振荡环节G(s)=1/(T^2s^2+2§Ts+1),令wn=1/T则G(s)=wn^2/(s^2+2§wns+wn^2)的奈奎斯特图及波特图。

(绘图时令自然振荡频率wn=0.7,分别取§=0.1,0.3,0.7，1.0，1.5,2.0,4.0)

1.奈奎斯特图

Matlab代码：

>>

zeta=[0.1,0.3,0.7,1.0,1.5,2.0,4.0]

zeta =

0.1000

0.3000

0.7000

1.0000

1.5000

2.0000

4.0000

>> for

j=1:7

sys=tf([wn*wn],[1,2*zeta(j)*wn,wn*wn])

nyquist(sys);

hold on;

end

Transfer function:

0.49

-------------------

s^2 + 0.14 s + 0.49

Transfer function:

0.49

-------------------

s^2 + 0.42 s + 0.49

Transfer function:

0.49

-------------------

s^2 + 0.98 s + 0.49

Transfer function:

0.49

------------------

s^2 + 1.4 s + 0.49

Transfer function:

0.49

------------------

s^2 + 2.1 s + 0.49

Transfer function:

0.49

------------------

s^2 + 2.8 s + 0.49

Transfer function:

0.49

------------------

s^2 + 5.6 s + 0.49

>>

gtext('zeta=0.1');gtext('zeta=0.3');gtext('zeta=0.7');gtext('zeta=1.0');gtext('zeta=1.5');gtext('zeta=2.0');gtext('zeta=4.0')

其奈奎斯特图为

2.Bode图

Matlab代码：

>>

w=[0,logspace(-2,2,200)];

wn=0.7;

zeta=[0.1,0.3,0.7,1.0,1.5,2.0,4.0];

for j=1:7

sys=tf([wn*wn],[1,2*zeta(j)*wn,wn*wn])

bode(sys,w);

hold on;

end

Transfer function:

0.49

-------------------

s^2 + 0.14 s + 0.49

Transfer function:

0.49

-------------------

s^2 + 0.42 s + 0.49

Transfer function:

0.49

-------------------

s^2 + 0.98 s + 0.49

Transfer function:

0.49

------------------

s^2 + 1.4 s + 0.49

Transfer function:

0.49

------------------

s^2 + 2.1 s + 0.49

Transfer function:

0.49

------------------

s^2 + 2.8 s + 0.49

Transfer function:

0.49

------------------

s^2 + 5.6 s + 0.49

gtext('zeta=0.1');gtext('zeta=0.3');gtext('zeta=0.7');gtext('zeta=1.0');gtext('zeta=1.5');gtext('zeta=2.0');gtext('zeta=4.0')

其Bode图为