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AER509ControlSystems
Chapter5:SystemsimplificationReductionofmultiplesubsystemsBlockdiagramsandsignalflowgraphsMason’srule1AER509:RyersonUniversity
AER509:RyersonUniversity2
1.BlockdiagramsComponents3AER509:RyersonUniversity
Cascaded(series)subsystems??4AER509:RyersonUniversity
Parallelsubsystems5AER509:RyersonUniversity
Feedbackcontrolsystems6AER509:RyersonUniversity
Simplificationthroughleftandrightmoving7AER509:RyersonUniversityMultipliedbyGDividedbyG
ExamplesofsimplificationG2G3FFeedbackcontrol8AER509:RyersonUniversity
ExamplesofsimplificationRightmovingSimplifyingfeedbackRightmovingCollapseSummingjunctionsSimplifyingfeedback9AER509:RyersonUniversity
2.SignalflowgraphsComponentsBranchSystem(TF)NodeSignalInterconnectionRelationship(flow)?10AER509:RyersonUniversity
ThreetypesofcontrolsystemblocksCascadedsystemParallelsystemFeedbacksystem11AER509:RyersonUniversity
TransformingablockdiagramtoasignalflowgraphNodesignalSystemandconnectionSimplification12AER509:RyersonUniversity
3.Mason’sRuleWhatisthetransferfunctionofthissystem?Threeimportantconcepts:Loopgain,forwardpathgain,andnon-touchingloopgainLoopgain:Startsatanodeandendsatthesamenode,withoutpassingthroughanynodemorethanonce.Forwardpathgain:thegainsthroughapathfromtheinputnodetotheoutputnode.Non-touchingloopgain:thegainsfromthenon-touchingloopstaken2,3,4,andmore13AER509:RyersonUniversity
Mason’sRule14AER509:RyersonUniversity
Mason’sRuleapplicationLoopgain:Forwardpathgain:Non-touchingloopgain:15AER509:RyersonUniversity
Example5.76possiblecombinationsNocommonTF!!!4possiblecombinationsNoCommonTF!!!16AER509:RyersonUniversity
ApplyingManson’Rule17AER509:RyersonUniversity
AnotherexampleP.261.-12.-G43.-G3G44.-G2G3G46possiblecombinationsNocommonTF!!!1and2.G41and3.G3G44possiblecombinationsNocommonT
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