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>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold off; >> grid

>> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

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Page 1: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

>> Kp=100;

>> num=[Kp];

>> den=[1 10 20+Kp];

>> t=0:0.01:2;

>> step(num,den,t);

>> hold on;

>> Kp=300;

>> num=[Kp];

>> den=[1 10 20+Kp];

>> t=0:0.01:2;

>> step(num,den,t);

>> hold off;

>> grid

Page 2: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

>> Kp=30;

>> Ki=70;

>> num=[Kp Ki];

>> den=[1 10 20+Kp Ki];

>> t=0:0.01:2;

>> step(num,den,t)

>> hold on;

>> Ki=100;

>> num=[Kp Ki];

>> den=[1 10 20+Kp Ki];

>> step(num,den,t)

>> hold off;

>> grid

Page 3: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

>> Kp=300;

>> Kd=10;

>> num=[Kd Kp];

>> den=[1 10+Kd 20+Kp];

>> t=0:0.01:2;

>> step(num,den,t)

>> hold on;

>> Kd=20;

>> num=[Kd Kp];

>> den=[1 10+Kd 20+Kp];

>> step(num,den,t)

>> hold off;

>> grid

Page 4: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];
Page 5: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];
Page 6: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Ejercicio 1:

Determinar la función de compensación para un tiempo de asentamiento a la mitad de Ts del

sistema y un % de sobreimpulso del 15%

)1)(10)(3(

1)(

ssssG+

-

X(s) Y(s) K

Page 7: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 8: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 9: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 10: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 11: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 12: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 13: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL Ejercicio:

Determinar la función de compensación para un tiempo de asentamiento a la mitad de Ts del

sistema y un % de sobreimpulso del 15%

Page 14: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 15: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL Determinar la función de compensación para un tiempo de asentamiento a la mitad de Ts

del sistema y un % de sobreimpulso del 15%

Tasentamiento = Ts/2 = 3,35/2 = 1,675

Page 16: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 17: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 18: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

SISOTOOL

Page 19: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Ejercicio 2:

Diseñar un controlador PI

)1)(130)(110(

10)(

ssssG+

-

X(s) Y(s)

Page 20: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];
Page 21: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Recordemos que, en una constante de tiempo se alcanza cuando se logra 63,2% del cambio total

Con tiempo muerto

Page 22: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Para una K=10

Para t1 : 10*0,283 = 2,83

Para t2 : 10*0,632 = 6,32

Para 2.8301 t1 = 20.2365

De modo similar:

Para 6.32 t2 = 42.5340

Page 23: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

τ = 1,5*(42.5340-20.2365) = 33.44625 Entonces:

d = 42.5340 - 33.44625 = 9.08775

Ahora:

PI:

* Kp = [0.9*(33.44625/9.08775)]/10

= 0.33119584

* Ki = Kp/Ti

Ti = 9.08775/0.3 = 30.2925

Ki = 0.33119584/30.2925 = 0.010933262

PID:

* Kp = [1.2*(33.44625/9.08775)]/10

= 0.4416439713

* Ki = Kp/Ti

Ti = 2*9.08775 = 18.1755

Ki = 0.4416439713/18.1755 = 0.02429886228

*Kd = Kp*Td

Td = 0.5*9.08775 = 4.543875

Kd = 0.4416439713*4.543875 = 2.006775

Kp = Kp

Ki = Kp/Ti

Kd = Kp*Td

Sabemos que:

Page 24: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Para el PI:

Page 25: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

Para el PID:

Page 26: >> den=[1 10 20+Kp]; >> step(num,den,t); >> den=[1 10 20 ... · PDF file>> Kp=100; >> num=[Kp]; >> den=[1 10 20+Kp]; >> t=0:0.01:2; >> step(num,den,t); >> hold on; >> Kp=300; >> num=[Kp];

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