过控第一次作业

东南大学自动化学院过程控制第一次作业08012401刘亚楠08012406刘慧08012411沈霈霖08012421汪玉杰08012426杨永恒08012431曹起鸣08012436陈颖Astreamcontainsawastechemical,W,withaconcentrationof1mol/liter.TomeetEnvironmentalProtectionAgencyandstatestandards,atleast90%ofthechemicalmustberemovedbyreaction.Thechemicaldecomposesbyasecond-orderreactionwitharateconstantof1.5liter/(molhr.).Thestreamflowrateis100liter/hourandtwoavailablereactors(400and2000liters)havebeenplacedinseries(thesmallerreactorisplacedbeforethelargeone).Question:a.Writethemodelingequationsfortheconcentrationofthewastechemical.Assumeconstantvolumeandconstantdensity.LetCw1=concentrationinreactor1,mol/literCw2=concentrationinreactor2,mol/literF=volumetricflowrate,liter/hr.V1=liquidvolumeinreactor1,litersV2=liquidvolumeinreactor2,litersK=second–orderrateconstant,liter/(molhr.)solutionAsthechemicaldecomposesbyasecond-orderreactionwiththerateofK,Wecaneasilygettheequationbelowbyimitatingtheexampleinthisbookbefore:b.Showthatthesteady-stateconcentrationsare0.33333mol/liter(reactor1)and0.09005mol/liter(reactor2),sothespecificationismet.(Hint:Youneedtosolvequadraticaquaticequationstoobtaintheconcentrations.)solutionWhenitcomestothesteady-state,It’snecessarytomeettheconditionsbelow:SowithFin=100liter/hourCWin=1mol/literandV1=400liters,CWin=1mol/liter.SolutetheequationCW1=0.33333mol/liter.Andwith,wecangetthesolutionCW2=0.09005mol/litec.Linearizeatsteadystateanddevelopthestatespacemodel(analytical)oftheformWhere，solutiond.ShowthattheAandBmatricesare，(Also,showtheunitsassociatedwitheachcoefficient).solutionFromtheresultofC,wecanknowthat,.e.Assumingthateachstateisanoutput,showthattheCandDmatricesare，solutioneachstateisanoutput,uisnotcontained.,f.FindtheeigenvaluesofusingtheMATLABeigfunction,andfindtheeigenvaluesbyhand,bysolvingdet()=0.solution，UsingMATLAB,andwecangettheanswer:Theeigenvaluesare-0.3201and-1.2500.g.Solveforthenonlineardifferentialequations,usingode45.Comparethelinearandnonlinearvariablesonthesameplots(makecertainyoucovertfromdeviationtophysicalvariablesforthelinearresults)forastepchangeintheflowratefrom100liters/hourto110liters/hour.Assumetheinitialconcentrationsarethesteady-statevalues(0.3333and0.09005).Comparethelinearandnonlinearresponsesofthereactorconcentrations.Istheremovalspecificationstillobtained?solutionUsingthesamemethodabove,whenF=110liters/hour,werecalculatethematrixAandB:Andthesteadystateofandis:,sotheremovalspecificationisstillobtained.Thecurveof:Thecurveof:Matlabcode:%Linear.mfunctiondcw=Linear(t,cw)dcw=zeros(2,1);A=[-1.313630;0.055-0.34246];B=[0.0016340.275;0.00012520];x=[cw(1)-0.34621;cw(2)-0.09582];u=[0;0];dcw=A*x+B*u;end%Non_linear.mfunctiondcw=Non_linear(t,cw)dcw=zeros(2,1);dcw(1)=-1.5*cw(1)*cw(1)+(1-cw(1))*110/400;dcw(2)=-1.5*cw(2)*cw(2)+(cw(1)-cw(2))*110/2000;end%Main.m[tcw1]=ode45('Linear',[030],[0.33330.09005]);[tcw2]=ode45('Non_linear',[030],[0.33330.09005]);figure('NumberTitle','off','Name','Cw1');plot(t,cw1(:,1),'r',t,cw2(:,1),'b');gridon;legend('linear','non-linear');xlabel('t');ylabel('Cw1');figure('NumberTitle','off','Name','Cw2');plot(t,cw1(:,2),'r',t,cw2(:,2),'b');gridon;legend('linear','non-linear');xlabel('t');ylabel('Cw2');h.Wouldbettersteady-stateremovalofWbeobtainediftheorderofthereactionvesselswasreversed?Whyorwhynot?(Showyourcalculations.)solutionNomattertheorderofvessels.Thetwoequationsaresame:ButherewechangeV1into2000litersandV2into400liters(becauseof