How can I plot the transfer function?

hgrlk · Nov 22, 2022 · 2.3K views
Question
Hello, I have a problem with plot the transfer function. I have to plot the precision model's transfer function. To understand my function and precision model, I'll insert a photo. Here, I must use numerator = []; denominator = []; sys = tf(numerator,denominator) stepplot(sys) But I cannot write the numerator and denominator. I have numerator = KH * ( TL*s + 1 ) * exp(-t*s) and denominator = ( TI*s + 1 ) * ( ( (p^2) / (WN^2) ) + ( ( (2*zetaN) / (WN) ) * p ) + (1). As I understand, I must write these numerator and denominator as coefficients of s variable. But I couldn't write. Could you help me please? How can I plot the transfer function?   Also, I want to plot step function with 1 amplitude for compare it with transfer function. How can I do that? Is it just step(sys)?? Is this the same thing with stepplot? If you could help me, I will be very glad. Thanks!  
Expert Answer
Profile picture of Prashant Kumar
Prashant Kumar PhD Expert
Answered Aug 20, 2026

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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