华科电气自动控制理论m14

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1、Module14NyquistAnalysisandRelativeStability14.1ConditionalStabilityK(τs+1)ExampleG(s)=2s(Ts+1)ω=0+[GH][GH]ω=∞ω=∞00（-1，j0）（-1，j0）ω=0+τTP=0,N=0,Z=0P=0,N=2,Z=2systemunconditionallysystemunconditionallystableforallK>0unstableforallK>0KExample：G(s)=s(2s+1)(3s+1)K

2、M=whenφ=−180°(2)2+1(3)2+116ωωω=M=Kω65−1−1φ=∠GH=−90°−tg2ω−tg3ω6∴whenK<1(K<0.83)5thesystemmaybestableforK<0.832Conclusion(P274:1.~5.)1.Writetheopen-looptransferfunctioninBodeform,andwritedownexpressionsforthemagnitudeandphase.2.SketchtheNyquistdiagramforanarbitrar

3、yvalueofgaintodeterminewhetherthecriticalpointpassestotheleftorrightofanobservermovingalongthefrequencyresponsecurveinthedirectionofincreasingfrequency.3.Usingcomputermethod,ifnecessary,determinethefrequencythatmakesthecorrespondingangle-180º.4.Substitutethisval

4、ueoffrequencyintothemagnitudeequationanddeterminethecorrespondingmagnitude.5.Ifthemagnitudeislessthanunityandthecriticalpointpassestotheleft,thesystemisstable;otherwiseitisnot.•Conditionalstablesystemandunstablesystem条件稳定系统和结构不稳定系统条件稳定系统：由于开¢结构不稳定系统：无论环传递函数的某些参数

5、开环传递函数的参数如改变，闭环系统的稳定何改变，闭环系统总是性发生改变，即闭环系不稳定性的。统的稳定是有条件的。如：KG(s)=2s(Ts+1)结构稳定系统：无论开环传递函数的参数如何改变，闭环系统总是稳定的。Example：Aunity-feedbackcontrolsystemhasthenyquistdiagramwhichisshowninfollowingfigure(K=10,P=0,v=1).FindtherangeofKconsistentwithstability.j-1-2ω=+∞-1.5-0.50

6、ωω=0+Solution：theopen-looptransferfunctionofthissystemcanbeobtained:KKG(s)=G(S)G(jω)=G(jω);i=1,2,31i1isjωiWhenK=10,jG(jω)=−2,G(jω)=−1.5,G(jω)=−0.5ωωω123123-2-1ω=+∞ifG(jω)=−1i-1.5-0.50−1−1ωK===511−2+G1(jω1)ω=0jω10120K=;23K=2030

7、ableω=0+unstablejK>KjK

8、tingthismeasure–––GainandPhaseMargin.j[GH]K（-1，j0）0KCω=0Gainmargin∠G(jω)H(jω)=(2k+1)πϕϕ1GM=h=

9、GH(jω)

10、ϕ(ω为相位穿越频率)φPhasemarginM(ω)=

11、G(jω)H(jω)

12、=1cccPM=γ=180°+∠G(jω)H(jω