matlab code:
t=0:0.001:10;
f=3*exp(-3*t)+5*exp(-2*t)+exp(-t).*(4*cos(3*t)+6*sin(3*t))+exp(-4*t);
figure
plot(t,f),grid on
r=[3;5;2;2;-3*i;3*i;1];
p=[-3;-2;-1+3*i;-1-3*i;-1+3*i;-1-3*i;-4];
k=[];
[b a]=residue(r,p,k)
sys=tf(b,a)
figure
pzmap(sys)
p=pole(sys)
z=zero(sys)
figure
bode(sys)
margin(sys)
output:
b =
13 142 834 3352 8536 13392 10824
a =
1 13 86 384 1180 2516 3560 2400
sys =
13 s^6 + 142 s^5 + 834 s^4 + 3352 s^3 + 8536 s^2 + 13392 s +
10824
---------------------------------------------------------------------
s^7 + 13 s^6 + 86 s^5 + 384 s^4 + 1180 s^3 + 2516 s^2 + 3560 s +
2400
Continuous-time transfer function.
p =
-1.0000 + 3.0000i
-1.0000 - 3.0000i
-1.0000 + 3.0000i
-1.0000 - 3.0000i
-4.0000 + 0.0000i
-3.0000 + 0.0000i
-2.0000 + 0.0000i
z =
-0.9147 + 3.7651i
-0.9147 - 3.7651i
-3.8609 + 0.0000i
-2.6326 + 0.0000i
-1.3001 + 1.9407i
-1.3001 - 1.9407i
impulse responce:
p-z map:
bode plot:
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