MATLAB: Transfer fuction representation needed

Control System Toolboxtransfer function

sys = ss(tf({1,1,1},{[1 .5 1],[1 1],[.7 .5 1]}));
need explanation

Best Answer

Hi,
this is a compact way to express 1 transfer function with 3 inputs and convert it to a state space representation.You can find this also as an similar example in the documentation of tf function for the case of 2 outputs. Consider:
>> sys = tf({1,1,1},{[1 .5 1],[1 1],[.7 .5 1]})
sys =
 
  From input 1 to output:
         1
  ---------------
  s^2 + 0.5 s + 1
 
  From input 2 to output:
    1
  -----
  s + 1
 
  From input 3 to output:
           1
  -------------------
  0.7 s^2 + 0.5 s + 1
 
Continuous-time transfer function.
Now with the ss function, the 1x3 transfer function is converted to the correspondig state space representation of the system:
>> sys = ss(sys)
sys =
 
  A = 
            x1       x2       x3       x4       x5
   x1     -0.5       -1        0        0        0
   x2        1        0        0        0        0
   x3        0        0       -1        0        0
   x4        0        0        0  -0.7143   -1.429
   x5        0        0        0        1        0
 
  B = 
       u1  u2  u3
   x1   1   0   0
   x2   0   0   0
   x3   0   1   0
   x4   0   0   1
   x5   0   0   0
 
  C = 
          x1     x2     x3     x4     x5
   y1      0      1      1      0  1.429
 
  D = 
       u1  u2  u3
   y1   0   0   0
 
Continuous-time state-space model.
The code you posted in your question just combines both steps in one line of code.
sys = ss(tf({1,1,1},{[1 .5 1],[1 1],[.7 .5 1]}));
Best regards
Stephan
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