d) expansión en fracciones parciales de la salida Y(s)
numy =
0 0 0 1.0000 3.6600 3.9800 1.3200 0
deny =
1.0000 4.5600 9.0740 10.9900 9.3320 3.9240 0 0
residuos =
0.1270 – 0.0384i
0.1270 + 0.0384i
-0.2875 – 0.0927i
-0.2875 + 0.0927i
-0.0154
0.3364
0
polos =
-1.5474 + 0.5980i
-1.5474 – 0.5980i
-0.2059 + 1.1451i
-0.2059 – 1.1451i
-1.0533
0
0
directo =
[]
ans =
e) la respuesta nalítica de la salida
gc =
s*(s+1)/(s+7/5)/(s+1/2)
s (s + 1)
-------------------
(s + 7/5) (s + ½)
gp =
(s+2)/s/(s^2+2*s+2)
s + 2
----------------
2
s (s + 2 s + 2)
h =
3/2/(s+33/50)
1
3/2 ------
33
s + --
50
g1 =
(s+1)/(s+7/5)/(s+1/2)*(s+2)/(s^2+2*s+2)
(s + 1) (s + 2)
----------------------------------
2
(s + 7/5) (s + ½) (s + 2 s + 2)
g =
(s+1)/(s+7/5)/(s+1/2)*(s+2)/(s^2+2*s+2)/(1+3/2*(s+1)/(s+7/5)/(s+1/2)*(s+2)/(s^2+2*s+2)/(s+33/50))
/ 2
(s + 1) (s + 2)/|(s + 7/5) (s + ½) (s + 2 s + 2)
|
|
\
/ (s + 1) (s + 2) \\
|1 + 3/2 -------------------------------------------||
| 2 / 33\||
| (s + 7/5) (s + ½) (s + 2 s + 2) |s + --|||
\ \ 50///
r =
1/s
y =
(s+1)/(s+7/5)/(s+1/2)*(s+2)/(s^2+2*s+2)/(1+3/2*(s+1)/(s+7/5)/(s+1/2)*(s+2)/(s^2+2*s+2)/(s+33/50))/s
/ -----
| \ 3
1/5868923746672015605 | ) (2296083319608571655 _alpha
| /
| -----
\_alpha = %1
4
+ 739667049141244250 _alpha + 889829914704736419
2
+ 2003476572203267322 _alpha + 1181569934729637614 _alpha)
\
|
exp(_alpha t)|
|
|
/
5 4 3 2
%1 := RootOf(500 _Z + 2280 _Z + 4537 _Z + 5495 _Z + 4666 _Z + 1962)
ans =
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