transfer fuction representation needed

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

need explanation

Answer 1

[Stephan]

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

[M S PRADEEP KUMAR PATNAIK]

Respected Stephan first of all thanks for spending your precious time for answering, actually I searched many sites but couldn't find the solution. You explained very briefly in detail. If interested then I want to get associated with you academically to enhance my skills...

[Stephan]

I think the better way is that you post questions here in the forum, to let others learn from them also.

[M S PRADEEP KUMAR PATNAIK]

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

can u explain what do you mean by sys=ss(sys), i want to know the value of (sys) in sys=ss(sys)?

even about a,b,c,d values..