# What does s = tf ('s') do?

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Leonardo Wayne on 1 Apr 2017
Commented: Walter Roberson on 28 Jan 2019
I am currently doing an exercise in PID control, the first line in the code is
s = tf ('s');
What does it do? according to Mathworks website:
sys = tf(M) creates a static gain M (scalar or matrix)
from what I know that tf is supposed to create a transfer function with a denominator and numerator. what does static gain mean?

Star Strider on 1 Apr 2017
Using:
s = tf('s');
allows you to enter the transfer function in the next line in symbolic form rather than as numerator and denominator vectors. You can easily recover the numerator and denominator vectors from the system object created:
s = tf('s');
sys = (244.2*s + 244.2) / (0.015*s^4 + 1.525*s^3 + 2.51*s^2 + 245.2*s + 1221);
num = [sys.Numerator{:}]
den = [sys.Denominator{:}]
num =
0 0 0 244.2 244.2
den =
0.015 1.525 2.51 245.2 1221

Rik on 1 Apr 2017
You could think of this as something similar to uint8(5). It is a way to generate a variable with the correct data-type, so you can more easily manipulate it. Static gain in this case means that you have a transfer function that simply multiplies your input with a number and does nothing else.
Walter Roberson on 28 Jan 2019
not really . the 's' is detected specially. The static gain situation only applies for numeric input.

Janakiraman S on 28 Jan 2019
It creates a continuous time function of variable s (to be given as a text input in quotes) which can be used in defining transfer funtion models
Matlab code and result
s=tf('s')
s =
s
Continuous-time transfer function.