How can I plot the transfer function? HELP Please.

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!

Answer 1

[Paul]

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

[hgrlk]

Thank you! :) I totally understand what you did. I think when I'm trying to get numerical values like KH, exp.. etc. in the function directly I got mistake.

The plot part is actually this; I must plot to these transfer function and also I must plot the step function which is amplitude 1. When I'm looking the documentation there is a code which is stepplot(F). But how can I plot the step function? I want it to reach an amplitude of 1 in 1 second.

The reason I do this will be to compare these two graphs.

About the step: https://www.mathworks.com/help/control/ref/lti.step.html

Answer 2

[Image Analyst]

You're using both p and s to describe the same p in the formula. Change s to p and I think it should work:

numerator = KH * ( TL*p + 1 ) * exp(-t*p)
term1 = TI*p + 1
term2 = p^2 / WN^2
term3 = 2 * zetaN * p / WN
denominator = term1 * (term2 + term3 + 1)
FH = numerator / denominator

If you'd rather call the independent variable s instead of p, then just change all the p to s.

numerator = KH * ( TL*s + 1 ) * exp(-t*s)
term1 = TI*s + 1
term2 = s^2 / WN^2
term3 = 2 * zetaN * s / WN
denominator = term1 * (term2 + term3 + 1)
FH = numerator / denominator

but don't mix s and p - that could be a disaster if they are separate variables and have different values.

[hgrlk]

I'm sorry, you're right. I've looking 2 different articles for the model function. That's why I accidently mixed s and p while writing the question. Actually they are the same.

The thing is, I understood what you did as numerator and denominator. But when I'm looking tf documentation (https://www.mathworks.com/help/control/ref/tf.html#mw_d0fa2ae4-8b6d-41ad-89ae-172b8422d0d6), it says that I must write numerator and denominator as just coefficients. For example;

numerator = 1;
denominator = [2,3,4];
sys = tf(numerator,denominator)
sys =
 
         1
  ---------------
  2 s^2 + 3 s + 4

When I try to seperate s parameter from the function and trying to get coefficient, everything just mixed up.

[Image Analyst]

Sorry, I don't know anything about that function. You'll just have to read the documentation or hope someone else knows about it.

[hgrlk]

Thank you! @Paul solved my problem. :)