# Proposing a Transfer Function from a Response Graph

I need to propose a transfer function from the following graph. The K value (or amplifier gain?) we were given is 2 and it has a step response of 2 as well. When looking at the graph though it looks as if the K value we were given is incorrect if it has an output voltage of around 5v. Can anyone help me propose a transfer function for this? Or point me to some resources that could show me?

A generic, first order transfer function is expected to be of the form $$\frac{K}{\tau s + 1}$$ and I expected K = 5/2.

• The K value is 2 and the driving input step is 2 volts. Commented Nov 30, 2022 at 11:07
• K is in reference to the amplifier gain. Not really sure how to attach an image to this comment. New here Commented Nov 30, 2022 at 16:55
• Additional information is to be directly added to the question using edit option below the question. Comments may get deleted automatically and should not be relied on to deliver additional information.
– AJN
Commented Nov 30, 2022 at 16:58
• My reasoning in thinking it was incorrect is that in a generic tranfer function K is the numerator (K/s*tau+1). So how could K be equal to 2 if it is equal to Vout/Vin (5/2)? Commented Dec 1, 2022 at 18:17
• OK. That is why I requested for context on the question. if your problem is solved, please self answer the question in sufficient detail, below for people visiting this page in the future.
– AJN
Commented Dec 2, 2022 at 2:30

## 1 Answer

Sorry, I have to answer rather than comment as I'm a noob as well. Are you asking in general for a transfer function, or are you after some PID controller TF?

https://www.youtube.com/watch?v=F4w0rslb04E seems to go into excessive detail (I didn't watch the whole thing) but should cover your question.

• Ah thanks very much, I'll watch that tonight. Commented Nov 30, 2022 at 11:08