MATLAB: Is there a way to extract the 3 transfer function in matlab given these equations.

MATLABtransfer function

I have these 3 equations

X1(s)*[m1*s^2 + c1*s+(k01+k12)] = F(s) + k12*X2(s)

X2(s)*[m2*s^2 + c2*s +(k12+k23)] = k12*X1(s)+k23*X3(s)

X3(s) [m3*s^2 + c3*s +(k23+k34)] = k23*X2(s)

and I am wondering if there is a possibility to be able to extract my 3 transfer functions, X1(s)/F(s), X2(s)/F(s), and X3(s)/F(s).

Ive really havent explore this part of Matlab and am interested to know if it is possible. I ask because currently I am doing it by hand and setting the left side S polynomial to be P1, P2, and P3 respectively.

but it is alot of algabra and I fear I will make a simple arithmetic mistake and ruin the whole thing.

Can this be done.

Best Answer

Hi Jorje German,

The transfer functions for your case in given in the first column of the

matrix. You can use the functions in Symbolic Math toolbox to simplify the rational expressions. Hope my answer helps.

Related Solutions

MATLAB: Convert state-space representation (MIMO) to transfer function matrix

https://www.mathworks.com/help/matlab/ref/ss2tf.html

But if you have an existing ss system created with https://www.mathworks.com/help/control/ref/ss.html then use tf()

A = [-1.5,-2;1,0];
B = [0.5;0];
C = [0,1];
D = 0;
sys = ss(A,B,C,D)
sys =
 
  A = 
         x1    x2
   x1  -1.5    -2
   x2     1     0
 
  B = 
        u1
   x1  0.5
   x2    0
 
  C = 
       x1  x2
   y1   0   1
 
  D = 
       u1
   y1   0
 
Continuous-time state-space model.
sys_as_tf = tf(sys)
sys_as_tf =
 
        0.5
  ---------------
  s^2 + 1.5 s + 2
 
Continuous-time transfer function.

MATLAB: Can a descriptor state space change into transfer function representaion

The easiest way to determine that (or anything else that is not explicitly documented) is to try it and see the result.

A=[-10 -35 -50 -24;1 0 0 0;0 1 0 0; 0 0 1 0 ];
B=[1 0; 0 1; 1 1; 1 0];
C=[1 -1 0 1;0 1 1 1];
E=eye(4);
D=0;
H=dss(A,B,C,D,E);
figure
bode(H)
Htf = tf(H);
figure
bode(Htf)

These seem to be the same to me.

EDIT — (21 Jun 2020 at 20:15)

The ‘Htf’ transfer functions are:

Htf =
 
  From input 1 to output...
          2 s^3 - 64 s^2 + 95 s + 110
   1:  ---------------------------------
       s^4 + 10 s^3 + 35 s^2 + 50 s + 24
 
           2 s^3 + 22 s^2 + 7 s + 38
   2:  ---------------------------------
       s^4 + 10 s^3 + 35 s^2 + 50 s + 24
 
  From input 2 to output...
           -s^3 - 94 s^2 - 13 s + 45
   1:  ---------------------------------
       s^4 + 10 s^3 + 35 s^2 + 50 s + 24
 
           2 s^3 + 22 s^2 + 6 s + 21
   2:  ---------------------------------
       s^4 + 10 s^3 + 35 s^2 + 50 s + 24
 
Continuous-time transfer function.

Different format, same result.

Best Answer

Related Solutions

MATLAB: Convert state-space representation (MIMO) to transfer function matrix

MATLAB: Can a descriptor state space change into transfer function representaion

Related Question