【硕士论文】工业包装线上开口容器内液体的晃动控制

IM.GrundiliusIIANSYS/FLOTRANIIIOptimalControlofLiquidSloshingofOpenContainersonaPackagingLineABSTRACTThispaperconsiderstheoptimalcontrolofliquidsloshofopencontainersinanindustrialpackagingmachine.Themovingtimeandtheoscillationnaturalfrequency,twofactorsofliquidslosh,areinvestigated.Theconditioninwhatlinearmodelsuitstheproblemisgiven.Andonewaytomodifythelinearmodelisemployedandtested.Themostadvanceddetailedmodelisdescribedbyasetofthreedimensionalnonlinearpartialdifferentialequations.Forsuchmodelsarehardtouseincontrollerdesign,theapproximatelinearmodelissetinthispaper.Thestateequationsoflinearliquidfilledcontrolsystemareestablishedforrespectiverectangulartank,circularcylindrictankandarbitraryaxisymmetrictank.Basedonminimum-energyoptimization,theaccelerationprofileisobtained.Therelationshipbetweenthemovementtimestepandthesurfaceelevationiscalculated.Andthatonebetweentheoscillationnaturalfrequencyandthesurfaceelevationisobtainedtoo.Forthenonlineareffectisignoredinthelinearmodel,theerrorexistsinevitably.Thewaytomodifythelinearmodeliscalled.ThenumericalsimulationexperimentismadeforliquidinrectangularIVcontainerwhichistreatedasanonlinearsystemunderacertaincontrol.Thetheoreticalresultandthesimulativeonearecomparedandtheeffectofresidueenergyofliquidsloshafteronecycleofmovementisstudied.Atlastthewaytomodifytheaccelerationprofileisgivenandcertifiedefficiently.Keywords:Liquidslosh,Optimalcontrol,ANSYS/FLOTRAN[10]Moiseev[11,12]AbramsonJ.W.Miles[18][1521]MAC[29]VOF[28]ALE3[37]FEM[8]BEM[9][36]FEMBEMMACVOFALEVOFALE[35]MattiasGrundelius[1]1.2MattiasGrundelius[1]MattiasMattias′′′2.22.2[439]OxyrO′y′x′7⎪⎪⎪⎩⎪⎪⎪⎨⎧∂=⋅++∂∂∂=∂∂∂∂∂=∂∂=∇fwfVgtVnVtnV,0,0,,002razjjzjj2.1.12.1.1Ritz()()()()()()∑∑=Φ=kkkkkktqxxxHtxxxtqxxxtxxx321321321321,,,,,,,,,,zj&2.1.2()321,,xxxkΦ),,(321xxxHk00=a⎪⎪⎪⎩⎪⎪⎪⎨⎧∂=+∂∂∂=∂∂∂∂∂=∂∂=∇fwfVgtVnVtnV,0,0,,02zjjzjj2.1.3()()()()tixxxHtixxxiwzwwjexp,,,exp,,321321=Φ=2.1.4w1ah()()(){}()(){}fwfVVVyaxyxVhyaxyxV∂∂=∂=∈=∂-∈∈=\0,,0,0,,,0,2.1.52.1.32.1.42.1.58()axkahkakHhyakaxkahkagkpppppppwcossinhcoshcostanh=+=Φ=2.1.62.1.62.1.222.3ah()(){}()(){}fwfVVVzarzrVhzarzrV∂∂=∂=∈=∂-∈∈=\0,,0,,0,),,0(,,qq2.1.72.1.32.1.42.1.7qxxxqxxxxwmaharJaHmahzarJahagmkmkmmkmkmkmkmmkmkmkmkcossinh)(coscosh)(tanh=⎟⎠⎞⎜⎝⎛+=Φ=2.1.8)(xJmmBesselmkx0)(=′xJm2.1.82.1.2Oyzrqx92.22.1.22.1.1()()()()0,2=⋅++Φ∑ra0kkkkktqtqyxw&&2.2.12.2.1nHrfV∂()L&&,2,1002==⋅++nqqnnnnnaawm2.2.2∫∫∂∂=Φ=ffVnnVnnndSHdSHrarrm,2.1.2()()tqxH11=z()tqH1max,1max=z⎟⎠⎞⎜⎝⎛=axahaHpppcossinhmaxmax,12.2.20011max,1max2max=⋅++aamzwzH&&2.2.31m1a2.211()()()0201021101212max2maxmax=+++∫∫adxxxJdxxJxJgaxxxwxwxhx&&&a1JBesselx()01=′xJ⎟⎠⎞⎜⎝⎛=ahagxxwtanh0837.0202max2maxmax=+++agawxwxhx&&&(2.2.7)()tagaxxxxxxxx043214321010/837.001000000000002⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛-+⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡--=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛wwwhw&&&&(2.2.8)()tagaxxxxxxxx043214321010/01000000000002⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛-+⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡--=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛wbwwhw&&&&(2.2.9)ab()()∫∫ΦΦΦ±=10211012max1dxaxxdxaxxb()T4321xxxx=x2.2.62.2.82.2.9120aBAxx+=&(2.2.10)0a2.31()2max0m/s81.9=≤ata2()m035.0max2=≤ztx3()[]T00000=x4()[]T000LT=xm2=LTTGrundelius122()()()()∫+=TdttRatt020T21QxxJ(2.3.1)()[]T00000=x()[]T000LT=xHamilton()()0T20T21aRaBAxQxxH+++=lEuler-Lagrange1300=∂∂∂∂-=∂∂=aHHHxxll&&⎪⎪⎩⎪⎪⎨⎧-=--=+=lllT0T01BAQxBAxxRaa&&(2.3.2)(2.3.2)0a⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡---=⎥⎦⎤⎢⎣⎡llxAQBBAxM444344421&&TT1R(2.3.3)(2.3.3)()()()()()()()⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡000022211211lllxxxFFFFFttt(2.3.4)()tetM=F3(2.3.4)()()()()()()002212lllttttFF==x(2.3.5)4()()()TTx1120-=Fl(2.3.6)(2.3.5)()tl(2.3.6)(2.3.2)()()()()TTtRtaxB11222T01--=FF(2.3.7)[1]m07.0=am.2.0=h0.44s0.46sm2.0=L0=h(2.3.1)1=R0=Q(2.3.7)2.42.4152.52.52-1sm2s/m0.300.063533.860.350.047816.370.390.03919.8380.4140.03497.5370.460.02815.0730.500.02284.2040.550.01753.9740.600.01533.9400.700.01392.7220.800.01041.703162-10.30.40.50.60.70.80.010.020.030.040.050.060.07Surfaceelevation(m)tuningtimeofmotion(s)2.60.30.40.50.60.70.805101520253035Maximumacceleration(m/s2)tuningtimeofmotion(s)2.7172.622.71sT414.0≥2sT39.0≥10.414s2-20.414sw2-2wah(1s-)m2s/m14.330.150.200.070920.817.550.100.200.048712.018.500.090.200.044210.419.620.080.200.03968.8920.980.070.200.03497.5422.660.060.200.02996.4924.820.050.200.02416.0927.750.040.200.01776.9632.040.030.200.01508.6539.250.020.200.01146.47181020304050600.000.010.020.030.040.050.060.070.08Surfaceelevation(m)Frequence(s-1)2.82.82.80.07m0.05m29%19FLUENTCFDMSC/DYTRANANSYS/FLOTRANFLUENTCFDDYTRANANSYSANSYS/FLOTRANANSYS/FLOTRANANSYS/FLOTRAN3.1ANSYS/FLOTRANAnsysAnsys20AnsysAnsysFlotran3.1.1AnsysSolutionFlotranAnsysPOST1POST26Ansys213.1.2FlotranALEVOFVOFVOFFF1F0F01VOFALELagrangeEulerLagrangeEulerLagrangeLagrangeLagrangeEulerVOFEulerEuler1974HirtCWLagrangeEulerALEEulerLagrangeAnsysFlotran223.1.3FlotranAnsysFlotranFLUID141FLUID142FLUID141FLUID1423.1.4FlotranAnsysFlotran1Jobname.RFL2Jobname.PFL3Jobname.RSWYPlus4Jobname.RDF235Jobname.DBG6Jobname.RFO7Jobname.CFDFlotranAns