自动控制理论的MATLAB仿真实例（二）

%求方程的解

x=sym('x');

fx=(3*x*x+2*x)*(x*x+2.32*x+4)-(2*x+2.32)*(x*x*x+x*x)

fx = 

expand(fx)

ans = 

den=[1 116/25 358/25 8];

roots(den)

ans = 3×1 complex

-1.9750 + 2.7738i
-1.9750 - 2.7738i
-0.6900 + 0.0000i

 

 

 

%绘制根轨迹图

num=[1 1 0 0];

den=[1 2.32 4];

s1=tf(num,den)%多项式相除，得分式

s1 =

s^3 + s^2
----------------
s^2 + 2.32 s + 4

Continuous-time transfer function.

rlocus(s1)

 

%绘制根轨迹图

num=1;

den=conv([1 1],[1 6 10])%展开多项式

den = 1×4

1 7 16 10

 

 

s1=tf(num,den)

s1 =

1
-----------------------
s^3 + 7 s^2 + 16 s + 10

Continuous-time transfer function.

rlocus(s1)

 

%绘制伯德图，求相角裕度、增益裕度

num=1;

den=conv([1 1],conv([0.8 1],[0.2 1]));

s1=tf(num,den);

bode(s1)

hold on

margin(s1)

hold off

 

%反馈校正

num=100;

den=conv([1 0],conv([0.1 1],[0.0067 1]));

s1=tf(num,den)

s1 =

100
----------------------------
0.00067 s^3 + 0.1067 s^2 + s

Continuous-time transfer function.

hold on;

num1=0.0167*[1 0 0];

den1=[0.2 1];

s2=tf(num1,den1)

s2 =

0.0167 s^2
----------
0.2 s + 1

Continuous-time transfer function.

s0=feedback(s1,s2)

s0 =

20 s + 100
------------------------------------------
0.000134 s^4 + 0.02201 s^3 + 1.977 s^2 + s

Continuous-time transfer function.

bode(s0)

 

%非最小相位系统

close all

num=[1 1];

den=[2 1];

s1=tf(num,den)

s1 =

s + 1
-------
2 s + 1

Continuous-time transfer function.

bode(s1)

hold on;

num=-[1 -1];

den=[2 1];

s1=tf(num,den)

s1 =

-s + 1
-------
2 s + 1

Continuous-time transfer function.

bode(s1)

hold off

 

%根轨迹&阶跃响应

num=[1 1];

den=conv([1 0],[1 -3]);

s1=tf(num,den);

rlocus(s1)

num=9*[1 1];

den=conv([1 0],[1 -3]);

s1=tf(num,den);

H=1;

cloop=feedback(s1,H);

step(cloop)

 

%滞后系统根轨迹

num=1;

den=[1 1];

s1=tf(num,den)

s1 =

1
-----
s + 1

Continuous-time transfer function.

[num1,den1]=pade(1,10);

sdelay=tf(num1,den1);

s2=s1*sdelay;

rlocus(s2);

 

%单位脉冲响应

close all

num=25;

den=[1 4 25];

s1=tf(num,den);

step(s1)

hold on

impulse(s1)

hold off

legend({'step','impulse'});

 

%求截止频率

num=100*[0.25 1];

den1=conv([1 0 0],[0.005 1]);

s1=tf(num,den1);

bode(s1)

[mag,phase,w]=bode(s1);

[l,c]=size(mag);

mag1=zeros(c,1);

for i=1:c

mag1(i)=20*log10(mag(1,1,i));

end

wc=interp1(mag1,w,0,'spline')

wc = 25.1177