自动控制原理-线性系统的频域分析实验报告

线性系统的频域分析一、实验目的1．掌握用MATLAB语句绘制各种频域曲线。2．掌握控制系统的频域分析方法。二、实验内容1．典型二阶系统2222)(nnnsssG绘制出6n，1.0，0.3，0.5，0.8，2的bode图，记录并分析对系统bode图的影响。解:程序如下:num=[0036];den1=[11.236];den2=[13.636];den3=[1636];den4=[19.636];den5=[12436];w=logspace(-2,3,100);bode(num,den1,w)gridholdbode(num,den2,w)bode(num,den3,w)bode(num,den4,w)bode(num,den5,w)-100-80-60-40-20020Magnitude(dB)10-210-1100101102103-180-135-90-450Phase(deg)BodeDiagramFrequency(rad/sec)分析：随着1.0的增大,伯德图在穿越频率处的尖峰越明显,此处用渐近线代替时误差越大.2．系统的开环传递函数为)5)(15(10)(2ssssG)106)(15()1(8)(22ssssssG)11.0)(105.0)(102.0()13/(4)(ssssssG绘制系统的Nyquist曲线、Bode图和Nichols图，说明系统的稳定性，并通过绘制阶跃响应曲线验证。解:程序如下奈氏曲线:(1)num1=[0,0,10];den1=conv([1,0],conv([1,0],conv([5,-1],[1,5])));w=logspace(-1,1,100);nyquist(num1,den1,w)-20020406080100120140160180-80-60-40-20020406080NyquistDiagramRealAxisImaginaryAxis(2)num2=[8,8];den2=conv([1,0],conv([1,0],conv([1,15],[1,6,10])));w=logspace(-1,1,100);nyquist(num2,den2)-10-8-6-4-202-0.25-0.2-0.15-0.1-0.0500.050.10.150.20.25NyquistDiagramRealAxisImaginaryAxis(3)num3=[4/3,4];den3=conv([1,0],conv([0.02,1],conv([0.05,1],[0.1,1])));w=logspace(-1,1,100);nyquist(num3,den3)-1-0.8-0.6-0.4-0.200.20.40.60.8-15-10-5051015NyquistDiagramRealAxisImaginaryAxis分析：系统1，2不稳定，系统3稳定。伯德图:num1=[0,0,10];den1=conv([1,0],conv([1,0],conv([5,-1],[1,5])));num2=[8,8];den2=conv([1,0],conv([1,0],conv([1,15],[1,6,10])));num3=[4/3,4];den3=conv([1,0],conv([0.02,1],conv([0.05,1],[0.1,1])));bode(num1,den1)gridholdbode(num2,den2)bode(num3,den3)-300-200-1000100Magnitude(dB)10-210-1100101102103-360-270-180-900Phase(deg)BodeDiagramFrequency(rad/sec)分析：系统1，2不稳定，系统3稳定。尼科尔斯图(1)num1=[0,0,10];den1=conv([1,0],conv([1,0],conv([5,-1],[1,5])));w=logspace(-1,1,500);[mag,phase]=nichols(num1,den1,w);plot(phase,20*log10(mag))ngrid25303540455055606570-80-60-40-200204060(2)num2=[8,8];den2=conv([1,0],conv([1,0],conv([1,15],[1,6,10])));w=logspace(-1,1,500);[mag,phase]=nichols(num2,den2,w);plot(phase,20*log10(mag))ngrid-280-260-240-220-200-180-160-70-60-50-40-30-20-10010206dB3dB1dB(3)num3=[4/3,4];den3=conv([1,0],conv([0.02,1],conv([0.05,1],[0.1,1])));w=logspace(-1,1,500);[mag,phase]=nichols(num3,den3,w);plot(phase,20*log10(mag))ngrid-100-95-90-85-80-75-70-505101520253035分析：系统1，2不稳定，系统3稳定。阶跃响应曲线（1）num1=[0,0,10];den1=conv([1,0],conv([1,0],conv([5,-1],[1,5])));step(num1,den1)grid0102030405060708000.511.522.533.544.5x108StepResponseTime(sec)Amplitude（2）num2=[8,8];den2=conv([1,0],conv([1,0],conv([1,15],[1,6,10])));step(num2,den2)grid05001000150001234567x104StepResponseTime(sec)Amplitude（3）num3=[4/3,4];den3=conv([1,0],conv([0.02,1],conv([0.05,1],[0.1,1])));step(num3,den3)grid05001000150001000200030004000500060007000StepResponseTime(sec)Amplitude3．已知系统的开环传递函数为)11.0(1)(2ssssG。求系统的开环截止频率、穿越频率、幅值裕度和相位裕度。应用频率稳定判据判定系统的稳定性。解：绘出系统伯德图，程序如下num=[0011];den=[0.1100];w=logspace(-2,3,100);bode(num,den,w)[gm,pm,wcg,wcp]=margin(num,den);gm,pm,wcg,wcpgridBodeDiagramFrequency(rad/sec)-150-100-50050100System:sysFrequency(rad/sec):1.26Magnitude(dB):0.00391Magnitude(dB)10-210-1100101102103-180-150-120System:sysFrequency(rad/sec):1.26Phase(deg):-136Phase(deg)gm=0pm=44.4594wcg=0wcp=1.2647分析：系统截止频率Wc=1.2647，相角裕度r=44.4594,幅值裕度hg=0，穿越频率Wg=0因此系统稳定。三．实验结果及分析四．实验心得与体会总结：通过这次实验，我掌握了各种图形的matlab绘制方法，加深了对课本上各种稳定性判别方法的理解，学会了用软件作图判定系统稳定性，进一步了解了各种系统参数对系统性能的影响。