feedback control-5

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1、TobuildatypicalelementbyusingOA-+R1kurR2uc-+CRucur-+R1urR2ucCTobuildinitialelement-+-+4.7k4.7k10kCRkurucUr(s)Uc(s)-+Tobuildatypical2ndordersystemk−Ur(s)Uc(s)-+-+4.7k4.7k10k10k-+RCR2CWhatif?-+-+4.7k4.7k10kR1-+R2C2C1k−Ur(s)Uc(s)3.9SignalFlowGraphsAsweknowthesystemistherelationshipofvariable

2、s.Byusingoftransferfunctionthevariablerelationshipoflinearsystemislinearalgebrarelation.Signalflowgraphisoneofbesttoolsforlinearalgebra3.9SignalFlowGraphsForalineardynamicsystemwheretheYj(s)isvariablewhileGij(s)istheTFofelementorsubsystem.effectcause3.9SignalFlowGraphscauseeffectInsignalf

3、lowgraph,junctionpointsornodesareusedtorepresentthevariables(signal).Brancheswitharrowareusedtorepresentelementsorsubsystem.3.9SignalFlowGraphsThegainofelementnormallyisputabovethebranch.Anexampleofsignalflowgrapha32(a)y2=a12y1+a32y3y3y4y5y2y1a12a23a32a43(b)y2=a12y1+a32y3,y3=a23y2+a43y4y3

4、y4y5y2y1a12a32(a)y2=a12y1+a32y3y3y4y5y2y1a12Anexampleofsignalflowgraph(c)y2=a12y1+a32y3,y3=a23y2+a43y4,y4=a24y2+a34y3+a44y4a34a44y3a24a23a32a43y4y5y2y1a12Anexampleofsignalflowgrapha34a25(d)Completesignalflowgrapha44y3a24a23a32a43y4y5y2y1a12a45SummaryofBasicrulesofSignalFlowGraph（1）Asignal

5、flowgraphappliesonlytolinearsystems.Theequationsbasedonwhichasignalflowgraphisdrawnmustbealgebraicequationsintheformofeffectsasfunctionsofcauses.Nodesareusedtorepresentvariables.Normally,thenodesarearrangedfromlefttoright,followingasuccessionofcausesandeffectsthroughthesystem.Signaltravel

6、alongbranchesonlyinthedirectiondescribedbythearrowsofbranches.Thebranchdirectingfromnodeyktoyj,representsthedependenceofthevariableyj,uponyk,butnotthereverse.Asignalyktravelingalongabranchbetweennodesykandyjismultipliedbythegainofthebranch,akj,sothatasignalakjykisdeliveredatnodeyj.Summary

7、ofBasicrulesofSignalFlowGraph（2）DefinitionforSignalFlowGraphs(1)Outputnode(sink).Anoutputnodeisanodewhichhasonlyincomingbranches.Inputnode(source).Aninputnodeisanodethathasonlyoutgoingbranches.a34a25y3a24a23y4y5y2y1a12Inputnodeoutputnodea45a44a43a32y51DefinitionforS