Building a transfer function.

   Function I want to build is this:
           Gp(s)
   ----------------------
     1 + Gc(s)Gp(s)H(s)

              1                      
   Gp(s) =   ----      Gc(s) =  0.8(s+12.5)  H(s) = 1 
            s(s+10)

However, I can't seem to construct the transfer function due to Gp(s) being a fraction over itself.

My attempts at doing so do not result in the same answer as when I calculate it manually.

Thanks!

Answer 1

[Robert U]

Hi Jason Gauthier,

I do not see any troubles in constructing the transfer function you wrote above:

 Gp = tf(1, [1 10 0]);
 Gc = 0.8*tf([1 12.5],1);
 H = tf(1,1);
 Gp/(1 + Gc*Gp*H)

Result:

 >> ans =

             s^2 + 10 s
  --------------------------------
  s^4 + 20.8 s^3 + 118 s^2 + 100 s

Continuous-time transfer function.

The result shows the transfer function without cancelling poles and zeros. If you do so, you come up with the same transfer function behaviour:

 bodeplot(Gp/(1+Gc*Gp*H))
 hold on
 bodeplot(tf(1,[1 10.8 10]))

Kind regards,

Robert

[Jason Gauthier]

Thanks. The example I had is using a method that includes conv(), and it wasn't clear. I was able to produce the same output by building the transfers function like this:

s= tf('s')
Gp = (1/(s*(s+10))

But, one of the requirements presented was to build a function that accepted the numerator and denominator as arguments, of Gp, and Gc. Your method was much better for this, because I can provide those and build the transfer function out of them directly.

Thanks for presenting me with (yet) another method to accomplish this!

[Robert U]

Hi Jason Gauthier,

Thank you for your positive feedback. If you like my answer, please, vote for it by clicking on the "thumb up"-symbol.

In case it serves your needs and answers your question thoroughly, accept it.

Kind regards,

Robert

Answer 2

[Thembelani]

1/43.79s + 1