Problem in conversion the state-space of the system to transfer function

I want to return the state-space to transfer function, if the system reduced is by balanced real technique.

I have this code

   s=tf('s');
   G=(s^3+11*s^2+36*s+26)/(s^4+14.6*s^3+74.96*s^2+156.7*s+99.65);
   [A,B,C,D]=ssdata(G);
   [AA, BB, CC,DD] = balreal(A, B, C);
   [b,a] = ss2tf(AA,BB,CC,DD);

if i want to convert state-space representation to transfer function using the function 'ss2tf', i find this error :

Error using ss2tf (line 26)
The C and D matrices must have the same number of rows.

Can any one help me how can i solve this error ?

Answer 1

[Stephan]

Hi,

this appears to run:

s=tf('s');
G=(s^3+11*s^2+36*s+26)/(s^4+14.6*s^3+74.96*s^2+156.7*s+99.65);
[sys,g] = balreal(G);
[b,a] = ss2tf(sys.A, sys.B, sys.C, sys.D);

result is:

>> transfun = tf(a,b)

transfun =

    s^4 + 14.6 s^3 + 74.96 s^2 + 156.7 s + 99.65
    --------------------------------------------
              s^3 + 11 s^2 + 36 s + 26

Continuous-time transfer function.

Best regards

Stephan

[Sandi J]

I used 'balreal' function for reduced original system to system with low order, which i want, but you found original system ,why?

[Stephan]

Hi,

then use modred to reduce the system, by using the result g of balreal :

s=tf('s');
G=(s^3+11*s^2+36*s+26)/(s^4+14.6*s^3+74.96*s^2+156.7*s+99.65);
[sys,g] = balreal(G);
elim = g < 10e-4;
rsys = modred(sys,elim);
[b, a] = ss2tf(rsys.A, rsys.B, rsys.C, rsys.D);
transfun = tf(b,a);

You can control the order of the resulting system with the bound you set on elim variable by:

elim = g < 10e-4;

Before reduction g is:

g =

      0.1374
      0.0069
      0.0003
      0.0002

If elim has 2 entries after setting the bound by using:

elim = g < 10e-4;

elim =

    4×1 logical array

     0
     0
     1
     1

then your resulting system has order 2:

transfun =

    -0.0001171 s^2 + 0.9978 s + 1.119
    ---------------------------------
          s^2 + 4.634 s + 4.288

If you change the value for g to a bigger value:

elim = g < 10e-3;

elim =

    4×1 logical array

     0
     1
     1
     1

and your resulting system has order 1:

transfun =

-0.01389 s + 1.174
------------------
    s + 4.498

So this is how you can control, what modred does in detail.

Best regards

Stephan