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1、ModelingandsimulationofsystemsusingMATLABandSimulinkChapter2ProblemSituationProblemDefinitionDirectExperimentationModelBuildingModelSimulationAnalysisDecisionMakingModelBuildingStep–1ObservetherealsystemanditsinteractionsbetweencomponentsCollectdataonitsbehavior.Consulttotheexpertsford

2、etailedknowledge.Asmodeldevelopmentproceeds,newquestionsmayraiseandmodeldeveloperwillreturntothisstep.ContinuousSystemSimulation(WaterReservoirSystem)ReservoirRiverInflowDirectRainfallSeepagelossEvaporationlossSupplytomeetdemandProblemDefinitionDeterminethevolumeofwaterstoredintherese

3、rvoir,sothatitwillnotspilloverornoshortageinsummer.Seepagelossisfunctionofvolume.Seepageloss=f(Volume)Evaporationlossisfunctionofareaofexposedsurfaceandcoefficientofevaporation.-Evaporationloss=f(SurfaceArea,Cevap)Thestatevariableisthevolumewhichchangeswithtime.ModelSimulationtime=100y

4、ears(1200months)Stepsize=1monthCalculatetotalinputVin=Rain+RiverFlowGrossVolume=Vin+EarlierVolumeTotalloss=Seepage+EvaporationNetVolume=GrossVolume–TotalLossIfDemand>=NetVolumeThenReservoirisdryandshortageofwater(=Dem-Vnet)OtherwiseDiff=Demand–VnetIfDiff>CapThenSpillover.AChemicalReact

5、orInacertainchemicalreactionsubstancesAandBproducethirdchemicalsubstanceC.A(1gm)+B(1gm)C(2gm)RateofformationofCproportionaltoamountsofAandB(Forwardreaction).RateofCDecompositionofCisproportionaltoamountofCpresentinthemixer(Backwardreaction).ModelDifferentialEquationsda/dt=K2c–K1abdb/dt

6、=K2c–K1abdc/dt=2K1ab–2K2cInitialconditionsK1,K2,a,baregiven.c=0,t=0,choosesuitablevalueofdt.Usesomeintegrationtechniquetogetthetimeprofileofa,bandc.SelectionofIntegrationMethodEuler’smethodSimplestmethodofintegrationVnew=Vold+dt*dv/dt.Thismethodisrarelyusedbecauseofrapidaccumulationofe

7、rrorandalsonotverystable.RungeKuttamethodVnew=Vold+K2whereK2=dt*f(tn+0.5dt,V+0.5k1)K1=dt*f(tn,V)FourthOrderRungaKuttaMethodVnew=Vold+K1/6+K2/3+K3/3+K4/6whereK1=dt*f(tn,V)K2=dt*f(tn+0.5dt,V+0.5K1)K3=dt*f(tn+0.5dt,V+0.5K2)K4=dt*f(tn+dt,V+K3)Simpson’sRuleOne-ThirdRuleV=dt*(K1+4K2+K3)/3w