Ingeniería de Sistemas 1.Reducción de diagramas de bloques en MatLab y Ejercicios Definición de las funciones de transferencia de cada bloque. n1 corresponde n1 = …; al numerador del bloque 1 y d1 a su denominador, n2 y d2 para el bloque 2 , d1 = …; etc. …; nblocks = …; Número total de bloques en el diagrama. Construir matrices de estado. blkbuild Definir interconexión de bloques. q = […….]; Bloque de entrada. input = …; Bloque de salida. output = …; Calcula el modelo del sistema en el espacio de estados connect Transforma función de variables de estado en función de transferencia en s. ss2tf Elimina los polos y ceros comunes. minreal Muestra el sistema. printsys
EJEMPLO R(s)
R(s)
1 1
>> >> >> >> >> >> >> >> >> >> >>
+
+
10 -
C(s)
s+5
10 -
C(s)
s+5
2
n1 = 1; d1 = 1; n2 = 10; d2 = [1 5]; 5]; nblocks = 2; blkbuild input = 1; output = 2; q = [2 1 –2]; [a,b,c,d] = connect (a,b,c,d,q,input,output); [num,den] = ss2tf (a,b,c,d); [num,den] = minreal (num,den); printsys (num,den);
C ( s ) R ( s )
=
10 s
+
15
EJERCICIO 1
R(s)
+
1 -
C(s)
10
s
s
+
5
1 s
+
C ( s )
2
=
R ( s )
10s + 20 s
3
+
7s 2
+
10 s + 10
EJERCICIO 2
4
R(s)
+
-
3
+
1 -
3
s+2
s+
+
4
C(s)
+
C ( s ) R ( s )
12 s + 57
=
s
2
+
7 s + 21
EJERCICIO 3 C ( s )
3s s
R(s)
+
-
+
+
R ( s )
1
8
-
+
+
1
s
2
4
+
28s 3
2
+ s +
+ +
18s 2
71s 2
+ +
C(s)
s
s
2 s
=
5s 3
10
16 s
224 s + 180
EJERCICIO 4
R(s)
1 +
-
+
-
s
+
+
1
+
s
-
C ( s ) R ( s )
=
C(s)
1
1 +
-
s
-
1 s
3
+
5s
2
7s + 3
+
EJERCICIO 5
25 s
R(s)
1
+
-
3
+
s
s
+
+
1
+
-
1
2
30
1 s
6
C ( s ) R ( s )
=
180s 3 s
4
+
1132 s 3
+
+
180s 2
1141s 2
+
120s + 60
1 s
C(s)
SOLUCION 1
n1 = [ 1] ; d1 = [ 1] ; n2 = [ 1] ; d2 = [ 1 0] ; n3 = [ 10] ; d3 = [ 1 5] ; n4 = [ 1] ; d4 = [ 1 2] ; nbl ocks = 4; bl kbui l d q = [ 2 1 - 4; 3 2 0; 4 3 0] ; i nput = 1; out put = 3; [ a, b, c , d] = c onnec t ( a, b, c , d, q, i nput , out put ) ; [ num, den] = ss2t f ( a, b, c, d) ; [ num, den] = mi nr eal ( num, den) ; pr i nt sys ( num, den) ;
SOLUCION 2
n1 = [ 3] ; d1 = [ 1] ; n2 = [ 1] ; d2 = [ 1 2] ; n3 = [ 4] ; d3 = [ 1] ; n4 = [ 3] ; d4 = [ 1 4] ; n5 = [ 1] ; d5 = [ 1] ; n6 = [ 1] ; d6 = [ 1] ; nbl ocks = 6; bl kbui l d q = [ 1 - 4 5; 2 1 - 2; 3 2 0; 4 2 0; 6 3 4] ; i nput = 5; out put = 6; [ a, b, c , d] = c onnec t ( a, b, c , d, q, i nput , out put ) ; [ num, den] = ss2t f ( a, b, c, d) ; [ num, den] = mi nr eal ( num, den) ; pr i nt sys ( num, den) ;
SOLUCION 3
n1 = [ 1] ; d1 = [ 1] ; n2 = [ 1] ; d2 = [ 1] ; n3 = [ 3 0] ; d3 = [ 1 1] ; n4 = [ 8] ; d4 = [ 1] ; n5 = [ 2] ; d5 = [ 1 2] ; n6 = [ 1 0] ; d6 = [ 1 1 10] ; n7 = [ 1] ; d7 = [ 1] ; nbl ocks = 7; bl kbui l d q = [ 2 1 - 6; 3 1 0; 4 2 - 5; 5 7 0; 6 7 0; 7 4 - 3] ; i nput = 1; out put = 6; [ a, b, c , d] = c onnec t ( a, b, c , d, q, i nput , out put ) ; [ num, den] = ss2t f ( a, b, c, d) ; [ num, den] = mi nr eal ( num, den) ; pr i nt sys ( num, den) ;
SOLUCION 4
n1 = [ 1] ; d1 = [ 1] ; n2 = [ 1] ; d2 = [ 1] ; n3 = [ 1] ; d3 = [ 1 1] ; n4 = [ 1] ; d4 = [ 1 0] ; n5 = [ 1] ; d5 = [ 1] ; n6 = [ 1] ; d6 = [ 1 0] ; nbl ocks = 6; bl kbui l d q = [ 2 1 - 6; 3 - 3 2; 4 3 - 5; 5 4 - 6; 6 5 - 6] ; i nput = 1; out put = 6; [ a, b, c , d] = c onnec t ( a, b, c , d, q, i nput , out put ) ; [ num, den] = ss2t f ( a, b, c, d) ; [ num, den] = mi nr eal ( num, den) ; pr i nt sys ( num, den) ;
SOLUCION 5
n1 = [ 1] ; d1 = [ 1] ; n2 = [ 3] ; d2 = [ 1] ; n3 = [ 1 0] ; d3 = [ 1 1] ; n4 = [ 2] ; d4 = [ 1] ; n5 = [ 30] ; d5 = [ 1] ; n6 = [ 1] ; d6 = [ 1 0] ; n7 = [ 25] ; d7 = [ 1 1] ; n8 = [ 1] ; d8 = [ 1 0] ; n9 = [ 6] ; d9 = [ 1] ; nbl ocks = 9; bl kbui l d q = [ 2 1 - 9; 3 2 - 7; 4 3 - 8; 5 4 0; 6 5 0; 7 4 0; 8 6 0; 9 6 0] ; i nput = 1; out put = 6; [ a, b, c , d] = c onnec t ( a, b, c , d, q, i nput , out put ) ; [ num, den] = ss2t f ( a, b, c, d) ; [ num, den] = mi nr eal ( num, den) ; pr i nt sys ( num, den) ;
