Plant Model/ Transfer Function for PID loop code


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When a transfer function is determined from a plant model for a control system. If Laplace transforms are used does one apply the PID equation (position or velocity) to the transformed plant directly or does it have to be converted back to the time domain?

Also does one have to take the difference of equations to dynamically asses the error term? I'm trying to avoid the standard "cookbook" PID code and get something that is specific to my system being measured (temp controller). Any clarification on this manner would be greatly appreciated.
I have posted and continue to post an article that I think is relevant to your question. One of the most effective ways to arrive at a reliable pid equation for your process is to model your process with a FOPDT equation. This can be done with a step test. Once you have a FOPDT equation for your process, it is easy to arrive at a PID equation that works.

Pls see: