第8讲现代控制系统分析设计(7)

例8_22

系统传递函数模型为

H(s)?s?1?0.5se 3(s?2)求出有理传递函数的频率响应，然后在同一张图上绘出以四阶pade近似表示的系统频率响应。 num=[1 1];

den=conv([1 2],conv([1,2],[1,2])); w=logspace(-1,2); t=0.5;

[m1,p1]=bode(num,den,w); p1=p1-t*w'*180/pi; [n2,d2]=pade(t,4); numt=conv(n2,num); dent=conv(den,d2);

[m2,p2]=bode(numt,dent,w); subplot(2,1,1);

semilogx(w,20*log10(m1),w,20*log10(m2),'r--'); subplot(2,1,2);

semilogx(w,p1,w,p2,'r--'); subplot(2,1,1); grid on;

title('Bode plot');

xlabel('Frequency (rad/sec)'); ylabel('Gain dB'); subplot(2,1,2); grid on;

xlabel('Frequency (rad/sec)');

ylabel('Phase deg'); Bode plot0-20Gain dB-40-60-80-100-110010010Frequency (rad/sec)1102Phase deg-1000-2000-3000-4000-11010010Frequency (rad/sec)1102 回目录

例8_23

离散二阶系统

H(z)?0.632

z2?1.368z?0.568求系统的离散Bode图 num=0.632;

den=[1 ,-1.368,0.568]; grid on;

dbode(num,den,0.1);

title('Discrete Bode Plot'); Discrete Bode PlotFrom: U(1)2010Phase (deg); Magnitude (dB)0-10-201000To: Y(1)-100-200-300-400110Frequency (rad/sec) 回目录

例8_24

开环系统

H(s)?50

(s?5)(s?2)绘制出系统的Nyquist曲线，并判别系统的稳定性，最后求出闭环系统的单位冲激响应。 k=50; z=[];

p=[-1,-5,2];

[num,den]=zp2tf(z,p,k); figure(1);

nyquist(num,den);

title('Nyquist Plot'); figure(2);

[num1,den1]=cloop(num,den); impulse(num1,den1);

title('Impulse Response');

Impulse ResponseFrom: U(1)1050-5AmplitudeTo: Y(1)-10-15-20-25-30-3500.511.522.5Time (sec.) 回目录

例8_25

开环系统

H(s)?50

(s?1)(s?5)(s?2)绘制出系统的Nyquist曲线，并判别系统的稳定性，最后求出闭环系统的单位冲激响应。 k=50; z=[];

p=[-1,-5,2];

[num,den]=zp2tf(z,p,k); figure(1);

nyquist(num,den);

title('Nyquist Plot'); figure(2);

[num1,den1]=cloop(num,den); impulse(num1,den1);

title('Impulse Response'); Impulse ResponseFrom: U(1)1050-5AmplitudeTo: Y(1)-10-15-20-25-30-3500.511.522.5Time (sec.) 回目录

例8_26

线性系统状态空间模型

?100??0?0???0??0?011??x???u????x?001??0?0? ??????62.5?213.8?204.2?54???1???y??1562187500x??绘制出系统的Bode图和Nyquist曲线，判断系统的稳定性，并绘制闭环系统的单位冲激响应进行验证。

a=[0,1,0,0;0,0,1,0;0,0,0,1;-62.5,-213.8,-204.2,-54]; b=[0,0,0,1]';

c=[1562,1875,0,0]; d=0;

w=logspace(-1,1); figure(1);

bode(a,b,c,d,1,w); title('Bode Plot'); figure(2);

nyquist(a,b,c,d,1,w); title('Nyquist plot'); [z,p,k]=ss2zp(a,b,c,d); p

figure(3);

[a1,b1,c1,d1]=cloop(a,b,c,d); impulse(a1,b1,c1,d1);

title('Impulse Response');

p =

-50.0011 -2.4969 -1.0027 -0.4992