Fall 2008 1ME451: Control SystemsME451: Control SystemsDr. Dr. JongeunJongeunChoiChoiDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringMichigan State UniversityMichigan State UniversityLecture 23Lecture 23Bode diagram of simple systemsBode diagram of simple systemsFall 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 3Frequency response (review)Frequency response (review)Steady state output Steady state output FrequencyFrequencyis same as the input frequencyis same as the input frequencyAmplitudeAmplitudeis that of input (A) multiplied byis that of input (A) multiplied byPhasePhaseshiftsshiftsFrequency response functionFrequency response function(FRF): (FRF): G(jG(jωω))Bode plotBode plot: Graphical representation of : Graphical representation of G(jG(jωω))GainGainG(sG(s))y(ty(t))StableStableFall 2008 4Bode plot of Bode plot of G(jG(jωω) (review)) (review)Bode plot consists of Bode plot consists of gain plotgain plot& & phase plotphase plotLogLog--scalescaleFall 2008 5Sketching Bode plotSketching Bode plotBasic functions (Today)Basic functions (Today)Constant 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 functions (Next lecture)Product of basic functions (Next lecture)1.1.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!Fall 2008 610-210-11001011021919.52020.52110-210-1100101102-1-0.500.51Bode plot of a constant gainBode plot of a constant gainTFTFFall 2008 710-210-1100101102-40-200204010-210-11001011028989.59090.591Bode plot of a differentiatorBode plot of a differentiatorTFTFFall 2008 8Bode plot of an integratorBode plot of an integratorTFTF10-210-1100101102-40-200204010-210-1100101102-91-90.5-90-89.5-89Mirror image of Mirror image of the bode plot of the bode plot of 1/s with respect 1/s with respect to to ωω--axis.axis.Fall 2008 910-210-1100101102-100-5005010010-210-1100101102-181-180.5-180-179.5-179Bode plot of a double integratorBode plot of a double integratorTFTFFall 2008 10Bode plot of a 1st order systemBode plot of a 1st order systemTF TF 10-210-1100101102-50-40-30-20-10010-210-1100101102-100-80-60-40-200Corner frequencyCorner frequencyStraight lineStraight lineapproximationapproximationFall 2008 11Bode plot of an inverse systemBode plot of an inverse systemTF TF 10-210-11001011020102030405010-210-1100101102020406080100Mirror image of Mirror image of the original bode the original bode plot with respect plot with respect to to ωω--axis.axis.Fall 2008 12Bode plot of a 2nd order systemBode plot of a 2nd order systemTFTFResonant freqResonant freqPeak gainPeak gain10-1100101-60-40-2002010-1100101-200-150-100-500resonanceresonanceFall 2008 1310-210-1100101102-1-0.500.5110-210-1100101102-6000-4000-20000Bode plot of a time delayBode plot of a time delayTFTFHuge phase lag!Huge phase lag!As can be explained with As can be explained with NyquistNyquiststability criterion, stability criterion, this phase lag causes instability of the closedthis phase lag causes instability of the closed--loop system,loop system,and hence, the difficulty in control.and hence, the difficulty in control.Fall 2008 14RemarkRemarkUse Use MatlabMatlab““bode.mbode.m””to obtain precise shape. to obtain precise shape. ALWAYS check the correctness ofALWAYS check the correctness ofLow frequency gain (DC gain) Low frequency gain (DC gain) High frequency gainHigh frequency gainExampleExampleFall 2008 15ExercisesExercisesSketch bode plot.Sketch bode plot.Fall 2008 16SummarySummaryBode plot of various simple transfer functions.Bode plot of various simple transfer functions.Constant gainConstant gainDifferentiator, integratorDifferentiator, integrator1st order and 2nd order systems1st order and 2nd order systemsTime delayTime delaySketching Bode plot is just Sketching Bode plot is just ……..to get a rough idea of the characteristic of a system.to get a rough idea of the characteristic of a system.to interpret the result obtained from computer.to interpret the result obtained from computer.to detect erroneous result from computer.to detect erroneous result from computer.Next, Bode plot of connected systemsNext, Bode plot of connected
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