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Codes Results: Num (0 0 2 1) Den (6 10 20 5) Printsys (Num, Den,)

The document contains code that defines and analyzes various continuous-time transfer functions using MATLAB. It defines transfer functions using the tf() function, converts them to other representations like zpk models and state-space, and takes the Laplace transform. Key steps include defining a transfer function, obtaining its poles and zeros, converting it to alternative models, and taking the Laplace inverse to find the impulse response.

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Manzur Prokorsho
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76 views5 pages

Codes Results: Num (0 0 2 1) Den (6 10 20 5) Printsys (Num, Den,)

The document contains code that defines and analyzes various continuous-time transfer functions using MATLAB. It defines transfer functions using the tf() function, converts them to other representations like zpk models and state-space, and takes the Laplace transform. Key steps include defining a transfer function, obtaining its poles and zeros, converting it to alternative models, and taking the Laplace inverse to find the impulse response.

Uploaded by

Manzur Prokorsho
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Codes Results

num=[0 0 2 1] num/den =
den=[6 10 20 5]
printsys(num, den, 's')
2s+1
-------------------------
6 s^3 + 10 s^2 + 20 s + 5

>> num=[0 0 2 1]; num/den =


den=[6 10 20 5];
printsys(num, den, 's'); 2s+1
sys=tf(num, den) -------------------------
6 s^3 + 10 s^2 + 20 s + 5

sys =

2s+1
-------------------------
6 s^3 + 10 s^2 + 20 s + 5

Continuous-time transfer function.

>> num=[0 0 2 1];


den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den)
step(num,den)
num=[0 0 2 1]; r=
den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den); -0.0137 - 0.1026i
step(num,den); -0.0137 + 0.1026i
[r,p,k]=residue(num,den) 0.0275 + 0.0000i
root=roots(r)

p=

-0.6917 + 1.5694i
-0.6917 - 1.5694i
-0.2833 + 0.0000i

k=

[]
num=[0 0 2 1]; root =
den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den); 1.0000 + 0.0000i
step(num,den); -0.0352 + 0.2629i
[r,p,k]=residue(num,den)
root=roots(r) >>

num=[0 0 2 1]; system =


den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den); 10 (s+2)
step(num,den); -----------------
[r,p,k]=residue(num,den); (s+3) (s+5) (s+1)
root=roots(r);
system = zpk([-2], [-3 -1 -5], 10) Continuous-time zero/pole/gain model.

num=[0 0 2 1]; system =


den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den); 10 (s+2) (s+1)
step(num,den); -----------------
[r,p,k]=residue(num,den); (s+3) (s+5) (s+1)
root=roots(r);
system = zpk([-2 -1], [-3 -1 -5], 10) Continuous-time zero/pole/gain model.
num=[0 0 2 1];
den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den);
step(num,den);
[r,p,k]=residue(num,den);
root=roots(r);
system = zpk([-2 -1], [-3 -1 -5], 10)
step(system)

num=[0 0 2 1]; system2 =


den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den); 10 s^2 + 20 s + 30
step(num,den); -----------------------
[r,p,k]=residue(num,den); s^3 + 9 s^2 + 23 s + 15
root=roots(r);
system = zpk([-2 -1], [-3 -1 -5], 10) Continuous-time transfer function.
step(system)
system2=tf([0 10 20 30], [1 9 23 15])

num=[0 0 2 1];
den=[6 10 20 5];
printsys(num, den, 's');
sys=tf(num, den);
step(num,den);
[r,p,k]=residue(num,den);
root=roots(r);
system = zpk([-2 -1], [-3 -1 -5], 10)
step(system)
system2=tf([0 10 20 30], [1 9 23 15])
step(system2)
s=sym('s')
system3=(10*s^2+30*s+20/(s^3+9*s^2+23*s+15))

system3 =

30*s + 20/(s^3 + 9*s^2 + 23*s + 15) + 10*s^2


pretty(system3) system3 =

30*s + 20/(s^3 + 9*s^2 + 23*s + 15) + 10*s^2

20 2
30 s + --------------------- + 10 s
3 2
s + 9 s + 23 s + 15
ilaplace(system3) >> ilaplace(system3)

ans =

(5*exp(-t))/2 - 5*exp(-
3*t) + (5*exp(-5*t))/2 +
30*dirac(1, t) +
10*dirac(2, t)

t=sym('t') 2*exp(-t) - 2*t*exp(-2*t)


f=2*exp(-t)-2*t*exp(-
2*t)
laplace(t)
pretty(laplace(t)) ans =

1/s^2

1
--
2
s

>>
system1=tf([0 0 1], [2 system1 =
20 10])
1
-----------------
2 s^2 + 20 s + 10

Continuous-time
transfer function.

[A,B,C,D]=tf2ss([0 0 A=
1], [2 20 10])
-10 -5
1 0

B=

1
0

C=

0 0.5000
D=

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