Question

Solve the following using MATLAB:

3. Consider the transfer function: H S ) = 6 2s2 + 6s 2s4 + 8 s +3 .4 L + 3 a) Write lines of code to find the zeros and poles of the above transfer function. b) Write lines of code to find a partial fraction expansion of the above transfer function.

Answer 1

[10:33 pm, 28/04/2020] Computer Sir: MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the numerator and denominator polynomial coefficients
num = 6*[2 6 0];
den = [2 0 0 8 3];

% Question a
% obtain the zeros
zeros = roots(num) % Zeros are nothing but the roots of the numerator polynomial
poles = roots(den) % poles are nothing but the roots of the denominator polynomial

% Question b
% partial fraction expansion
[r,p,k] = residue(num,den) % This gives the residues, poles and gain

RESULTS:

zeros =

0
-3

poles =

0.9076 + 1.3876i
0.9076 - 1.3876i
-1.4349
-0.3802

r =

-0.0712 - 2.8830i
-0.0712 + 2.8830i
1.7234
-1.5811

p =

0.9076 + 1.3876i
0.9076 - 1.3876i
-1.4349
-0.3802

k =

[]

The partial fraction expansion is given by:

H(s) = (-0.0712 - 2.8830i)/(s - ( 0.9076 + 1.3876i)) + (-0.0712 + 2.8830i)/(s-(0.9076 - 1.3876i)) + 1.7234 /( s+1.4349)   

-1.581 /( s+-0.3802)