Matrix of transfer functions

How do I define a matrix whose arrays are different transfer functions. I would like to do matrix multiplication and inversion later. I would like to avoid using symbolic definition of transfer functions.

[CONGBO BAO]

Hi, Dear Davood;

I am facing the same problem.

Did you solve it?

Yours sincerely

Answer 1

[Robert U]

Hi Davood Raoofsheibani,

you can define arrays of transfer functions similar to numeric arrays by using tf():

% define array
A = [tf([1],[1/(2*pi*24e3) 2/(2*pi*12e3) 1]), tf([1],[1/(2*pi*12e3) 2/(2*pi*8e3) 1]);...
     tf([1],[1/(2*pi*6e3) 2/(2*pi*12e3) 1]), tf([1],[1/(2*pi*12e3) 2/(2*pi*12e3) 1])];
% use operations on array
A^2

ans =
 
  From input 1 to output...
                                      3.958e-10 s^4 + 1.759e-09 s^3 + 5.305e-05 s^2 + 0.0001194 s + 2
   1:  ------------------------------------------------------------------------------------------------------------------------------
       1.547e-20 s^8 + 1.857e-19 s^7 + 6.417e-15 s^6 + 5.424e-14 s^5 + 9.236e-10 s^4 + 4.75e-09 s^3 + 5.306e-05 s^2 + 0.0001194 s + 1
 
                                       5.277e-10 s^4 + 1.935e-09 s^3 + 7.295e-05 s^2 + 0.0001061 s + 2
   2:  -------------------------------------------------------------------------------------------------------------------------------
       6.189e-20 s^8 + 4.951e-19 s^7 + 1.867e-14 s^6 + 9.799e-14 s^5 + 1.847e-09 s^4 + 5.805e-09 s^3 + 7.295e-05 s^2 + 0.0001061 s + 1
 
  From input 2 to output...
                                       2.639e-10 s^4 + 1.495e-09 s^3 + 4.642e-05 s^2 + 0.0001326 s + 2
   1:  -------------------------------------------------------------------------------------------------------------------------------
       1.547e-20 s^8 + 1.857e-19 s^7 + 5.833e-15 s^6 + 5.133e-14 s^5 + 7.917e-10 s^4 + 4.574e-09 s^3 + 4.643e-05 s^2 + 0.0001326 s + 1
 
                                       5.277e-10 s^4 + 2.111e-09 s^3 + 6.632e-05 s^2 + 0.0001194 s + 2
   2:  -------------------------------------------------------------------------------------------------------------------------------
       6.189e-20 s^8 + 4.951e-19 s^7 + 1.633e-14 s^6 + 9.566e-14 s^5 + 1.583e-09 s^4 + 5.981e-09 s^3 + 6.632e-05 s^2 + 0.0001194 s + 1
 
Continuous-time transfer function.

s = tf('s');
A.*s

ans =
 
  From input 1 to output...
                      s
   1:  -------------------------------
       6.631e-06 s^2 + 2.653e-05 s + 1
 
                      s
   2:  -------------------------------
       2.653e-05 s^2 + 2.653e-05 s + 1
 
  From input 2 to output...
                      s
   1:  -------------------------------
       1.326e-05 s^2 + 3.979e-05 s + 1
 
                      s
   2:  -------------------------------
       1.326e-05 s^2 + 2.653e-05 s + 1
 
Continuous-time transfer function.

A^(-1)

ans =
 
  From input 1 to output...
       8.842e-06 s^6 + 7.074e-05 s^5 + 2.334 s^4 + 11 s^3 + 1.759e05 s^2 + 3.519e05 s + 3.79e09
   1:  ----------------------------------------------------------------------------------------
                        s^4 + 3.333 s^3 + 7.54e04 s^2 + 5.027e04 s + 4.403e-07
 
       -4.421e-06 s^6 - 3.979e-05 s^5 - 1.333 s^4 - 7.667 s^3 - 1.257e05 s^2 - 3.519e05 s - 3.79e09
   2:  --------------------------------------------------------------------------------------------
                          s^4 + 3.333 s^3 + 7.54e04 s^2 + 5.027e04 s + 4.403e-07
 
  From input 2 to output...
       -8.842e-06 s^6 - 6.189e-05 s^5 - 2.333 s^4 - 9.333 s^3 - 1.759e05 s^2 - 3.016e05 s - 3.79e09
   1:  --------------------------------------------------------------------------------------------
                          s^4 + 3.333 s^3 + 7.54e04 s^2 + 5.027e04 s - 3.418e-07
 
       1.768e-05 s^6 + 0.0001061 s^5 + 3.334 s^4 + 12.67 s^3 + 2.011e05 s^2 + 3.519e05 s + 3.79e09
   2:  -------------------------------------------------------------------------------------------
                         s^4 + 3.333 s^3 + 7.54e04 s^2 + 5.027e04 s - 3.418e-07
 
Continuous-time transfer function.

Kind regards,

Robert