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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

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  • $\begingroup$ So there is a PID controller active on the system, but you can't look up its gains directly and wish to derive them from data obtained from the physical closed loop system? So you know the error signal going into the controller and the generated signals going out of the controller? $\endgroup$
    – fibonatic
    Aug 4, 2021 at 10:21

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There are methods to determine PID gains, but they require online testing. If you're not willing (or able) to do the testing with a real system then you would need to create a mathematical model of your system and do the tuning in a virtual environment. How appropriate your virtual gains are to your physical system depends on how well your model represents reality.

All real systems are going to have some degree of measurement noise or other inaccuracies, so you can approach that by implementing a filter to try to reduce the effects of noise on your readings.

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