Modelagem e sistemas dinamicos

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modelagem e sistemas dinâmicos

SIMULAR a curva

 t=0:0.1:10; y=0.5-0.5*exp(-2*t); plot(t,y) xlabel('Tempo [seg]') ylabel('Resposta y(t)') 1-b) Usando FUNÇÃO de TRANSFERÊNCIA vs. MATLAB: num=[1]; den=[1 2]; step(num,den); % Entrada =1/s

1ª)

>> t=0:0.1:10;

>> y= 0.5-0.5*exp(-2*t);

>> plot (t,y)

>> xlabel ('tempo [seg]')

>> ylabel ('resposta y(t)')

[pic 1]

1b)

>> num=[1]

num =

     1

>> den=[1 2]

den =

     1     2

>> step(num,den); %entrada =1/s

>>

[pic 2]

2) questão de número 2

SIMULAR:

 a=0.1 ; b=10; t=0:0.1:15; y=(2*a+b)*exp(-t)-(a+b)*exp(-2*t); plot(t,y) grid xlabel('Segundos') ylabel('Resposta y(t)') FUNÇÃO de TRANSFERÊNCIA vs. MATLAB: num=[a b+3*a]; den=[1 3 2]; impulse(num,den)

>> a=0.1;

b=10;

t= 0:0.1:15;

Y=(2*a+b)*exp(-t)-(a+b)*(-2*t);

>> plot(t,Y)

>> grid

>> xlabel('segundos')

>> ylabel ('resposta y(t)')

[pic 3]Resposta ao impulso...

>> num=[a b+3*a];

>> den= [1 3 2];

>> impulse(num,den)

[pic 4]

3)

A Resposta: y(t) , usando Matlab: b=1; k=10; m=5; num=[b k]; den=[m b k]; impulse(num,den) R= roots(den) R = -0.1000 + 1.4107i -0.1000 - 1.4107i P=poly(R) P = 1.0 0.20 2.0

>> b=1;

>> k=10;

>> m=5;

>> num= [b k];

>> den= [m b k];

>> impulse (num,den)

[pic 5]

>> R=roots(den)

R =

  -0.1000 + 1.4107i

  -0.1000 - 1.4107i

>> p=poly (R)

p =

    1.0000    0.2000    2.0000

4) caso 1...

Resposta:

 f(t) , usando MATLAB: R=[0 -1 -3]; poly(R) ans = 1 4 3 0 num=[1 2]; den=[1 4 3 0]; impulse(num,den) You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com) Simulando uma entrada senoidal t=0:0.1:10; u=sin(2*pi*t) lsim(num,den,u,t) Dado o sistema (caso 2) R=[-2 -2 -2 -3]; poly(R) ans = 1 9 30 44 24 num=[1]; den=[1 9 30 44 24]; impulse(num,den) hold on step(num,den) lsim(num,den,u,t)

>> r=[0 -1 -3];

>> poly(r)

ans = 1     4     3     0

>> num=[1 2];

>> den=[1 4 3 0];

>> impulse (num,den)

[pic 6]

>> T=0:0.1:10;

>> u=sin(2*pi*T);

>> lsim (num,den,u,T)

[pic 7]

b) segundo caso...

>> R=[-2 -2 -2 -3];

poly(R)

ans =

     1     9    30    44    24

>> num=[1];

>> den= [1 9 30 44 24];

>> impulse (num,den)

>> hold on

>> step(num,den)

[pic 8]

[pic 9]

...