How can I plot the transfer function?

Prashant Kumar answered . 2024-12-21 01:50:11

Because you want to make plots, I'm going to assume that you have numerical values for each parameter in your model. For example, suppose we have:

 Kh = 2; Tl = 1; Ti = 0.5; wn = 1; zetan = 0.7; tau = 0.2;

At this point, there are several options to form the transfer function F(s). Perhaps the easiest is to start with a product of low order terms:

>> F = Kh*tf([Tl 1],[Ti 1])*tf(1,[1/wn^2 2*zetan/wn 1])

F =
 
             2 s + 2
  -----------------------------
  0.5 s^3 + 1.7 s^2 + 1.9 s + 1
 
Continuous-time transfer function.

 

Now the only part that is missing is the exp(-tau*s). That can be included by either setting the 'InputDelay' or 'OutputDelay' property of F or by mutiplying F by exp(-tau*s) explicilty. For example of the latter:

>> F = F*exp(-tau*tf('s'))

F =
 
                           2 s + 2
  exp(-0.2*s) * -----------------------------
                0.5 s^3 + 1.7 s^2 + 1.9 s + 1
 
Continuous-time transfer function.

If you'd rather see F expressed in terms of the variable p, you can do:

>> F.Variable='p'

F =
 
                           2 p + 2
  exp(-0.2*p) * -----------------------------
                0.5 p^3 + 1.7 p^2 + 1.9 p + 1
 
Continuous-time transfer function.

which is just for display purposes and doesn't change any mathematical properties of F. It's not clear what is meant by "plot the ... transfer function." Once F is defined, all sorts of different plots can be developed, most typically:

doc bode
doc step
doc impulse

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