华科电气自动控制理论m15-1

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1、Module15BodeDiagramsObjectives:&UnderstandthebasicideasofBodeplotsmethod.&PlotBodediagramsforcomplexsystems.&ObtaintransferfunctionsofsystemsthroughtheirBodediagrams.Bodeplotsarethethirdmethod(rootlocusandNyquistaretheothertwo),usedtodesignastableclosedloopsystem.Bodeplotsaresimi

2、lartotheNyquistdiagrams,inthesensethatweplotthephaseandmagnitudeoftheOpenLoopTF,butthistimeagainstthefrequency.IncomparisonwiththeNyquistdiagrams,theBodeplotscontainadditionalinformationaboutthesysteminthefrequencydata.KnowingtheBodeplotonecanconstructthecorrespondingNyquistdiagr

3、am,butthereverseisnotpossible.Considertheclosedloopsystemdescribedbelow.15.1DefinitionofBodeDiagrams（对数频率特性曲线图）∑M,L(ω)M=20lgM=20lg

4、G(jω)

5、dbdb∑φ(ω)Φ(ω)=∠G(jω)¢对数幅频曲线的纵坐标按M线性db分度，单位为分贝，简化计算；¢对数频率曲线的横坐标按lgω分度，便于表示在较大ω范围频率特性的变化，单位为rad/s；¢对数相频曲线的纵坐标按φ(ω)线性分度，单位为度(o)。Mdb(dB)db−−decibel

6、M=20lgMAdecadedb=20lgGH(jω)0.1110100ω∠GH(jω)φ0.1110100ω−90°−180°Mdb（dB）-20dB/dec20-20dB/dec0210-100101101ω(rad/sec)-60dB/decΦ(deg)90º0º-90º-180º-270º210-100101101ω(rad/sec)•AdvantageofBodeplotsm12m2ζsslK∏∏(1+τs)[1+2+]i2i==11lωnlωnl11G(s)==K⋅⋅...(τs+1)...n12n2sνTs+11ζsssν∏∏(1+Ts)[

7、1+2r+]1k2k==11rωnrωnrnTypification(典型化)nj∑ϕi(ω)G(j)G(s)

8、M()ei=1ω==∏ω⋅s=jωii=1nMdb=20lgM(ω)=∑20lgMi(ω)Logarithmic(对数化)ni=1ϕ(ω)=∑ϕi(ω)i=1¾Themodulus-frequencyplotforthecompoundTFisobtainedbyaddingthecomponentplots¾Thephase-frequencyplotforthecompoundTFisobtainedbyaddingthecomponent

9、plots¾Thegainandphasemarginsareobtainedwithoutcomputermethod.15.2ElementalBodeDiagramsWewillfirstlearnhowtoplotBodeDiagramsofsimple(elemental)TFsandthenlearnhowtocombinethem.Ingeneralanopen-loopTFwillhavethefollowingform:一阶微分环节二阶微分环节比例环节m12m2ζsslK∏∏(1+Tis)[1+2+2]i==11lωnlωnlG(s)=

10、n12n2ζsssν∏∏(1+Ts)[1+2r+]k2k==11rωnrωnrν<0微分环节振荡环节惯性环节ν>0积分环节m12m2ω2ζωlK∏∏(1+jωT)[1−+j]i2i==11lωωnlnlG(jω)=G(s)

11、=s=jωn12n2ω2ζωνr(jω)∏∏(1+jωT)[1−+j]k2k==11rωωnrnr1)ProportionalelementG(s)=KM=KG(jω)=KK=100M=20lgK40db30ϕ(ω)=0°K=1020¢增益K为常数，对数100幅频特性为一水平直线，改变K，会上升或下降,90o45o相应的相角不变，为0

12、；0o¢K>1,分贝值为正，-45oK<1，分贝值为负。-90o10-11001