1ME451: Control SystemsME451: Control SystemsDr. Dr. JongeunJongeunChoiChoiDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringMichigan State UniversityMichigan State UniversityLecture 8Lecture 8Modeling of DC motorsModeling of DC motors2Course roadmapCourse roadmapLaplace transformLaplace transformTransfer functionTransfer functionModels for systemsModels for systems••electricalelectrical••mechanicalmechanical••electromechanicalelectromechanicalBlock diagramsBlock diagramsLinearizationLinearizationModelingModelingAnalysisAnalysisDesignDesignTime responseTime response••TransientTransient••Steady stateSteady stateFrequency responseFrequency response••Bode plotBode plotStabilityStability••RouthRouth--HurwitzHurwitz••NyquistNyquistDesign specsDesign specsRoot locusRoot locusFrequency domainFrequency domainPID & LeadPID & Lead--laglagDesign examplesDesign examples((MatlabMatlabsimulations &) laboratoriessimulations &) laboratories3What is DC motor?What is DC motor?An actuator, converting electrical energy into An actuator, converting electrical energy into rotational mechanical energyrotational mechanical energy(You will see DC motor during Lab 1 and 4.)(You will see DC motor during Lab 1 and 4.)4Why DC motor?Why DC motor?Advantages: Advantages: high torquehigh torquespeed controllabilityspeed controllabilityportability, etc.portability, etc.Widely used in control applications: robot, tape Widely used in control applications: robot, tape drives, printers, machine tool industries, radar drives, printers, machine tool industries, radar tracking system, etc.tracking system, etc.Used for moving loads whenUsed for moving loads whenRapid (microseconds) response is not requiredRapid (microseconds) response is not requiredRelatively low power is requiredRelatively low power is required5How does DC motor work?How does DC motor work?ArmatureArmature(from Dorf and Bishop book)6Model of DC motorModel of DC motoreeaa(t(t))iiaa(t(t))RRaaLLaaeebb(t(t))JBBmmArmature circuitArmature circuitMechanical loadMechanical loadInputInputOutputOutput7Armature circuitArmature circuitConnection between mechanical/electrical partsConnection between mechanical/electrical partsMotor torqueMotor torqueBack EMFBack EMFMechanical loadMechanical loadAngular positionAngular positionModeling of DC motor: time domainModeling of DC motor: time domainLoad torqueLoad torque8Armature circuitArmature circuitConnection between mechanical/electrical partsConnection between mechanical/electrical partsMotor torqueMotor torqueBack EMFBack EMFMechanical loadMechanical loadAngular positionAngular positionModeling of DC motor: sModeling of DC motor: s--domaindomain9DC motor: Block diagramDC motor: Block diagramFeedback systemFeedback systemTachometer Tachometer (Page 46)(Page 46)Encoder Encoder (Page 44)(Page 44)10Useful formula for feedbackUseful formula for feedbackNegative feedback systemNegative feedback systemEEaaMemorize this!Memorize this!11Ex: Derivation of transfer functionsEx: Derivation of transfer functionsEEaaEEaaCompute transfer functions from Compute transfer functions from R(sR(s) to ) to Y(sY(s).).EEaaEEaa12DC motor: Transfer functions (TF)DC motor: Transfer functions (TF)22ndndorder systemorder system13DC motor: Transfer functions (contDC motor: Transfer functions (cont’’d)d)Note:Note:In many cases La<<Ra. Then, an In many cases La<<Ra. Then, an approximated TF is obtained by setting La=0.approximated TF is obtained by setting La=0.11ststorder systemorder system22ndndorder systemorder system14Summary and ExercisesSummary and ExercisesModeling of DC motorModeling of DC motorWhat is DC motor and how does it work?What is DC motor and how does it work?Derivation of a transfer functionDerivation of a transfer functionBlock diagram with feedbackBlock diagram with feedbackNextNextStabilityStabilityof linear control systems, one of the most of linear control systems, one of the most important topics in feedback controlimportant topics in feedback controlExercisesExercisesGo over the derivation for DC motor transfer functions Go over the derivation for DC motor transfer functions by yourself. Obtain by yourself. Obtain T(s)/ET(s)/Eaa(s(s).).15Main message until this pointMain message until this pointMany systems Many systems can be represented can be represented as as transfer functionstransfer functions!!Using the transfer functions, Using the transfer functions, ……. . (to be continued)(to be
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