物流系统三色Petri网建模与分析

200322:100026788(2003)0220073207Petri,(,250061):,PetriLPetri,PetriLPetri,LPetriL:;Petri;;;:N945.12:AThreeColoursPetriNetBasedModelingandAnalyzingofPerformancesforMaterialFlowSystemsLIQi2qiang,JIALei(SchoolofControlScienceandEngineering,ShandongUniversity,Ji’nan250061,China)Abstract:AimedatsomecharacteristicsofmaterialflowsystemsweproposethreecoloursPetrinet,presentthedefinitionofthePetrinet,analyzeitssomeperformances,andintroducesomecorrespondingmodelingmethods.BasedonthethreecoloursPetrinetwemodelthematerialflowcontrolofautomatedsortingsystem,andanalyzethecoherence,liveness,boundednessandsafenessofthesystem.Theprac2ticalapplicationdemonstratesthevalidityofthethreecoloursPetrinet.Keywords:materialflow;Petrinet;status;entity;information:2001209206:863(2001AA413420);(Z2000G1);(9901):(1964-),,L;(1959-),,,1L,,,L,LLPetri,[1-3]LPetri,L1962CarlA.PetriPetri,Petri[4]LPetriPetri,PetriPetriPetriPetri,,LPetri[5,6],MILP[7][8]LPetri,,,LMILP,,,L,L,Petri©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.L,PetriL2PetriPetriZ=(P,T,I,O,m0),,P,T,I:PTN(),O:PTN(),m0P,N={0,1,2,3,...}ZPetri,ZPetriZ2.1Petri1PetriZ=(P,T,A,M,I,O,S,m0),1)P={P1,P2,,Pn},ZûPû=nE1ZPi1(a)Za2;b2;c2;d2;e2;f2;g2;h2;i2;j21Petri2)T={t1,t2,,tq},Si(i=1,2,,q)ZûTû=qE1Zti1(b)Z3)A=AUASAIAFANZAU;AS;AI;AF;ANZûAû1Z1(c),(d),(e),(f),(g)Z4)M=MUMSMI,M;MU;MS;MIZûMû=ûPû=nE1Z1(h),(i),(j)Z5)I:PATN()ZN=0,1,2,ZûIûE1,Z6)O:TAPN()ZN=0,1,2,ZûOûE1,Z7)S={S1,S2,,Sq}ZûSû=ûTû=qE1Z8)m0PZûm0û=ûPû=nE1Z22.22PetriZ,,Z2t1Z2.33PetriZ,,Z2t2ZPetri,PetriZZ,PetriZ4720032©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2.44PetriZ,Z2P1P6Z2.55PetriZ,Z2P2P4Z32.66PetriZ,Z2P3P5Z2.77PetriZ,Z3P8P9Z2.88PetriZ,Z3P12Z2.99PetriZ,,,,Z3P8,t3,P10,t4,P11,t5,P12,P9,t3,P10,t4,P11,t5,P12Z2.1010PetriZ,,,,Z3t3,P10,t4,P11,P11t3Z3Petri1PetriZ,,ZZ2AFAN,,I(Pi,AF,tj)=0I(Pi,AN,tj)=0,Z,,;,,Z3ZAK=AFAN,I(Pi,Ak,tj)=0Z3PetriZ,1,6ASI(Pi,AS,tj)F1,6AsO(tj,AS,Pi)F1;1,6AII(Pi,AI,tj)F1,6AIO(tj,AI,Pi)F1Z4PetriZ,2,6A=ASAII(Pi,A,tj)F2;2,6A=ASAIO(tj,A,Pj)F2Z5PetriZ,MM,572Petri©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,MM,,Z6PetriZ,Petri,,M(Pi)FNZ,PiP,NZ,ZNZ=1,Z1PetriZ,,6iI(Pi,A,tj)=16kO(tj,A,Pk)=2,2Z2PetriZ,,6iI(Pi,A,tj)=26kO(tj,A,tk)=1,2Z3PetriZ,,MU(Pi)FN,MS(Pi)=0,MI(Pi)=0,N=0,1,2,,2Z4PetriZ,,,MS(Pi)Mi(Pi),2Z5PetriZ,tj,Z,M(Pi)E1,6iI(Pi,A,tj)E16kO(tj,A,Pk)E1Z1,,,,,;,Z{tj,tj+1,,tj+n},{Pi,Pi+1,,Pi+m},Z23,6AI(Pi,A,tj)F1,6AO(tj,A,Pi)F1{tj,tj+1,,tj+n},SjESj+1ESj+n,M(Pi+m)=0,M(Pk)F1,k=i,i+1,,i+m-1ZM(Pi+m)FL,,tj,M(Pk)FL,k=i,i+1,,i+mZM(Pk)FL,k=i,i+1,,i+m,ZZ1,,,,;,Z{t1,t2,,tr},{P1,P2,,Pn},{tj,tj+1,,tj+q}{Pi,Pi+1,,Pi+m},,,1,M(Pk)FL,k=i,i+1,,i+m,Pi,M(Pk)FL,k=1,2,,n,ZZ44.1PetriZ[9],4Z6720032©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.4Z,Z(),Z,,,Z,,Z,,Z,Z,()Z()Z,PLCLPLC,,,,,[9]Z,:,ZZ4.2Petri(P)(T)(A)Z(I,O)(M,m0)(S)ZZ,Z,,Z,2319Z3,6,14Z:4.2.1P1;P2;P8Z4.2.2P3;P4;P5;P6,,;P7;P9Z4.2.3P10;P11;P12;P13;P14;P15PLC;P16PLC;P17;P18;P19;P20;P21;P22;P23Z4.2.4t1,S1=2;t2,S2=1;t3,S3=1;t4,S4=1;t5772Petri©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,S5=1;t6,,S6=3;t7,S7=0;t8,S8=0;t9,S9=0;t10,S10=0;t11,,S11=0;t12,S12=0;t13PLC,S13=0;t14PLC,S14=0;t15,S15=0.1;t16,S16=0.1;t17,S17=0.5;t18,S18=0.5;t19,S19=0.8Z4.3Petri,5PetriZ5Petri4.4Petri1.5,PetriPetri,,,,Z2.,,,Z5Petri5.15P1,P17P18,P8,P9,P21,P22P23,Z5,P7,P10,P11,P12,P16,P19,P20,ZPetri,Z,1FM(P1)FL,M(Pk)=0,k=2,3,,23,LZP4t1,S1S2=S3,1,M(Pi)F1,i={2,3,4}ZP6t4,S4=S5,1,M(Pj)F1,j={5,6}ZP15t11,1,M(Pk)F1,k={13,14,15}Zt10,I(P11,AI,t10)=1,M(P11)F1Zt11P6,t2M(P3)=M(P11)=1,M(Pi)+M(Pj)=2,i={2,3,4},j={5,6},M(P12)=2,M(P12)F2ZP7t6t9,t6t9,S6S9,M(P7)F1Z8720032©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.P10P16P17,t15t16t7t8,M(Pl)F1,l={10,16,19,20}Z,M(P12)F2,M(Pi)F1,i{1,2,8,9},ZM(P12)F2,Z,P6t1,P6t4P4t2,Z5.2,,,,Z,:1);2),M(P7)F1;3)ZZ,,P6t4,M(P7)F1Z,t1;Z5.35,t2,t4,t6,t11t14,5Zt2,t4t11t6t14Zt6,t14Z,t6Zt6,PLCZ,,Z6PetriPetri,L,,L,,,LPetriLPetriL:[1]ZurawskiR,ZhouMC.Petrinetsandindustrialapplication:atutorial[J].IEEETransIndustrialElectronics,1994,41(6):567-583.[2]PetersonJL.PetriNetTheoryandtheModelingofSystems[M].EnglewoodCliffs,NJ:Prentice2Hall,1981.[3].Petri[J].,1990,(1):29-37.[4]DavidR,AllaH.Petrinetsformodelingdynamicsystems-asurvey[J].Automatic,1994,30(2):175-202.[5],.Petri[J].,1998,18(11):87-91.[6],,.CIMSPetriMSPN[J].,2001,(1):15.[7],,,.[J].,2000,18(6):18-22.[8],.MIS[J].,2000,21(7):767-769.[9],.[J].,1993,21(5):293-295.972Petri©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.