A metric of a physical system is being controlled by a PID controller (in this case a valve controls the temperature of a liquid by mixing hot liquid into a stream of cold liquid). All measurement data regarding the valve, temperatures etc. is given, however, there is a certain error included.
I would like to calculate the PID parameters used, but for every time step it varies a little because of the error. Can I use optimization to find the best solution for the respective timeframe, and if yes, how do I use it?
PS. I do possess proficiency in Python and Excel