Conversion from State Space to TF and then back to State Space

I created a state space model with 2 inputs 4 outputs 4 states

used the

if true
sys_tf = tf(sys);
end

function to convert SS to tf. sys_tf comes out to a 4 X 2 matrix

Once I obtained this TF I added a PID feedback control to sys_tf(1,2) and sys_tf(3,2). Now when I convert this sys_tf to a state space model using

if true
  [A,B,C,D] = ssdata(sys_tf);
  sys1 = ss(A,B,C,D);
end

This creates s state space model with 2 inputs, 4 outputs and 30states. Why and how is this happening.

Thanks. Shilp

[Arkadiy Turevskiy]

can you paste your code?

[Shilp Dixit]

if true
sys_mimo = SS(A, B, C, D, 'statename',states,...
  'inputname',inputs,...
  'outputname',outputs);
size(sys_mimo)
sys_mimo_tf = tf(sys_mimo);
Kd = 208025;
Kp = 832100;
Ki = 624075;
C = pid(Kp,Ki,Kd);
sys_mimo_tf(1,2) = sys_mimo_tf(1,2)*feedback(sys_mimo_tf(1,2),C);
% PID control for sys_mimo_tf(3,2)
Kd = 208;
Kp = 83;
Ki = 624;
C = pid(Kp,Ki,Kd);
sys_mimo_tf(3,2) = sys_mimo_tf(3,2)*feedback(sys_mimo_tf(3,2),C);
[A,B,C,D] = SSDATA(sys_mimo_tf);
sys_mimo1 = ss(A,B,C,D);
size(sys_mimo1)
end

Answer 1

[Jonathan Epperl]

Some points:

Don't do "algebra" with tf variables, use the functions series, parallel and feedback.

sys_mimo1 = ss(sys_mimo) is going to convert the tf model to a ss model, I don't think there is a need for the extra step with ssdata.

This one here

sys_mimo_tf(1,2) = sys_mimo_tf(1,2)*feedback(sys_mimo_tf(1,2),C);

is probably not doing what you want it to, it will give you the transfer function

sys_mimo_tf(1,2)^2 /  1 + sys_mimo_tf(1,2)*C

so that's probably where many extra states come from. You should expect 2 extra states per added PID.

Lastly, look at the Hankel Singular Values or a similar measure to figure out whether there might be a lot of almost unobservable/almost uncontrollable states in your resulting model. That would indicate numerical issues.

[Shilp Dixit]

Thank you... Will do as you suggested.