How to know the gain value used in this controller when I know the input and output of the pid controller

I only know the input data of the pid controller and the output data obtained through the controller.

How can I know the gain value used in this controller when I know the input and output of the pid controller

After using tfestimate function, I wonder what to do next in details

Answer 1

[Christopher McCausland]

Mathematically speaking gain is the output divided by the input of a system. The next question is if this produces a linear or non-linear response. If you know the topology of the PID controller you should be able to generate the complete transfer function and work from there.