第1章控制系统计算机协助设计概括第2章MATLAB语言程序设计基础第3章线性控制系统的数学模型第4章线性控制系统的计算机协助剖析第5章Simulink在系统仿真中的应用第6章控制系统计算机协助设计第1章控制系统计算机协助设计概括1】.mathworks.cn/已阅，略2】已阅，略3】已经掌握help命令和Help菜单的使用
方法
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4】区别：MATLAB语言实现矩阵的运算特别简单快速，且效率很高，而用其他通用语言则不然，好多通用语言所实现的矩阵运算都是对矩阵维数拥有一点限制的，即便限制稍小的，凡是维数过大，就会造成运算上的溢出犯错或许运算犯错，甚至无法办理数据的负面结果5】8】输入激励为正弦信号输入激励为脉冲模拟信号输入激励为时钟信号输入激励为随机信号输入激励为阶跃信号=0.3=0.05=0.7结论：随着非线性环节的死区增大，阶跃响应曲线的围渐渐被压缩，能够想象当死区δ足够大时，将不再会有任何响应产生。所以能够获得结论，在该非线性系统中，死区的大小能够改变阶跃响应的幅值和超调量。死区越大，幅值、超调量将越小，而调整时间几乎不受其影响第2章MATLAB语言程序设计基础1】A=[1234;4321;2341;3241]A=1234432123413241>>B=[1+4i,2+3i,3+2i,4+i;4+i,3+2i,2+3i,1+4i;2+3i,3+2i,4+i,1+4i;3+2i,2+3i,4+i,1+4i]B=1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i4.0000+1.0000i3.0000+2.0000i2.0000+3.0000i1.0000+4.0000i2.0000+3.0000i3.0000+2.0000i4.0000+1.0000i1.0000+4.0000i3.0000+2.0000i2.0000+3.0000i4.0000+1.0000i1.0000+4.0000iA(5,6)=5A=123400432100234100324100000005∴若给出命令A(5,6)=5则矩阵A的第5行6列将会赋值为5，且其余空出部分均补上0作为新的矩阵A，此时其阶数为5×62】相应的MATLAB命令：B=A(2:2:end,:)A=magic(8)A=64236160675795554121351501617474620214342244026273736303133323435292838392541232244451918484915145253111056858595462631B=A(2:2:end,:)B=95554121351501640262737363031334123224445191848858595462631∴从上面的运行结果能够看出，该命令的结果是正确的3】>>symsxs;f=x^5+3*x^4+4*x^3+2*x^2+3*x+6f=x^5+3*x^4+4*x^3+2*x^2+3*x+6[f1,m]=simple(subs(f,x,(s-1)/(s+1)))f1=19-(72*s^4+120*s^3+136*s^2+72*s+16)/(s+1)^5m=simplify(100)4】>>i=0:63;s=sum(2.^sym(i))=6155】fori=1:120if(i==1|i==2)a(i)=1;elsea(i)=a(i-1)+a(i-2);endif(i==120)a=sym(a);disp(a);endend[1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903,2971215073,4807526976,7778742049,,,,,,5,7,2,9,1,20,61,81,42,723,565,288,853,141,0994,9135,0129,9264,9393,28657,78050,06707,84757,91464,,,,,,8,5,3,8,31,89,20,09,29,738,167,905,072,977,6049,9026,5075,4101,9176,83277,82453,65730,48183,413913,662096,076009,738105,814114,0552219,6366333,6918552,3284885,0203437,93488322,23691759,17180081,40871840]6】>>k=1;fori=2:1000forj=2:iifrem(i,j)==0ifj
D)+(h.*x/D).*(abs(x)<=D)-h.*(x<-D)【10】functiony=fib(k)ifnargin~=1,error('ifnargout>1,error('ifk<=0,error('犯错：输入变量个数过多，输入变量个数只允许为犯错：输出变量个数过多！');end犯错：输入序列应为正整数！');end1！');endifk==1|k==2,y=1;elsey=fib(k-1)+fib(k-2);endend13】10.80.60.40.20-0.2-0.4-0.6-0.8-1-1-0.500.5114】t=[-1:0.001:-0.2,-0.1999:0.0001:0.1999,0.2:0.001:1];y=sin(1./t);plot(t,y);gridon;10.80.60.40.20-0.2-0.4-0.6-0.8-1-0.8-0.6-0.4-0.200.20.40.60.81-115】>>t=-2*pi:0.01:2*pi;r=1.0013*t.^2;polar(t,r);axis('square')904012060301502030101800210330240300270(2)>>t=-2*pi:0.001:2*pi;r=cos(7*t/2);polar(t,r);axis('square')901120600.80.6150300.40.21800210330240300270>>t=-2*pi:0.001:2*pi;r=sin(t)./t;polar(t,r);axis('square')901120600.80.6150300.40.21800210330>>t=-2*pi:0.001:2*pi;r=1-cos(7*t).^3;902120602403001.52701501300.5polar(t,r);axis('square')17】z=xy>>[x,y]=meshgrid(-3:0.01:3,-3:0.01:3);1800210330240300270z=x.*y;mesh(x,y,z);>>contour3(x,y,z,50);1050-5-10232010-2-1-2-3z=sin(xy)[x,y]=meshgrid(-3:0.01:3,-3:0.01:3);z=sin(x.*y);mesh(x,y,z);>>contour3(x,y,z,50);10.50-0.5-123201-2-2-30-1第3章线性控制系统的数学模型1】>>s=tf('s');G=(s^2+5*s+6)/(((s+1)^2+1)*(s+2)*(s+4))Transferfunction:s^2+5s+6--------------------------------s^4+8s^3+22s^2+28s+16(2)>>z=tf('z',0.1);H=5*(z-0.2)^2/(z*(z-0.4)*(z-1)*(z-0.9)+0.6)Transferfunction:5z^2-2z+0.2---------------------------------------z^4-2.3z^3+1.66z^2-0.36z+0.6Samplingtime(seconds):0.12】该方程的数学模型num=[6422];den=[1103232];G=tf(num,den)Transferfunction:6s^3+4s^2+2s+2------------------------s^3+10s^2+32s+32该模型的零极点模型G=zpk(G)Zero/pole/gain:6(s+0.7839)(s^2-0.1172s+0.4252)-------------------------------------(s+4)^2(s+2)由微分方程模型能够直接写出系统的传达函数模型5】>>P=[0;0;-5;-6;-i;i];Z=[-1+i;-1-i];G=zpk(Z,P,8)Zero/pole/gain:8(s^2+2s+2)-------------------------s^2(s+5)(s+6)(s^2+1)P=[0;0;0;0;0;8.2];Z=[-3.2;-2.6];H=zpk(Z,P,1,'Ts',0.05,'Variable','q')Zero/pole/gain:(q+3.2)(q+2.6)---------------q^5(q-8.2)Samplingtime(seconds):0.058】闭环系统的传达函数模型s=tf('s');G=10/(s+1)^3;Gpid=0.48*(1+1/(1.814*s)+0.4353*s/(1+0.4353*s));G1=feedback(Gpid*G,1)Transferfunction:7.58s^2+10.8s+4.8--------------------------------------------------------------0.7896s^5+4.183s^4+7.811s^3+13.81s^2+12.61s+4.8状态方程的
标准
excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载
型实现G1=ss(G1)a=x1x2x3x4x5x1-5.297-2.473-2.186-0.9981-0.7598x240000x302000x400200x50000.50b=u1x12x20x30x40x50c=x1x2x3x4x5y1000.60.42730.3799d=u1y10Continuous-timestate-spacemodel.零极点模型G1=zpk(G1)Zero/pole/gain:9.6(s^2+1.424s+0.6332)--------------------------------------------------------(s+3.591)(s^2+1.398s+0.6254)(s^2+0.309s+2.707)11】Ga=feedback(s/(s^2+2)*1/(s+1),(4*s+2)/(s+1)^2);Gb=feedback(1/s^2,50);G=3*feedback(Gb*Ga,(s^2+2)/(s^3+14))Transferfunction:3s^6+6s^5+3s^4+42s^3+84s^2+42s---------------------------------------------------------------------------s^10+3s^9+55s^8+175s^7+300s^6+1323s^5+2656s^4+3715s^3+7732s^2+5602s+140013】c1=feedback(G5*G4,H3)=G5*G4/(1+G5*G4*H3)c2=feedback(G3,H4*G4)=G3/(1+G3*H4*G4)c3=feedback(c2*G2,H2)=c2*G2/(1+c2*G2*H2)=G3*G2/(1+G3*H4*G4+G3*G2*H1)G=feedback(G6*c1*c3*G1,H1)=G6*c1*c3*G1/(1+G6*c1*c3*G1*H1)=G6*G5*G4*G3*G2*G1/(1+G3*H4*G4+G3*G2*H1+G5*G4*H3+G5*G4*H3*G3*H4*G4+G5*G4*H3*G3*G2*H1+G6*G5*G4*G3*G2*G1*H1)14】s=tf('s');c1=feedback(0.21/(1+0.15*s),0.212*130/s);c2=feedback(c1*70/(1+0.0067*s)*(1+0.15*s)/(0.051*s),0.1/(1+0.01*s));G=(1/(1+0.01*s))*feedback(130/s*c2*1/(1+0.01*s)*(1+0.17*s)/(0.085*s),0.0044/(1+0.01*s))Transferfunction:0.004873s^5+1.036s^4+61.15s^3+649.7s^2+1911s---------------------------------------------------------------------------4.357e-014s^10+2.422e-011s^9+5.376e-009s^8+6.188e-007s^74.008e-005s^6+0.001496s^5+0.03256s^4+0.4191s^32.859s^2+8.408s第4章线性控制系统的计算机协助剖析1】>>num=[1];den=[3212];G=tf(num,den);eig(G)ans=-1.00000.1667+0.7993i0.1667-0.7993i剖析：由以上信息可知，系统的极点有2个是在s域的右半平面的，因此系统是不稳定的>>num=[1];den=[63211];G=tf(num,den);eig(G)ans=-0.4949+0.4356i-0.4949-0.4356i0.2449+0.5688i0.2449-0.5688i剖析：由以上信息可知，系统的极点有2个是在s域的右半平面的，因此系统是不稳定的>>num=[1];den=[11-3-12];G=tf(num,den);eig(G)ans=-2.0000-1.00001.00001.0000剖析：由以上信息可知，系统的极点有2个是在s域的右半平面的，因此系统是不稳定的>>num=[31];den=[3006005031];G=tf(num,den);eig(G)ans=-1.9152-0.14140.0283+0.1073i0.0283-0.1073i剖析：由以上信息可知，系统的极点有2个是在s域的右半平面的，因此系统是不稳定的>>s=tf('s');G=0.2*(s+2)/(s*(s+0.5)*(s+0.8)*(s+3)+0.2*(s+2));eig(G)ans=-3.0121-1.0000-0.1440+0.3348i-0.1440-0.3348i剖析：由以上信息可知，系统的所有极点都在s域的左半平面，因此系统是稳定的2】>>num=[-32];den=[1-0.2-0.250.05];H=tf(num,den,'Ts',0.5);abs(eig(H)')ans=0.50000.50000.2000剖析：由以上信息可知，所有特点根的模均小于1，因此该系统是稳定的>>num=[3-0.39-0.09];den=[1-1.71.040.2680.024];H=tf(num,den,'Ts',0.5);abs(eig(H)')ans=1.19391.19390.12980.1298剖析：由以上信息可知，由于前两个特点根的模均大于1，因此该系统是不稳定的>>num=[13-0.13];den=[11.3520.44810.0153-0.01109-0.001043];H=tf(num,den,'Ts',0.5);abs(eig(H)')ans=0.87430.15200.27230.23440.1230剖析：由以上信息可知，所有特点根的模均小于1，因此该系统是稳定的>>num=[2.1211.7615.91];den=[1-7.368-20.15102.480.39-340];H=tf(num,den,'Ts',0.5,'Variable','q');abs((eig(H))')ans=8.23493.21152.34152.34322.3432剖析：由以上信息可知，所有特点根的模均大于1，因此该系统是不稳定的3】(1)>>A=[-0.2,0.5,0,0,0;0,-0.5,1.6,0,0;0,0,-14.3,85.8,0;0,0,0,-33.3,100;0,0,0,0,-10];eig(A)ans=-0.2000-0.5000-14.3000-33.3000-10.0000剖析：由以上信息可知，性系的A矩的所有特点根的部均数，因此系是定的(2)>>F=[17,24.54,1,8,15;23.54,5,7,14,16;4,6,13.75,20,22.5589;10.8689,1.2900,19.099,⋯21.896,3;11,18.0898,25,2.356,9];abs(eig(F)')ans=63.720723.539312.436613.323119.7275剖析：由以上信息可知，离散系的F矩的所有特点根的模均大于1，因此系是不定的4】A=[-3121;0-4-2-1;12-11;-1-11-2];B=[10;02;03;11];C=[122-1;21-12];D=[00;00];x10-6Pole-ZeroMap6G=ss(A,B,C,D);tzero(G)pzmap(G)ans=-3.6124-1.2765：∴能够获得系的零点-3.6124、-1.276541)2-sdnoces(si0xAyraniga-2mI-4-6-3.5-3-2.5-2-1.5-1-0.50-4RealAxis(seconds-1)剖析：由以上信息可知，系的特点根的部均位于s域的左半平面，因此系是定的5】s=tf('s');G=0.2*(s+2)/(s*(s+0.5)*(s+0.8)*(s+3)+0.2*(s+2));Gc=sscanform(G,'ctrl')Go=sscanform(G,'obsv')a=x1x2x3x4x10100x20010x30001x4-0.4-1.4-4.3-4.3b=u1x10x20x30x41c=x1x2x3x4y10.40.200d=u1y10Continuous-timestate-spacemodel.a=x1x2x3x4x1000-0.4x2100-1.4x3010-4.3x4001-4.3b=u1x10.4x20.2x30x40c=x1x2x3x4y10001d=u1y10Continuous-timestate-spacemodel.9】(1)>>num=[1851459823638012266422208818576040320];den=[1365464536224496728411812410958440320];[R1,P1,K1]=residue(num,[den0]);[R1,P1]ans=-1.2032-8.0000-1.0472-7.00000.2000-6.00000.7361-5.0000-2.8889-4.00002.2250-3.0000-2.0222-2.00003.0004-1.00001.00000[n,d]=rat(R1);sym([n./d]')ans=[-379/315,-377/360,1/5,53/72,-26/9,89/40,-91/45,7561/2520,1][阶跃响应的解析解]y(t)=(-379/315)*e-8t+(-377/360)*e-7t+(1/5)*e-6t+(53/72)*e-5t+(-26/9)*e-4t+(89/40)*e-3t+(-90/45)*e-2t+(7561/2520)*e-t+1>>num=[1851459823638012266422208818576040320];den=[1365464536224496728411812410958440320];[R2,P2,K2]=residue(num,den);[R2,P2]ans=9.6254-8.00007.3306-7.0000-1.2000-6.0000-3.6806-5.000011.5556-4.0000-6.6750-3.00004.0444-2.0000-3.0004-1.0000[n,d]=rat(R2);sym([n./d]')ans=[3032/315,887/121,-6/5,-265/72,104/9,-267/40,182/45,-7561/2520][脉冲响应的解析解]y(t)=(3032/315)*e-8t+(887/121)*e-7t+(-6/5)*e-6t+(-265/72)*e-5t+(104/9)*e-4t+(-267/40)*e-3t+-2t-t(182/45)*e+(-7561/2520)*e(3)>>symst;u=sin(3*t+5);Us=laplace(u)Us=(3*cos(5)+s*sin(5))/(s^2+9)s=tf('s');Us=(3*cos(5)+s*sin(5))/(s^2+9);num=[1851459823638012266422208818576040320];den=[1365464536224496728411812410958440320];G=tf(num,den);Y=Us*G;num=Y.num{1};den=Y.den{1};[R3,P3,K3]=residue(num,den);[R3,P3]ans=1.1237-8.00000.9559-7.0000-0.1761-6.0000-0.6111-5.00002.1663-4.0000-1.1973-0.0010i0.0000+3.0000i-1.1973+0.0010i0.0000-3.0000i-1.3824-3.00000.8614-2.0000-0.5430-1.0000[n,d]=rat(R3);sym([n./d]')ans=[109/97,282/295,-59/335,-965/1579,951/439,-449/375+(18*i)/17981,-449/375-(18*i)/17981,-1663/1203,317/368,-82/151][正弦信号时域响应的解析解]y(t)=(109/97)*e-8t-7t-6t-5t-4t+(282/295)*e+(-59/335)*e+(-965/1579)*e+(-449/375)*e+(-1663/1203)*e-3t+(317/368)*e-2t+(-82/151)*e-t-2.3947sin(3t)[输出波形]num=[1851459823638012266422208818576040320];den=[1365464536224496728411812410958440320];G=tf(num,den);LinearSimulationResults2.5t=[1:.1:20]';u=sin(3*t+5);lsim(G,u,t);剖析：由解析解可知，输出信号的稳态部分是振荡的，并且其幅值与相位始终在抵达稳态的时候保持不变，因此右图所示的输出波形与解析解所得的结论是一致的21.510.5edutil0pmA-0.5-1-1.5-210】因为PI或PID控制器均含有Ki/s项，这是一个对误差信号的积分环节，假定去掉这一环节，则当Kp→∞，即|e(t)|很小也会存在较大扰动，这会影响到系统的动向特性；当加入这一环节后，如果要求|e(t)|→0，则控制器输出u(t)会由Ki/s环节获得一个常值，此时系统能够获得较好的动向特性，因此这两个控制器能够除去闭环系统的阶跃响应的稳态误差(2)不稳定系统能用PI或PID控制器除去稳态误差。因为PI或PID控制器均含有积分控制，在积分控制中，控制器的输出与输入误差信号的积分红正比关系。对一个自动控制系统，如果在进入稳态后存在稳态误差，则称这个控制系统是有稳态误差的或简称有差系统。为了除去稳态误差，在控制器中必须引入“积分项”。积分项对误差取决于时间的积分，随着时间的增加，积分项会增大。这样，即便误差很小，积分项也会随着时间的增加而加大，它推动控制器的输出增大使稳态误差进一步减小，直到等于零。因此，比率+积分(PI)控制器，能够使系统在进入稳态后无稳态误差，即不稳定系统能用PI或PID控制器除去稳态误差13】>>P=[0;-3;-4+4i;-4-4i];Z=[-6;6];G=zpk(Z,P,1);rlocus(G),gridRootLocus50500.130.090.060.03400.1940300.26301)20200.4-sd10no100.65ces(si0xAyr0.65a-10ni10ga0.4m-20I20-300.2630-400.1940-500.130.090.060.03-6-4-25002468-8RealAxis(seconds-1)剖析：根据根轨迹图可知，可知不论K取何值，均无法保证所有极点均在s域左半平面，因此使单位负反应系统稳定的K值围是不存在的>>num=[122];den=[111480];G=tf(num,den);rlocus(G),grid)1dnoces(sixAyranigamIRootLocusSystem:G0.0650.040.0186Gain:5.426Pole:-0.0027+4.34i0.095Damping:0.00062255Overshoot(%):99.8Frequency(rad/s):4.3440.13430.193220.310.5510-10.551-20.32-30.190.130.0950.0650.040.0183-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5RealAxis(seconds-1)剖析：根据根轨迹图可知，使单位负反应系统稳定的K值围为0>num=[1];den=[1/26001/2610];G=tf(num,den);rlocus(G),gridRootLocus1500.820.70.560.420.280.14System:GGain:101100Pole:0.22+51.2i0.91Damping:-0.0043Overshoot(%):1011)Frequency(rad/s):51.250-s0.975dnoces(00175150125100755025si0xAyranig0.975a-50mI-1000.91-1500.820.70.560.420.280.14-200-150-100-50050RealAxis(seconds-1)剖析：根据根轨迹图可知，使单位负反应系统稳定的K值围为0>s=tf('s');G=800*(s+1)/(s^2*(s+10)*(s^2+10*s+50));rlocus(G),gridRootLocus150.760.640.50.340.160.86System:GGain:3.2310Pole:0.0983+4.4iDamping:-0.02231)0.94Overshoot(%):1075Frequency(rad/s):4.4-sdn0.985oces(2017.51512.5107.552.5si0xAyran0.985iga-5mI0.94-100.86-150.760.640.50.340.16-15-10-50510-20RealAxis(seconds-1)剖析：根据根轨迹图可知，使单位负反应系统稳定的K值围为0>P=[0,-10,-20,-40];Z=[];RootLocus1000.760.640.50.340.16800.86601)400.94-sdno200.985ces(G=zpk(Z,P,1);rlocus(G),grid剖析：从右图的根轨迹图可知，存在能够使得闭环系统主导极点大概ξ=0.707阻尼比的K值，且其位于最右边的那段根轨迹上，下面将利用等阻尼线来寻找切合要求的点RootLocus0.6680.650.630.614.83.80.6884.73.71)System:G-s0.706Gain:2.24e+0044.6d3.6noPole:-3.44+3.44iceDamping:0.707s(Overshoot(%):4.32s3.54.5ixFrequency(rad/s):4.86Ayr0.724ani3.4ga4.4mI3.30.7424.33.2-3.1-3-2.9RealAxis(seconds-1)结论：由上图可知，能使得闭环系统主导极点有大概ξ=0.707阻尼比的K值为K≈2240020】>>s=tf('s');G=8*(s+1)/(s^2*(s+15)*(s^2+6*s+10));margin(G)>>nyquist(G);BodeDiagramGm=29.7dB(at1.58rad/s),Pm=4.23deg(at0.234rad/s)500)Bd-50(eNyquistDiagram0.250.20.150.1s0.05ixAyr0anigam-0.05I-0.1-0.15-0.2-0.25-8-6-4-202-10RealAxiseig(G)ans=00-15.0000-3.0000+1.0000i-3.0000-1.0000i由上述开环系统极点散布可知，开环系统是稳定的；再联合Nyquist图，能够发现Nyquist图不包围(-1,j0)点，因此闭环系统是稳定的StepResponse21.81.61.41.2>>step(feedback(G,1))闭环系统的阶跃响应结论：频域剖析与阶跃响应所得的结论一致>>s=tf('s');G=4*(s/3+1)/(s*(0.02*s+1)*(0.05*s+1)*(0.1*s+1));margin(G)nyquist(G))Bd(edutingaM)ged(esahPBodeDiagramGm=18.2dB(at38.5rad/s),Pm=88.8deg(at8.22rad/s)500-50-100-150-45-90-135-180-225-270-101234101010101010Frequency(rad/s)NyquistDiagram1510>>eig(G)ans=0-50.0000-20.0000-10.0000由上述开环系统极点散布可知，开环系统是稳定的；再联合图不包围(-1,j0)点，因此闭环系统是稳定的Nyquist图，能够发现Nyquist>>step(feedback(G,1))StepResponse10.90.80.70.6edutilp0.5mA0.40.30.20.1000.511.522.5Time(seconds)闭环系统的阶跃响应结论：频域剖析与阶跃响应所得的结论一致>>A=[021;-3-20;134];B=[4;3;2];C=[123];D=[0];G=ss(A,B,C,D);margin(G)nyquist(G),grid)Bd(edutingaM)ged(esahPBodeDiagramGm=10.6dB(at0rad/s),Pm=82.4deg(at15.7rad/s)20100-10-200-45-90-135-180-210-101210101010Frequency(rad/s)NyquistDiagram50dB432-2dB2dB-4dBs14dBi6dB-6dBx-10dBA10dByr0anigam-1I-2-3-4-5-0.500.511.52-1RealAxiseig(G)ans=-0.9463+1.8633i-0.9463-1.8633i3.8926由上述开环系统极点散布可知，因为系统中有一个极点位于s域的右半平面，故该开环系统是不稳定的；再联合Nyquist图，能够发现Nyquist图不包围(-1,j0)点，因此闭环系统是不稳定的>>step(feedback(G,1))26StepResponsex1018161412ed10utilp8A6420010203040506070Time(seconds)闭环系统的阶跃响应结论：频域剖析与阶跃响应所得的结论一致>>P=[0;1;0.368;0.99];Z=[-1.31;-0.054;0.957];G=zpk(Z,P,0.45,'Ts',0.1);margin(G)nyquist(G),grid)Bd(edutingaM)ged(esahPsixAryanigamIBodeDiagramGm=-0.375dB(at10.5rad/s),Pm=-1.77deg(at10.7rad/s)150100500-50-90-180-270-360-450-3-2-1012101010101010Frequency(rad/s)x104NyquistDiagram10dB0.80.60.40.20-0.2-0.4-0.6-0.8-1-500-400-300-200-1000100-600RealAxiseig(G)ans=01.00000.36800.9900由上述开环系统极点散布可知，因为除了一个点位于单位圆上，其他所有极点均位于单位圆，故该开环系统是不稳定的；再联合Nyquist图，能够发现Nyquist图不包围(-1,j0)点，因此闭环系统是不稳定的>>step(feedback(G,1))x1027StepResponse642e0dtuilpm-2-4-6-8050100150200250300350400450500Time(seconds)闭环系统的阶跃响应结论：频域剖析与阶跃响应所得的结论一致(5)>>s=tf('s');G=6*(-s+4)/(s^2*(0.5*s+1)*(0.1*s+1));margin(G)>>nyquist(G),grid)Bd(edutingaMBodeDiagramGm=-InfdB(at0rad/s),Pm=-127deg(at3.8rad/s)150100500-50-100-150180)ged(esahPsixAryanigamI900-90-2-10123101010101010Frequency(rad/s)NyquistDiagram2500dB200150100500-50-100-150-200-250-3000-2500-2000-1500-1000-5000500-3500RealAxiseig(G)ans=00-10.0000-2.0000由上述开环系统极点散布可知，开环系统是稳定的；再联合图顺时针包围(-1,j0)点1圈，因此闭环系统是不稳定的Nyquist图，能够发现Nyquist>>step(feedback(G,1))x1025StepResponse105edutilpmA0-505101520253035Time(seconds)闭环系统的阶跃响应结论：频域剖析与阶跃响应所得的结论一致>>num=[10-6011060];den=[11782130100];G=tf(num,den);margin(G)>>nyquist(G);grid)Bd(edutingaM)ged(esahPsixAryanigamIBodeDiagramGm=-0.669dB(at2.97rad/s),Pm=-20.8deg(at3.44rad/s)50-5-10-15-20-25450360270180900-90-2-10121010101010Frequency(rad/s)1.5NyquistDiagram2dB0dB-2dB4dB-4dB16dB-6dB0.5-10dB10dB20dB-20dB0-0.5-1-1.5-1-0.500.511.5-1.5RealAxiseig(G)ans=-10.0000-5.0000-1.0000+1.0000i-1.0000-1.0000i由上述开环系统极点散布可知，开环系统是稳定的；再联合图顺时针包围
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