控制系统计算机辅助设计第四章习题15-21

第四章习题第15题.程序：clc[nP,dP]=paderm(2,0,3);%将延时环节进行pade降阶近似s=tf('s');%定义laplace算子G=(s-1)/(s+1)^5;rlocus(G*tf(nP,dP))%画出函数的根轨迹结果：由图可知，当0K2.71时，系统稳定-6-4-2024-6-4-202460.280.420.560.70.820.910.9750.140.280.420.560.70.820.910.97512345671234567System:untitled1Gain:4.05Pole:0.0389+0.872iDamping:-0.0445Overshoot(%):115Frequency(rad/sec):0.873System:untitled1Gain:2.71Pole:-0.0112-0.851iDamping:0.0131Overshoot(%):96Frequency(rad/sec):0.851System:untitled1Gain:8.58e+004Pole:0.0204-4.81iDamping:-0.00425Overshoot(%):101Frequency(rad/sec):4.81System:untitled1Gain:7.11e+004Pole:-0.00783+4.69iDamping:0.00167Overshoot(%):99.5Frequency(rad/sec):4.690.14RootLocusRealAxisImaginaryAxis第16题程序：clcs=tf('s');%定义laplace算子G=1/(s*(s+1)*(s+20)*(s+40));%输入传递函数rlocus(G),grid%画出根轨迹图形结果：如图所示：能使闭环主导极点在阻尼大约为0.707时，K=367RootLocusRealAxisImaginaryAxis-2.5-2-1.5-1-0.500.511.5-2.5-2-1.5-1-0.500.511.520.640.760.860.940.9850.160.340.50.640.760.860.940.9850.511.522.5System:GGain:367Pole:-0.481+0.476iDamping:0.711Overshoot(%):4.17Frequency(rad/sec):0.6760.160.340.5第17题程序：clcz=tf('z');%定义z算子H=1/((z+0.8)*(z-0.8)*(z-0.99)*(z-0.368));%输入H函数rlocus(H);%画出函数的根轨迹K=0.223;%增益Kstep(feedback(H*K,1))%画出增益K=0.223时的系统阶跃响应曲线结果：如图所示，可以看出，当0K0.223时闭环系统稳定-5-4-3-2-1012345-5-4-3-2-1012345System:HGain:0.223Pole:0.0118Damping:Overshoot(%):Frequency(rad/sec):RootLocusRealAxisImaginaryAxis取K=0.223，画出阶跃响应曲线如下：020406080100120140160-1-0.500.511.52x106StepResponseTime(sec)Amplitude第18题程序：clcz=tf('z',0.1);%定义z算子H1=1/((z+0.8)*(z-0.8)*(z-0.99)*(z-0.368));%输入H函数H=d2c(H1);H2=z^(-8);[n,d]=paderm(8,0,3);Q=tf(n,d);R=H*Q;rlocus(R);%画出函数的根轨迹step(feedback(G*0.01,1))运行结果：-6-4-20246-6-4-2024System:RGain:0.0119Pole:0.0444+0.236iDamping:-0.185Overshoot(%):181Frequency(rad/sec):0.24RootLocusRealAxisImaginaryAxis0102030405060-2-1.5-1-0.500.511.522.5x105StepResponseTime(sec)Amplitude19题程序：clcs=tf('s');G=(s^2*(s^2+3*s+4.32))/(s^5+3*s^4+4.63*s^3+1.23*s^2+1.629*s+1.638);rlocus(G)figurestep(feedback(G*2.68,1))运行结果：从图上时看出K=2.68时系统稳定-3-2.5-2-1.5-1-0.500.5-2-1.5-1-0.500.511.52System:GGain:2.68Pole:0.00299+0.368iDamping:-0.00814Overshoot(%):103Frequency(rad/sec):0.368System:GGain:2.68Pole:0.00299-0.368iDamping:-0.00814Overshoot(%):103Frequency(rad/sec):0.368RootLocusRealAxisImaginaryAxis0500100015002000250030003500400045005000-2-1.5-1-0.500.511.52x106StepResponseTime(sec)Amplitude第20题（1）程序：clcs=tf('s');%定义laplace算子G=8*(s+1)/(s^2*(s+5)*(s^2+6*s+10));%输入开环传递函数模型bode(G)%画出bode图figure;nyquist(G),grid%画出nyquist图figure;nichols(G)%画出nichols图[Gm,r,wcg,wcp]=margin(G),grid%求系统的幅值裕度和相位裕度Step(feedback(G,1))运行结果：Gm=4.8750r=3.5676wcg=1.0000wcp=0.4125Gm1,r0所以系统稳定-150-100-50050Magnitude(dB)10-1100101102-360-315-270-225-180-135Phase(deg)BodeDiagramFrequency(rad/sec)-8-7-6-5-4-3-2-101-0.25-0.2-0.15-0.1-0.0500.050.10.150.20.250dB-20dB-10dB-6dB-4dB-2dB20dB10dB6dB4dB2dBNyquistDiagramRealAxisImaginaryAxis-360-315-270-225-180-135-90-450-160-140-120-100-80-60-40-20020406dB3dB1dB0.5dB0.25dB0dB-1dB-3dB-6dB-12dB-20dB-40dB-60dB-80dB-100dB-120dB-140dB-160dBNicholsChartOpen-LoopPhase(deg)Open-LoopGain(dB)05010015020025030035040000.20.40.60.811.21.41.61.82StepResponseTime(sec)Amplitude（2）程序：clcs=tf('s');%定义laplace算子G=(4*(s/3+1))/(s*(0.02*s+1)*(0.05*s+1)*(0.1*s+1));%输入开环传递函数模型bode(G)%画出bode图figure;nyquist(G),%figurenichols(G)[Gm,r,wcg,wcp]=margin(G),gridStep(feedback(G,1))运行结果：Gm=8.1405r=88.8362wcg=38.4943wcp=8.2231-100-50050Magnitude(dB)10-1100101102103-270-225-180-135-90-45Phase(deg)BodeDiagramFrequency(rad/sec)-1-0.8-0.6-0.4-0.200.20.40.60.8-15-10-5051015NyquistDiagramRealAxisImaginaryAxis00.511.522.500.10.20.30.40.50.60.70.80.91StepResponseTime(sec)Amplitude(3)程序：clcA=[021;-3-20;134];B=[4;3;2];C=[123];D=[];G=ss(A,B,C,D);G1=tf(G);bode(G1);%画出bode图figure;nyquist(G);%画出nyquist图figure;nichols(G);%画出nichols图[Gm,r,wcg,wcp]=margin(G)%求系统的幅值裕度和相位裕度Step(feedback(G,1))运行结果：-20-1001020Magnitude(dB)10-210-1100101102-180-135-90-450Phase(deg)BodeDiagramFrequency(rad/sec)-1-0.500.511.52-5-4-3-2-1012345NyquistDiagramRealAxisImaginaryAxis-180-135-90-450-20-15-10-5051015NicholsChartOpen-LoopPhase(deg)Open-LoopGain(dB)0246810121416180123456789x106StepResponseTime(sec)Amplitude（4）程序：clcz=tf('z',0.1);H=(0.45*(z+1.31)*(z+0.054)*(z-0.957))/z*(z-1)*(z-0.368)*(z-0.99);bode(H)%画出bode图figure;nyquist(H)%画出nyquist图figure;nichols(H)%画出nichols图[Gm,r,wcg,wcp]=margin(H),grid%求系统的幅值裕度和相位裕度figureStep(feedback(G,1))Gm=0.4904r=-62.7190wcg=15.2109wcp=11.3909系统不稳定-150-100-50050Magnitude(dB)10-210-11001011020180360540720900Phase(deg)BodeDiagramFrequency(rad/sec)-3-2-10123-4-3-2-101234NyquistDiagramRealAxisImaginaryAxis090180270360450540630720810900-160-140-120-100-80-60-40-20020406dB3dB1dB0.5dB0.25dB0dB-1dB-3dB-6dB-12dB-20dB-40dB-60dB-80dB-100dB-120dB-140dB-160dBNicholsChartOpen-LoopPhase(deg)Open-LoopGain(dB)0246810121416180123456789x106StepResponseTime(sec)Amplitude（5）clcs=tf('s');G=(6*(-s+4))/s^2*(0.5*s+1)*(0.1*s+1);bode(G)%画出bode图figure;nyquist(G)%画出nyquist图figure;nichols(G)%画出nichols图[Gm,r,wcg,wcp]=margin(G)%求系统的幅值裕度和相位裕度figureStep(feedback(G,1))程序：Gm=0r=Infwcg=0