How to simplify transfer function？

Hi guys

I have used the function

 s=tf('s')

to ceate a transfer function, but I find that Matlab do not simplify the tf at all.

for example.

s=tf('s');
A=1/(1+s);B=A/(1+A);

the result is 1+s/(s^2+3*s+2)

What I want is 1/(2+s)

Anyone know that how to simplify the tf in Matlab?

Thank you!

[Paul]

Use the feedback - Feedback connection of multiple models - MATLAB command.

s=tf('s');
A=1/(1+s); %B=A/(1+A);
B = feedback(A,1)

B = 
    1
  -----
  s + 2
 
Continuous-time transfer function.

Answer 1

[Thomas]

Try

s=tf('s');
A=1/(1+s);B=A/(1+A);
minreal(B)

[tqy]

Thanks a lot.

But in another case, I have to set the tolerance so that I can get what I want.

I think Matlab only keeps the default effective bit of the a number.

[Tim]

Looks like a solution to my problem, however I need to find variables from a rewritten tf.

I have a tf G like below

    lsys = ss(A B C D); % were all matrices are 3x3
    G = tf(lsys);
from which I am intersted in rewriting G(2,2)

G(2,2)=

    1.422e-05 s + 4.696e-06
    -----------------------
     s^2 + 21.76 s + 1.216
into

      a * (b*s + 1)
    -----------------
     (c*s +1)*(d*s+1)
to yield constants a b c d
MatLab does not accept 

minreal(G(2,2));

any suggestions?

Answer 2

[Artur Araujo]

You could try H = zpk(G(2,2))

[Zuhair Abduljabbar]

Thanks

[Anish Mitra]

In addition to this, you can set the DisplayFormat of the zpk model to 'timeconstant' which would show it in the format needed when displayed in the Command Window.

s = tf('s');
G = (1.422e-5*s + 4.696e-6)/(s^2 + 21.76*s + 1.216);
G_zpk = zpk(G);
G_zpk.DisplayFormat = 'timeconstant';
disp(G_zpk);

   3.8618e-06 (1+3.028s)
  -----------------------
  (1+0.04607s) (1+17.85s)
 
Continuous-time zero/pole/gain model.

If you want to store the time constants in variables, you can use zpkdata to first extract the zeros and poles and the compute it using those.

 [z,p,k] = zpkdata(G_zpk,'v');
 tau_z = -1./z

tau_z = 3.0281

 tau_p = -1./p

tau_p = 2×1

0.0461 17.8487

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Note that for a general approach you will have to account for complex poles and zeros.