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