热连轧精轧机组负荷分配的优化算法

13120012JOURNALOFIRONANDSTEELRESEARCHVol.13,No.1Feb.2001:(19712),,,;:1999211226;:2000203215,,,,(,110006):,,,:;;;:TG335.5:A:100120963(2001)0120026204OptimizingAlgorithmofPassScheduleforFinisherLUCheng,ZHAOQi2lin,LIULi2zhong,LIUXiang2hua,WANGGuo2dong(NortheasternUniversity,Shenyang110006,China)Abstract:Thepassscheduleoffinisherwasoptimizedonthebasisofproportionalpowerratio.Thenonlinearequationsinwhichunknownparametersaregaugesbetweenstandswasobtained.Anewmethod(BalanceIterationMethod)wasputforwardtosolvetheequations.Thecalculationofde2rivativeandinversematrixwasvoided.Keywords:finisher;passschedule;optimization;balanceiterationmethod,,,[1],,;[2],,,;[3],,Newton2Raphson,,,,,Newton2Raphson,,11.1[1],:F=B1kfmBR(H-h)Qpnt(1)F;B1;kfm;B;R;H;h;Qp;ntnt=1-0.7Sb+0.3Sfkfm(2)62Sb;Sf1.2[4],:R=1+C0FB(H-h)R(3)C0=16(1-T20)PE0(4)R;T0;E01.3[4],:M=B2FR(H-h)RR+RB(SbH-Sfh)(5)M;B21.4[1],:P=B3KvRRM(6)P;B3;K;vR2h0hn(n),(h1hn-1),,,:P1P2Pn=P1maxP2maxPnmax=A1A2An(7)P1,P2,Pn1,2,n;P1max,P2max,Pnmax1,2,n;n;A1,A2,An1,2,n,,,(7):A2P1-A1P2=0A3P2-A2P3=0AnPn-1-An-1Pn=0(8)(8)n-1j(j=1,2,,n)Pjhjhj-1,(8)(h1hn-1),n-1,,,,,,,13[(8)]Newton21Fig.1Flowchartofoptimzingpassschedule721:2Raphson,,,,:h(k+1)1=h(k)1A2P(k)1A1P(k)2m1h(k+1)2=h(k)2A3P(k)2A2P(k)3m2h(k+1)n-1=h(k)n-1AnP(k)n-1An-1P(k)nmn-1(9)h(k+1)1h(k+1)2h(k+1)n-1k+1h1h2hn-1;h(k)1h(k)2h(k)n-1kh1h2hn-1;P(k)1P(k)2P(k)nkP1P2Pn;m1m2mn-112n-1(9):h(k+1)i=h(k)iw(k)i(10)w(k)i=Ai+1P(k)iAiP(k)i+1mi(11)i,i=1,2,,n-1;w(k)ikikAi+1P(k)iAiP(k)i+1,w(k)i1,h(k+1)ih(k)iPihi,Pi+1hi,P(k+1)iP(k)i,P(k+1)i+1P(k)i+1wi,1w(k+1)iw(k)i,wi1,Ai+1Pi-AiPi+1=0,[(8)]kAi+1P(k)iAiP(k)i+1,,wi1,,(8):S(k)=2n-1i=1Ai+1P(k)iAiP(k)i+1-12n-1E1(12)S(k)k;E14,45.56mm1278mm5.48mm1278mm,880,1,2,323,,1Table1ParametersofdeviceF1F2F3F4F5F6F7ömmökW785100008101000083010000695100007109000725900075050002Table2ActualpassscheduleF1F2F3F4F5F6F7ömmö%ökNökNmökW45.5639.2166661176453827.7034.914981790406818.0430.513319522384512.5426.11058831836489.2620.9904818929157.3314.8730512821606.2412.2672211515890.4540.4070.3850.3650.3240.2400.318822001133Table3OptimizedpassscheduleF1F2F3F4F5F6F7ömmö%ökNökNmökW45.5635.414727987358929.4233.514184754358519.5630.313029529358213.6326.510737338357910.0222.5983122232177.7718.9949319232166.3013.1725412917860.3590.3590.3580.3580.3570.3570.3575,,Newton2Raphson,,,,:[1].[M].:,1979.[2]FumioYamada,KunioSekiguchi,MasashiTsugeno.HotStripMillMathematicalModelsandSet2UpCalculation[J].IEEETransactionsonIndustryApplications,1991,27(1):1312138.[3],,.ŠÓɄӱ™™‘˜ÆË[J]..1996,37(11):120721212.[4],.[M].:,1990.921:2