Programs To Find Transfer Function For The Block Diagram Using Block Diagram Reduction - Control Systems Lab - MSRIT - RIT

Hi!

BLOCK DIAGRAM REDUCTION:
1.



 display('controller')
n1=[1 2];d1=[1 3];
g1=tf(n1,d1)
display('plant')
n2=[1 1];d2=[1 6 8];
g2=tf(n2,d2)
display('resultant transfer function')
gs=series(g1,g2)

COMMAND WINDOW:
controller
g1 =
   s + 2
  -----
  s + 3
Continuous-time transfer function.
plant
g2 =
       s + 1
  -------------
  s^2 + 6 s + 8
 Continuous-time transfer function.
resultant transfer function
gs =
        s^2 + 3 s + 2
  -----------------------
  s^3 + 9 s^2 + 26 s + 24
 Continuous-time transfer function.

2 -


 Editor -

n1=1;d1=[1 1];
display('tf1 is:')
printsys(n1,d1);
n2=[1 2];d2=[0 1];
display('tf2 is:')
printsys(n2,d2);
n3=[1 0];d3=[1 0 2];
display('tf3 is:')
printsys(n3,d3);
n4=[1 0];d4=[0 1];
display('tf4 is:')
printsys(n4,d4);
[n5,d5]=parallel(n1,d1,n2,d2);
printsys(n5,d5);
[n6,d6]=feedback(n3,d3,n4,d4);
printsys(n6,d6);
[n7,d7]=series(n5,d5,n6,d6);
display('overall transfer function is:')
printsys(n7,d7);
pzmap(n7,d7);
sgrid;

Command Window -

tf1 is:

num/den = 

     1
   -----
   s + 1
tf2 is:

num/den = 

   s + 2
   -----
     1
tf3 is:

num/den = 

      s
   -------
   s^2 + 2
tf4 is:

num/den = 

   s
   -
   1

num/den = 

   s^2 + 3 s + 3
   -------------
       s + 1

num/den = 

       s
   ---------
   2 s^2 + 2
overall transfer function is:

num/den = 

      s^3 + 3 s^2 + 3 s
   -----------------------

   2 s^3 + 2 s^2 + 2 s + 2



3 -


Editor


n1=[1 0];d1=[1 0 1];
g1=tf(n1,d1)
n2=[1 2];d2=[1];
g2=tf(n2,d2)
n3=[1];d3=[1 1];
g3=tf(n3,d3)
n4=[1 0];d4=[1 0 2];
g4=tf(n4,d4)
n5=[1 0];d5=1;
h1=tf(n5,d5)
gp1=parallel(g2,g3)
gs1=series(g1,g4)
gt1=series(gp1,gs1)
display('the overall transfer function is:')
T=feedback(gt1,h1)

COMMAND WINDOW:
g1 =
     s
  -------
  s^2 + 1
 Continuous-time transfer function.
g2 =  s + 2
Continuous-time transfer function.
g3 =
    1
  -----
  s + 1
 Continuous-time transfer function.
g4 =
     s
  -------
  s^2 + 2
Continuous-time transfer function.
h1 =  s
 Continuous-time transfer function.
gp1 =
   s^2 + 3 s + 3
  -------------
      s + 1
 Continuous-time transfer function.
gs1 =
       s^2
  ---------------
  s^4 + 3 s^2 + 2
 Continuous-time transfer function.
gt1 =
           s^4 + 3 s^3 + 3 s^2
  -----------------------------------
  s^5 + s^4 + 3 s^3 + 3 s^2 + 2 s + 2
 Continuous-time transfer function.
the overall transfer function is:
T =            s^4 + 3 s^3 + 3 s^2
  ---------------------------------------
  2 s^5 + 4 s^4 + 6 s^3 + 3 s^2 + 2 s + 2
 Continuous-time transfer function.
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