Download - Problemas de Laplace y Fracciones Parciales
CRISTIAN QUISPE VENTURA
CÓDIGO: 12190027
CURSO: LABORATORIO DE SISTEMAS DE CONTROL 1
TEMA: TRANSFORMADA DE LAPLACE Y FRACIONES PARCIALES INFORME 3
PROFESOR: HILDA
DESARROLLO DEL CUESTIONARIO:
OBTENER LA TRANSFORMADA DE LAPLACE, SUS GRÁFICOS RESPECTIVOS DE LAS SIGUIENTES FUNCIONES TEMPORALES.
a) x1(t) = t^ (2)
t=sym('t');
s=sym('s');
xt=t^2;
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
2/s^3
b) x2(t) = sen (3t)
t=sym('t');
s=sym('s');
xt=sin (3*t);
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
3/(s^2 + 9)
c) x3(t) = cos (2t)
>> t=sym('t');
s=sym('s');
xt=cos (2*t);
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
s/(s^2 + 4)
d) x4(t) = sen (2t) +2t
>> t=sym('t');
s=sym('s');
xt= sin (2*t) +2*t;
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
2/(s^2 + 4) + 2/s^2
e) x5(t) = sen (3t)+cos (2*t)+exp (t)
>> t=sym('t');
s=sym('s');
xt= sin (3*t)+cos (2*t)+exp (t) ;
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
1/(s - 1) + s/(s^2 + 4) + 3/(s^2 + 9)
f) x6(t) = (t^2) cos2t
>> t=sym('t');
s=sym('s');
xt= (t^2)*cos(2*t) ;
xs=laplace(xt)
figure(1)
ezplot(xs),grid
xlabel('s')
figure(2)
ezplot(xt),grid
xlabel('tiempo (t)')
xs =
(8*s^3)/(s^2 + 4)^3 - (6*s)/(s^2 + 4)^2
OBTENER LA TRANSFORMADA INVERSA DE LAPLACE DE LOS RESULTADOS ANTERIORES:
>> t=sym('t'); s=sym('s');
xt=t^2;
xs=laplace(xt)
xt=ilaplace(xs)
xs =
2/s^3
xt =
t^2
>> t=sym('t'); s=sym('s');
xt=sin(3*t);
xs=laplace(xt)
xt=ilaplace(xs)
xs =
3/(s^2 + 9)
xt =
sin(3*t)
>> t=sym('t'); s=sym('s');
xt=cos(2*t);
xs=laplace(xt)
xt=ilaplace(xs)
xs =
s/(s^2 + 4)
xt =
cos(2*t)
>> t=sym('t'); s=sym('s');
xt=sin(2*t)+2*t;
xs=laplace(xt)
xt=ilaplace(xs)
xs =
2/(s^2 + 4) + 2/s^2
xt =
2*t + sin(2*t)
>> t=sym('t'); s=sym('s');
xt=sin(3*t)+cos(2*t)+exp(t) ;
xs=laplace(xt)
xt=ilaplace(xs)
xs =
1/(s - 1) + s/(s^2 + 4) + 3/(s^2 + 9)
xt =
cos(2*t) + sin(3*t) + exp(t)
>> t=sym('t');
s=sym('s');
xt= (t^2)*cos(2*t) ;
xt=ilaplace(xs)
xt =
t^2*cos(2*t)
HALLAR LAS FRACCIONES PARCIALES Y LA FUNCIÓN EN EL TIEMPO DE LOS SIGUIENTES EJERCICIOS.
Fs = (s2+2s+2) / (s + 1)
>> Ns = [1 2 2];
Ds = [1 1];
[r,p,k]=residue(Ns,Ds)
r =
1
p =
-1
k =
1 1
Fs = (2S +4) / (S^2 + 1)(S + 3)^2
>> Ns = [2 4];
expand((s + 3)^2);
d1 = [1 0 1];
d2 = [1 6 9];
Ds=conv(d1,d2);
[r,p,k]=residue(Ns,Ds)
r =
0.0800 + 0.0000i
-0.2000 + 0.0000i
-0.0400 - 0.2200i
-0.0400 + 0.2200i
p =
-3.0000 + 0.0000i
-3.0000 + 0.0000i
-0.0000 + 1.0000i
-0.0000 - 1.0000i
k =
[]
Fs = (s^2 + 4s + 8) / (s + 2)(s+4)^3
>> Ns = [1 4 8];
expand((s + 4)^3);
d1 = [1 2];
d2 = [1 12 48 64];
Ds=conv(d1,d2);
[r,p,k]=residue(Ns,Ds)
r =
-0.5000
-0.0000
-4.0000
0.5000
p =
-4.0000
-4.0000
-4.0000
-2.0000
k =
[]
Fs = (s+4) / (s^2 + 6s +25)
>> Ns = [1 4];
Ds = [1 6 25];
[r,p,k]=residue(Ns,Ds)
r =
0.5000 - 0.1250i
0.5000 + 0.1250i
p =
-3.0000 + 4.0000i