1ME451: Automatic ControlME451: Automatic ControlDr. Dr. JongeunJongeunChoiChoiDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringMichigan State UniversityMichigan State UniversityLecture 24Lecture 24Bode diagram of connected systemsBode diagram of connected systems2Course 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 &) laboratories3Sketching Bode plotSketching Bode plotBasic functionsBasic functionsConstant gainConstant gainDifferentiator and integratorDifferentiator and integratorDouble integratorDouble integratorFirst order system and its inverseFirst order system and its inverseSecond order systemSecond order systemTime delayTime delayProduct of basic functionsProduct of basic functions1.1.Sketch Bode plot of each factor, andSketch Bode plot of each factor, and2.2.Add the Bode plots graphically.Add the Bode plots graphically.Main advantage of Bode plot!Main advantage of Bode plot!4Bode plot of basic functions (review)Bode plot of basic functions (review)G(sG(s)=K)=K10-210-11001011021919. 52020. 52110-210-1100101102-1-0.500. 51G(sG(s)=s)=s10-210-1100101102-40-200204010-210-11001011028989.59090.5915Bode plot of basic functions (review)Bode plot of basic functions (review)G(sG(s)=1/(s*s))=1/(s*s)10-210-1100101102-100-5005010010-210-1100101102-181- 180.5-180- 179.5-179G(sG(s)=1/s)=1/s10-210-1100101102-40-200204010-210-1100101102-91-90. 5-90-89. 5-896Bode plot of basic functions (review)Bode plot of basic functions (review)G(sG(s)=1/(Ts+1))=1/(Ts+1)G(sG(s)=Ts+1)=Ts+110-210-1100101102-50-40-30-20-10010-210-1100101102-100-80-60-40-20010-210-11001011020102030405010-210-11001011020204060801001/T1/T1/T1/T7Bode plot of a 2nd order systemBode plot of a 2nd order system10-1100101-60-40-2002010-1100101-200-150-100-500resonanceresonanceResonant freq.Resonant freq.Peak gainPeak gain810-210-1100101102-1-0.500.5110-210-1100101102-6000-4000-20000Bode plot of a time delayBode plot of a time delayHuge phase lag!Huge phase lag!The phase lag causes instability of the closedThe phase lag causes instability of the closed--loop loop system, and thus, the difficulty in control.system, and thus, the difficulty in control.9An advantage of Bode plotAn advantage of Bode plotBode plot of a series connection GBode plot of a series connection G11(s)G(s)G22(s) is (s) is the addition of each Bode plot of Gthe addition of each Bode plot of G11and Gand G22..GainGainPhasePhaseWe use this property to design We use this property to design C(sC(s) so that ) so that G(s)C(sG(s)C(s) has a ) has a ““desireddesired””shape of Bode plot.shape of Bode plot.10Short proofsShort proofsUse polar representationUse polar representationThen,Then,Therefore,Therefore,11Sketch the Bode plot of a transfer functionSketch the Bode plot of a transfer function1.1.Decompose Decompose G(sG(s) into a product form:) into a product form:2.2.Sketch a Bode plot for each component on the Sketch a Bode plot for each component on the same graph.same graph.3.3.Add them all on both gain and phase plots.Add them all on both gain and phase plots.Example 1Example 112Example 1 (contExample 1 (cont’’d)d)dBdBdegdeg--202013Example 2Example 2dBdBdegdeg--202014Example 3Example 3dBdBdegdeg--2020--404015Example 4Example 4dBdBdegdeg+20+20--2020+45+45--4545--454516Example 5Example 5dBdBdegdeg+20+20--4040+45+45--4545--9090--202017Summary and exercisesSummary and exercisesSketching Bode plot Sketching Bode plot basic functionsbasic functionsconnections of basic functionsconnections of basic functionsExerciseExerciseRead Section 8.2 of the textbook.Read Section 8.2 of the textbook.18ExercisesExercisesSketch the Bode plot of:Sketch the Bode plot of:Find a transfer function having the gain plot:Find a transfer function having the gain
View Full Document
Unlocking...