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【自我实践4-1】某单位负反馈系统的开环传递函数()(1)(2)kGssss,求(1)当k=4时,计算系统的增益裕度,相位裕度,在Bode图上标注低频段斜率,高频段斜率及低频段、高频段的渐近相位角。(2)如果希望增益裕度为16dB,求出响应的k值,并验证。(1)当K=4时num=[4];den=[1,3,2,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagramofG(s)=4/[s(s+1)(s+2)]′)G=4-----------------s^3+3s^2+2sContinuous-timetransferfunction.Gm=1.5000,Pm=11.4304,Wcg=1.4142,Wcp=1.1431title(′BodeDiagramofG(s)=4/[s(s+1)(s+2)]′)低频段斜率为-20dB/dec,高频段斜率为-60dB/dec,低频段渐近相位角为-90度,高频段的渐近相位角为-270度。增益裕度GM=1.5000dB/dec,相位裕度Pm=11.4304度(2)当增益裕度为16dB时,算得K=0.951,对应的伯德图为:num=[0.951];den=[1,3,2,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagramofG(s)=4/[s(s+1)(s+2)]′)G=0.951-----------------s^3+3s^2+2sContinuous-timetransferfunction.Gm=6.3091,Pm=54.7839,Wcg=1.4142,Wcp=0.4276title(′BodeDiagram′)【自我实践4-2】系统开环传递函数()(0.51)(0.11)kGssss,试分析系统的稳定性。计算可得当K=12时系统的增益裕度,相位裕度为0.对应的程序为:num=[12];den=[0.05,0.6,1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridG=12----------------------0.05s^3+0.6s^2+sContinuous-timetransferfunction.Gm=1Pm=9.5374e-06Wcg=4.4721Wcp=4.4721当K=10时即当k12时的特例,对应的程序为:num=[10];den=[0.05,0.6,1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridG=10----------------------0.05s^3+0.6s^2+sContinuous-timetransferfunction.Gm=1.2000Pm=3.9431Wcg=4.4721Wcp=4.0776系统产生衰减震荡,增益裕度和相角裕度都大于0,系统稳定。当K=20时即当k12时的特例,对应的程序为:num=[20];den=[0.05,0.6,1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridG=20----------------------0.05s^3+0.6s^2+sContinuous-timetransferfunction.Gm=0.6000,Pm=-10.5320,Wcg=4.4721,Wcp=5.7247此时的增益裕度和相角裕度都小于0,系统不稳定。【自我实践4-3】某单位负反馈系统的开环传递函数31.6()(0.011)(0.11)Gssss,求(1)绘制Bode图,在幅频特性曲线上标出低频段斜率、高频段斜率、开环截止频率和中频段穿越频率;在幅频特性曲线标出:低频段渐近相位角、高频段渐近相位角和-180线的穿越频率。(2)计算系统的相位裕度和幅值裕度h,并确定系统的稳定性。程序为:num=[31.6];den=[0.001,0.11,1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=31.6------------------------0.001s^3+0.11s^2+sContinuous-timetransferfunction.Gm=3.4810,Pm=22.2599,Wcg=31.6228,Wcp=16.3053低频段斜率为-20dB/dec,高频段斜率为-60dB/dec,低频段渐近相位角为-90度,高频段的渐近相位角为-270度。增益裕度GM=3.4810dB/dec,相位裕度Pm=22.2599度,-180度线穿越频率为Wcg=31.6228。由伯德图可知系统的相位裕度和幅值裕度都大于零,故系统稳定。【自我实践4-4】某单位负反馈系统的开环传递函数2(1)()(0.11)ksGsss,令k=1作bode图,应用频域稳定判据确定系统的稳定性,并确定使系统获得最大相位裕度的增益k值。当K=1时的伯德图程序为:num=[1,1];den=[0.1,1,0,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridG=s+1-------------0.1s^3+s^2Continuous-timetransferfunction.Gm=0,Pm=44.4594,Wcg=0,Wcp=1.2647由图可知系统的相位裕度和幅值裕度都大于零,故系统稳定。由计算得当k=3.16系统获得最大相位裕度.【综合实践】试观察下列典型环节BODE图形状,分析参数变化时对BODE图的影响,填写下表。(1)比例环节:K(K=10、K=30)K=10num=[10];den=[0,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(BodeDiagram)K=30num=[30];den=[0,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(BodeDiagram)(2)惯性环节:1TsK(K=1、K=10、T=0.1、1)K=1,T=0.1cp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1---------0.1s+1Continuous-timetransferfunctionK=1,T=1num=[1];den=[1,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1-----s+1Continuous-timetransferfunction.Gm=InfPm=-180Wcg=NaNK=10,T=0.1num=[10];den=[0.1,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=10---------0.1s+1Continuous-timetransferfunction.Gm=InfPm=95.7406Wcg=NaNWcp=99.4731K=10,T=1num=[10];den=[1,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=10-----s+1Continuous-timetransferfunction.Gm=InfPm=95.7406Wcg=NaNWcp=9.9473(3)积分环节:sK(K=1、K=10)K=1num=[1];den=[1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1-sContinuous-timetransferfunction.Gm=InfPm=90Wcg=NaNWcp=1K=10num=[10];den=[1,0];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=10--sContinuous-timetransferfunction.Gm=InfPm=90Wcg=NaNWcp=10.0000(4)微分环节:Ks(K=1、K=10)K=1num=[1,0];den=[0,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=sContinuous-timetransferfunction.Gm=InfPm=-90Wcg=NaNWcp=1K=10num=[10,0];den=[0,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=10sContinuous-timetransferfunction.Gm=InfPm=-90Wcg=NaNWcp=0.1000(5)二阶惯性环节:2222ssK(K=1、K=10、=0.1、=1、=5、=1)K=1,=0.1,=1num=[1];den=[1,0.2,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1---------------s^2+0.2s+1Continuous-timetransferfunction.Gm=InfPm=16.2591Wcg=InfWcp=1.4000K=1,=1,=1num=[1];den=[1,2,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1-------------s^2+2s+1Continuous-timetransferfunction.Gm=InfPm=-180Wcg=InfWcp=0K=1,=5,=1num=[1];den=[1,10,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=1--------------s^2+10s+1Continuous-timetransferfunction.Gm=InfPm=-180Wcg=InfWcp=0K=10,=0.1,=1num=[10];den=[1,0.2,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(G)bode(num,den)gridtitle(′BodeDiagram′)G=10---------------s^2+0.2s+1Continuous-timetransferfunction.Gm=InfPm=3.7990Wcg=InfWcp=3.3137K=10,=1,=1num=[10];den=[1,2,1];G=tf(num,den)[Gm,Pm,Wcg,Wcp]=margin(
本文标题:实验二北京科技大学自控实验
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