Ingeniería de Sistemas

1.Reducción de diagramas de bloques en MatLab y Ejercicios

n1 = …; d1 = …; …;

Definición de las funciones de transferencia de cada bloque. n1 corresponde al numerador del bloque 1 y d1 a su denominador, n2 y d2 para el bloque 2 , etc.

nblocks = …; Número total de bloques en el diagrama. blkbuild Construir matrices de estado. q = […….]; Definir interconexión de bloques. input = …; Bloque de entrada. output = …; Bloque de salida. connect Calcula el modelo del sistema en el espacio de estados ss2tf Transforma función de variables de estado en función de transferencia en s. minreal Elimina los polos y ceros comunes. printsys Muestra el sistema.

EJEMPLO

+ - R(s) C(s)

510+s

+ - R(s) C(s)

510+s

1

1

2

>> n1 = 1; d1 = 1; >> n2 = 10; d2 = [1 5];

1510

)()(

+=

ssRsC>> 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);

101072010

)()(

23 ++++

=sss

ssRsC

2175712

)()(

2 +++

=ss

ssRsC

180224712816185

)()(

234

23

++++++

=ssss

ssssRsC

13+ss

+ - + - +-8102 ++ ss

s

2s2+

1

C(s)R(s)

+ R(s)

- C(s)

510+ss

1

1+s

EJERCICIO 1

2

EJERCICIO 2

+ - +++ - R(s)

4

21+s 4

3+s

3C(s)

EJERCICIO 3

R(s) 1

1+s s

1s1 C(s)

-+-+-++ - + -

EJERCICIO 4

375)( +++ ssssR1)(

23=sC

EJERCICIO 5

+ -

s1

+ -

+ -

125+s

1+ss

s12 303

6

1C(s)R(s)

6012011411132180180

)()(

234

23

+++++

=ssss

sssRsC

SOLUCION 1 n1 = [1]; d1 = [1]; n2 = [1]; d2 = [1 0]; n3 = [10]; d3 = [1 5]; n4 = [1]; d4 = [1 2]; nblocks = 4; blkbuild q = [2 1 -4; 3 2 0; 4 3 0]; input = 1; output = 3; [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); 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]; nblocks = 6; blkbuild q = [1 -4 5;2 1 -2; 3 2 0; 4 2 0; 6 3 4]; input = 5; output = 6; [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); 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]; nblocks = 7; blkbuild q = [2 1 -6; 3 1 0; 4 2 -5; 5 7 0; 6 7 0; 7 4 -3]; input = 1; output = 6; [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);

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]; nblocks = 6; blkbuild q = [2 1 -6; 3 -3 2; 4 3 -5; 5 4 -6; 6 5 -6]; input = 1; output = 6; [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); 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]; nblocks = 9; blkbuild 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]; input = 1; output = 6; [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);