how to get tf answer for this problem?

a=[40]

a = 40

b=[0.05 1]

b = 1×2

0.0500 1.0000

c=[1]

c = 1

d=[0.5 1]

d = 1×2

0.5000 1.0000

e=[0.8]

e = 0.8000

f=[1 1]

f = 1×2

1 1

g=[0.1]

g = 0.1000

h=[0.04 1]

h = 1×2

0.0400 1.0000

T1=tf(a,b)

T1 =
 
      40
  ----------
  0.05 s + 1
 
Continuous-time transfer function.

T2=tf(c,d)

T2 =
 
      1
  ---------
  0.5 s + 1
 
Continuous-time transfer function.

T3=tf(e,f)

T3 =
 
   0.8
  -----
  s + 1
 
Continuous-time transfer function.

T4=tf(g,h)

T4 =
 
     0.1
  ----------
  0.04 s + 1
 
Continuous-time transfer function.

A=(T1*T2*T3)

A =
 
                  32
  ----------------------------------
  0.025 s^3 + 0.575 s^2 + 1.55 s + 1
 
Continuous-time transfer function.

B=(T1*T2*T4)

B =
 
                  4
  ----------------------------------
  0.001 s^3 + 0.047 s^2 + 0.59 s + 1
 
Continuous-time transfer function.

C=1+B+A

C =
 
  2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.5701 s^3 + 5.341 s^2 + 27.22 s + 37
  -------------------------------------------------------------------------------
   2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.4381 s^3 + 1.537 s^2 + 2.14 s + 1
 
Continuous-time transfer function.

A/C

ans =
 
                         0.0008 s^6 + 0.056 s^5 + 1.386 s^4 + 14.02 s^3 + 49.17 s^2 + 68.48 s + 32
  ------------------------------------------------------------------------------------------------------------------------
  6.25e-07 s^9 + 5.813e-05 s^8 + 0.002128 s^7 + 0.0419 s^6 + 0.5302 s^5 + 4.678 s^4 + 25.42 s^3 + 68.81 s^2 + 84.57 s + 37
 
Continuous-time transfer function.

 i want A to be like this 32/((1+.05s)(1+0.5s)(1+s)) is this possible

Answer 1

[Star Strider]

Almost.

Use the zpk function to do the format transformation.

a=[40];
b=[0.05 1];
c=[1];
d=[0.5 1];
e=[0.8];
f=[1 1];
g=[0.1];
h=[0.04 1];


T1=tf(a,b);
T2=tf(c,d);
T3=tf(e,f);
T4=tf(g,h);
A=(T1*T2*T3)

A =
 
                  32
  ----------------------------------
  0.025 s^3 + 0.575 s^2 + 1.55 s + 1
 
Continuous-time transfer function.

Azpk = zpk(A)

Azpk =
 
         1280
  ------------------
  (s+20) (s+2) (s+1)
 
Continuous-time zero/pole/gain model.

B=(T1*T2*T4)

B =
 
                  4
  ----------------------------------
  0.001 s^3 + 0.047 s^2 + 0.59 s + 1
 
Continuous-time transfer function.

Bzpk = zpk(B)

Bzpk =
 
         4000
  -------------------
  (s+25) (s+20) (s+2)
 
Continuous-time zero/pole/gain model.

C=1+B+A

C =
 
  2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.5701 s^3 + 5.341 s^2 + 27.22 s + 37
  -------------------------------------------------------------------------------
   2.5e-05 s^6 + 0.00175 s^5 + 0.04333 s^4 + 0.4381 s^3 + 1.537 s^2 + 2.14 s + 1
 
Continuous-time transfer function.

Czpk = zpk(C)

Czpk =
 
  (s+34.37) (s+20) (s+8.593) (s+2) (s^2 + 5.036s + 125.3)
  -------------------------------------------------------
               (s+25) (s+20)^2 (s+2)^2 (s+1)
 
Continuous-time zero/pole/gain model.

AC = A/C

AC =
 
                         0.0008 s^6 + 0.056 s^5 + 1.386 s^4 + 14.02 s^3 + 49.17 s^2 + 68.48 s + 32
  ------------------------------------------------------------------------------------------------------------------------
  6.25e-07 s^9 + 5.813e-05 s^8 + 0.002128 s^7 + 0.0419 s^6 + 0.5302 s^5 + 4.678 s^4 + 25.42 s^3 + 68.81 s^2 + 84.57 s + 37
 
Continuous-time transfer function.

ACzpk = zpk(AC)

ACzpk =
 
                 1280 (s+25) (s+20)^2 (s+2)^2 (s+1)
  -----------------------------------------------------------------
  (s+34.37) (s+20)^2 (s+8.593) (s+2)^2 (s+1) (s^2 + 5.036s + 125.3)
 
Continuous-time zero/pole/gain model.

Amr = minreal(A)

Amr =
 
            1280
  ------------------------
  s^3 + 23 s^2 + 62 s + 40
 
Continuous-time transfer function.

Amrzpk = zpk(Amr)

Amrzpk =
 
         1280
  ------------------
  (s+20) (s+2) (s+1)
 
Continuous-time zero/pole/gain model.

Bmr = minreal(B)

Bmr =
 
             4000
  ---------------------------
  s^3 + 47 s^2 + 590 s + 1000
 
Continuous-time transfer function.

Bmrzpk = zpk(Bmr)

Bmrzpk =
 
         4000
  -------------------
  (s+25) (s+20) (s+2)
 
Continuous-time zero/pole/gain model.

Cmr = minreal(C)

Cmr =
 
  s^5 + 50 s^4 + 733 s^3 + 8144 s^2 + 5.074e04 s + 7.4e04
  -------------------------------------------------------
     s^5 + 50 s^4 + 733 s^3 + 2864 s^2 + 4180 s + 2000
 
Continuous-time transfer function.

Cmrzpk = zpk(Cmr)

Cmrzpk =
 
  (s+34.37) (s+8.593) (s+2) (s^2 + 5.036s + 125.3)
  ------------------------------------------------
            (s+25) (s+20) (s+2)^2 (s+1)
 
Continuous-time zero/pole/gain model.

ACmr = minreal(AC)

ACmr =
 
                1280 s^3 + 8.32e04 s^2 + 1.792e06 s + 1.28e07
  --------------------------------------------------------------------------
  s^6 + 88 s^5 + 2957 s^4 + 5.155e04 s^3 + 566600 s^2 + 4.228e06 s + 1.48e07
 
Continuous-time transfer function.

ACmrzpk = zpk(ACmr)

ACmrzpk =
 
                 1280 (s+25) (s+20)^2
  ---------------------------------------------------
  (s+34.37) (s+20)^2 (s+8.593) (s^2 + 5.036s + 125.3)
 
Continuous-time zero/pole/gain model.

.

[arian hoseini]

can we do something about (s+20)^2

the answer i need is this1280(s + 25)/( s 4 + 48s 3 + 637s 2 + 6870s + 37000)

by the way thank u ...ur solution is perfect

[Star Strider]

My pleasure!

The form you need is not an option in any of the representations I looked through. The zpk representation is as close as it is possible to get. Dividing the transfer function by (s+20)^2 changes nothing about it.

If you absolutely must have that representation, you will need to write it yourself, or possibly use the Symbolic Math Toolbox. Special representations such as that are simply not possible in the Control System Toolbox.

s = tf('s');
a=[40];
b=[0.05 1];
c=[1];
d=[0.5 1];
e=[0.8];
f=[1 1];
g=[0.1];
h=[0.04 1];


T1=tf(a,b);
T2=tf(c,d);
T3=tf(e,f);
T4=tf(g,h);
A=(T1*T2*T3);
% Azpk = zpk(A);

B=(T1*T2*T4);
% Bzpk = zpk(B)

C=1+B+A;
% Czpk = zpk(C)

AC = A/C;
% ACzpk = zpk(AC)

% Amr = minreal(A)
% Amrzpk = zpk(Amr)

% Bmr = minreal(B)
% Bmrzpk = zpk(Bmr)

% Cmr = minreal(C)
% Cmrzpk = zpk(Cmr)

ACmr = minreal(AC);
ACmrzpk = zpk(ACmr)

ACmrzpk =
 
                 1280 (s+25) (s+20)^2
  ---------------------------------------------------
  (s+34.37) (s+20)^2 (s+8.593) (s^2 + 5.036s + 125.3)
 
Continuous-time zero/pole/gain model.

.