+MW+MDMW=PLcosM=KBH[(lsin+r)(cos2-cos1)+lcos(sin1+sin2)](4),;P;KBH=Bh,B,h;1=arctanlsinx11-d+ra+lcosx11;2=arctanlsinx11-d+rL-a-lcosx11.,,ddt=%,d%dt=180J∋(M-M-MW).,J.d2dt2=180J∋(M-M-MW)(5),,,T1,ddt=ELdl1()d+dl2()dddt+4(1-∃4)-dv3dtT1+3(1+f3)(6),dl1()d=lcos(r-d-atan)(lsin+r-d)2+(a+rcos)2,dl2()d=lcos[r-d+(L-a)tan](lsin+r-d)2+(L-a-lcos)2.(1)~(4)(5),(6).X1=[x11,x12,x13,x14,x15]T=[,!,p1,p2,xv]T,X2=[x21,x22]T=[,3]T,W1(t)W2(t),,:x!11=x12x!12=f12+g12FF!=(A1g13+A2g14)x15-(A1f13+A2f14)x!15=-x15/T2+Kspi/T2+W1(t)x!21=EL-1[h(x11)x12+4(1-∃4)-x22(1+f3)]x!22=-x22/T1+3/T1+W2(t)(7),f12(x11,x21)=-180J∋{PLcosx11+KBHx21[(lsinx11+r)(cos2-cos1)+lcosx11(sin1+sin2)]},g12(x11)=180J∋rcos(!-x11-#),x!13=g13x15-f13,x!14=-g14x15+f14,g13=∃gx15[s(x15)ps-x13+s(-x15)x13]Vh1+2rA1sinx112,f13=∃rA1x12cosx112+Cm(x13-x14)Vh1+2rA1sinx112,g14=∃gx15[s(x15)x14+s(-xv)ps-x14]Vh2+2rA2sinx112,f14=∃rA2x12cosx112+Cm(x13-x14)Vh2+2rA2sinx112,h(x11)=lcosx11(r-d-atanx11)(lrsinx11-d)2+(a+lcosx11)2+lcosx11[r-d-(L-a)tanx11](lsinx11+r-d)2+(L-a-lcosx11)2.33#.:=26∃;=48MPa;E=21%105MPa;#=16∃,!=49∃;Ladlrr5519820270750138035m;f3=0082,J=048kN!m2;KBH=00136m2,3=3246m!s-1,4=4786m!s-1,P=8281N.:Vh1=12%10-3m3,Vh2=11%10-3m3,Cm=45%10-13m!s-1!Pa-1,∃=12%109Pa,%1=45%10-3m,&=900kg!m-3,Cd=06,A1=38%10-3m2,A2=35%10-3m2.,PI,3∃1MPa,[2],34.,,[2].!1355!323Fig.3Systemoutputswhenthesetvalueoflooperheightchanges,,,.,,56.5,(a),(b)4Fig.4Systemoutputswhenthesetvalueoftensionchanges.6,(a),(b).34(t#10s),1.,,,.5(a);(b)Fig.5Errorcurvesofthemodelwhenthesetvalueoflooperheightchanges:(a)errorcurvesoflooperheight;(b)errorcurvesoftension6(a);(b)Fig.6Errorcurvesofthemodelwhenthesetvalueoftensionchanges:(a)errorcurvesoftension;(b)errorcurvesoflooperheight1Table1Maximumerrorandmeansquareerrorofthemodelsintransitionprocess/(∃)/MPa[2][2]020058-006017000460069600011000874(7),,.,,,(ESO)!1356!10:,,.[9].1e11=y1d-x11,e!11=y!1d-x!11=y!1d-x12,e12=x12,d-x12,e!11=y!1d+e12-x12,d,x12,d=k11e11+y!1d,e!11=e12-k11e11.LyapunovV11=e211/2,V!11=-k11e211+e11e12.2eF=Fd-F,1,Fd=(e11+k12e12-x!12,d-f12)/g12,e!12=-e1-k12e12+g12eF.LyapunovV12=V11+e212/2,V!12=-k11e211-k12e212+g12e12eF.3,F!d,,,ESOF!d[1011].F!e!Fe!F=F!d-F!=F!d-[(A1g13+A2g14)x15-(A1f13+A2f14)](8)(8)ESO:z!F1=zF2-∃F1!(zF1-eF)-[(A1g13+A2g14)x15-(A1f13+A2f14)]z!F2=-∃F2!(zF1-eF)(9),∃F1∃F2ESO,ESOzF2F!d.(F2=zF2-F!d,x15,d=(zF2+k13eF+g12e12+A1f13+A2f14)/(A1g13+A2g14),e15=x15,d-x15,e!F=-g12e12-k13eF+(A1g13+A2g14)e15-(F2.LyapunovV13=V12+e2F/2,V!13=-k11e211-k12e212-k13e2F+(A1g13+A2g14)eFe15-(F2eF.4e15:e!15=x!15,d+(x15,d-e15)/T2-Kspi/T2-W1(t)(10)(10),ESOx!15,d-W1(t),.ESO:z!11=z12-z11/T2-∃11!(z11-e15)+x15,d/T2-Kspi/T2z!12=-∃12!(z11-e15)(11),∃11∃12ESO,ESOz12x!15,d-W1(t).(11=z11-e15,(12=z12-(x!15,d-W1(t))=z12+W1(t)-x!15,d,i=[x15,d-e15(T2k14+1)+T2(A1g13+A2g14)eF+T2z12]/Ksp(12)e!15=-(A1g13+A2g14)eF-k14e15-(12.LyapunovV14=V13+e215/2,V!14=-k11e211-k12e212-k13e2F-k14e214-(12e15-(F2eF..1e21=y2d-x!21,e22=x22,d-x22,x22,d=[L-1Ek21e21+hx12-4(1-∃4)]/1+f3,e!21=-L-1E(1+f3)e22-k21e21.LyapunovV21=e221/2,V!21=-L-1E(1+f3)e221e22-k21e221.2e22:e!22=x!22,d+(x22,d-e22)/T1-3/T1-W2(t)(13),(13)ESOW2(t):z!21=z12-z21/T1-∃21!(z21-e21)+x!22,d+x22,d/T1-3/T1z!22=-∃22!(z21-e21)(14),∃2