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1、6)Second-orderoscillatoryelement(振荡环节)240ω222ζωMdb()20lg(1ω=−−2)(+)20ωωstraight-lineapproximationnn20−40dB/decζωω-20nϕω()=−arctan2ω-401−2-60ωn(Dependonζandω/ω)180on90oω<<ω时,n0oM(ω)=0,ϕ(ω)=0°db>>时-90oωω,n-180oω=−=−°ωM(ω)40lg(),ϕ(ω)1800.1110100dbωωnn¢Theasymptoteisindependentofζ.when
2、ω=ωnThediscrepancydependsuponζ.(breakfrequency)¢PhaseiscentralsymmetryaboutM(ω)=−20lg2ζ,ϕ(ω)=−90°db(ω,-90º).nω=∞ω=0ζ=3.0ζ=1.0ζω↓↑,()Mζ>1，G（jω）趋近于半圆ζ=0.2ω=ωnζ=0.1dM()ω令=0dω21201<≤ζω时,有谐振频率=ω−2ζ,谐振峰值M=rrn2212ζ−ζζ=0.120ζ=0.2ζ=0.30ζ=0.5Approximatemagnitude-20ζ=0.7-40ζ=1.0−40dB/decζ=0.1
3、ζ=0.2ζ=0.3ζ=0.5-90ζ=0.7ζ=1.0-1807)Second-orderDifferentialelement22s2ζsω2ζωG(s)=++1G(jω)=1−+j22ωωωωnnnn2ζωωnjarctan22ω1−ω2ζω222ωnG(jω)=(1−)+()⋅e2ωωnnω<<ω时,nwhenω=ωnM(ω)=0,ϕ(ω)=0°db(breakfrequency)ω>>ω时,nM(ω)=20lg2ζ,ϕ(ω)=90°ωdbM(ω)=40lg(),ϕ(ω)=180°dbωn62ω22ζω260M(ω)=20lg(1−)+()db2ωω
4、40nnApproximatemagnitude2ζω20ωn40dB/decϕ(ω)=arctan20ω1−-202ωn-40(Dependonζandω/ω)n180o<<,90oωω时n()=0,()=0°0oMωϕωdbω>>ω时,-90on-180oωM(ω)=40lg(),ϕ(ω)=180°db0.1110100ωωnwhen=ωωωnn(breakfrequency)M(ω)=20lg2ζ,ϕ(ω)=90°dbAsymptotesofBodediagrams40ζ=1.040dB/decζ=0.720ζ=0.50ζ=0.3ζ=0.2-20ζ=0
5、.1ζ=1.0180ζ=0.7ζ=0.590ζ=0.3ζ=0.2ζ=0.1ωωn8)Delayelement(延迟环节)j−τsc(t)=1(t−τ)r(t−τ)G(s)=e−jωτG(jω)=eM(ω)=1,M(ω)=0－101dboϕ(ω)=−ωτ(rad)=−57.3ωτ（）Mdb20¢Magnitudeisindependentofω.0¢Phaseangledependsonω-200oandτ.－９0o－１８0o0.111010015.3StepsforPlottingBodeDiagramsnnj∑ϕi(ω)GH(j)GH(s)
6、M()ei=1
7、ω==∏ω⋅s=jωii=1nMdb=20lgM(ω)=∑20lgMi(ω)Logarithmic(对数化)i=1nϕ(ω)=∑ϕi(ω)i=1Method1:directlyaddingcomponentparts(SP15.2)500(s+2)GH(s)=2s(s+20)(s+4s+100)•PreparationStep–Writingtheopen-loopfrequencyresponseinBodeformfirstly:10.5(s+1)2GH(s)=1124s(s+1)(s+s+1)20100100•Step1–Calculatethebre
8、akfrequencies:ω=1;ω=2;ω=10ω=201234•Step2–Determinethefrequencyrangetobeplotted:0.1<ω<200•Step3–Plotthestraight-linemagnitudeapproximation•Step4–Graphicallyaddallelementmagnitudes.•Step5–PlotDeviations(画出转折频率处的偏差）•Step6–Completethemagnitudecurve.•Step7–Plottheindividualphasediagramo
9、fthecomponents.•Step8–Grap
