%%Creating transfer function from numerator and denominator num=[1 0 1]; %%s^2+1

Question

%%Creating transfer function from numerator and denominator
num=[1 0 1]; %%s^2+1
den=[1 0 0 1]; %%s^3+1
H=tf(num,den);
%%compute the residue
[r p k]=residue(num,den); %%residue, poles and system gain

%%Create transfer function from poles and zeros
p=[1 2]; %% poles
z=[0]; %%zeros
k=1; %%gain
H=zpk(z,p,k); %%transfer function
[num den]=zp2tf(z,p,k); %%get coefficients from the system
%%compute the residue
[r p k]=residue(num,den); %%residue, poles and system gain

. Use MATLAB's residue function can be used to directly compute the poles and the residues of the following transfer functions. You have pair the residue with the corresponding pole. (2X10-20 points) s2 +3s+Z Obtain the coefficients from the transfer function and calculate residue from them. (s1)

Explanation / Answer

a ) matlab code :

b = [1 3 2];
a = [1 1 1 1];
[r,p,k] = residue(b,a)

Result:

r =

-0.0000 + 0.0000i
0.5000 - 1.0000i
0.5000 + 1.0000i

p =

-1.0000 + 0.0000i
0.0000 + 1.0000i
0.0000 - 1.0000i

k =

[]

(1) 1 / (s + 1) ,

(2) (0.5000 - 1.0000i) / (s - 0.0000 -1.0000i ) ,

(3) (0.5000 +1.0000i) / ( s - 0.0000 + 1.0000i )

b ) matlab code

b = [1 2 1];
a = [1 0 4 0 0];
[r,p,k] = residue(b,a)

result :

r =

-0.2500 - 0.1875i
-0.2500 + 0.1875i
0.5000 + 0.0000i
0.2500 + 0.0000i

p =

0.0000 + 2.0000i
0.0000 - 2.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i

k =

[]

(1 ) ( -0.2500 - 0.1875i ) / ( s - 2i)

(2 ) ( -0.2500 + 0.1875i ) / ( s + 2i)

(3) ( 0.500 ) / ( s - i)

(3) ( 0.2500 ) / ( s - i)

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