Fall 2008 1ME451: Control SystemsME451: Control SystemsDr. Dr. JongeunJongeunChoiChoiDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringMichigan State UniversityMichigan State UniversityLecture 6Lecture 6Block diagramsBlock diagramsFall 2008 2Course 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 &) laboratoriesFall 2008 3Transfer function (review)Transfer function (review)A transfer function is defined byA transfer function is defined byA system is assumed to be at rest. (Zero initial A system is assumed to be at rest. (Zero initial condition)condition)Laplace transform of system outputLaplace transform of system outputLaplace transform of system inputLaplace transform of system inputFall 2008 4Impulse response (review)Impulse response (review)Suppose that Suppose that u(tu(t) is the unit impulse function ) is the unit impulse function and system is at rest.and system is at rest.The output The output g(tg(t) for the unit impulse input is called ) for the unit impulse input is called impulse responseimpulse response..Since Since U(sU(s)=1, the transfer function can also be )=1, the transfer function can also be defined as the defined as the Laplace transform of impulse Laplace transform of impulse responseresponse::SystemSystemFall 2008 5Elementary TF block diagramsElementary TF block diagramsSeries connectionSeries connectionFall 2008 6Elementary TF block diagramsElementary TF block diagramsSumming JunctionSumming Junction+-Fall 2008 7Elementary TF block diagramsElementary TF block diagramsParallel connectionParallel connectionFall 2008 8Feedback connectionFeedback connectionNegativeNegativefeedback systemfeedback systemEEaaBe careful when computing transfer functions Be careful when computing transfer functions from outside to inside the feedback!from outside to inside the feedback!Fall 2008 9Feedback loop Feedback loop formula,TFformula,TFRR→→YYFFgg: Forward gain from : Forward gain from R(sR(s) to ) to Y(sY(s) ) G(sG(s))LLgg: Loop gain:: Loop gain:G(s)K(s)(G(s)K(s)(--1) 1) EEaaThe loop gain is the product of all transfer functions that form the loopFall 2008 10Feedback loop Feedback loop formula,TFformula,TFRR→→EEFFgg: Forward gain from : Forward gain from R(sR(s) to ) to E(sE(s) ) 11LLgg: Loop gain:: Loop gain:G(s)K(s)(G(s)K(s)(--1) 1) EEaaFall 2008 11ExercisesExercisesFall 2008 12Summary and ExercisesSummary and ExercisesBlock diagramsBlock diagramsElementary diagramsElementary diagramsFeedback connectionsFeedback connectionsNextNextLinearizationLinearizationExercisesExercisesObtain Obtain TFsTFsfrom R to Y on the previous page.from R to Y on the previous page.Obtain Obtain TFsTFsfrom input F to outputs xfrom input F to outputs x11and xand x22for the for the quarter car problem in terms of Gquarter car problem in terms of G11, G, G22, and G, and
View Full Document
Unlocking...