rewrite system Then we should get its cascade form structure containing second-order sections ( Do not use any Matlab structure-function such as tf2sos, dir2cas,dir2par etc..)

This question needs to be solved by using Matlab

Given the overall system function;

Then we should get its cascade form structure containing second-order sections ( Do not use any Matlab structure-function such as tf2sos, dir2cas,dir2par etc..)

you can use conv function or residuez function.

I have no idea how to do this, please help me!

Answer 1

[SAI SRUJAN]

Hi Xuejian,

I understand that you are facing an issue solving the transfer function in MATLAB.

Compute the partial-fraction expansion described by the transfer function.This can be achieved by expressing both the numerator and the denominator as convolutions of polynomials. Utilize the 'residuez' function within MATLAB to resolve the equation.

Please go through the following code to proceed further,

% numerator
b = [3.5 9.45 17.3 22.15 18.73 11.02 3.67 1.3 0.72];
% denominator
a = [1 0.9 1.8 0.53 1.44 0.378 0.82 -0.116 0.448 -0.1152];

[r,p,k] = residuez(b,a);

zplane(b,a)
hold on
plot(p,'^r')
hold off

For a comprehensive understanding of the 'conv' and 'residuez' functions in MATLAB, please refer to the following documentation.

https://www.mathworks.com/help/matlab/ref/conv.html

https://www.mathworks.com/help/signal/ref/residuez.html

I hope this helps!