My aim is to keep temperature constant at a certain place. I don't have a mathematical model of the plant.
Currently, PID is used with some fixed Kp, Ki, and Kd, and I want to optimize these parameters for a stable system. PID is giving output to a non-linear control valve which is used to control a temperature by changing the flow of water.
The error input to the PID controller, control valve opening, and actual output temperature are available to me. For example, setpoint of 980 °C, actual output 998 °C, error -18 °C, valve opening 33%. I have many data points like this available to me.
I am confused what is my system here, the control valve which is injecting water for the corresponding PID input or the place where I want to keep the temperature constant?
Is it possible to tune the PID from the following data and get the plant model?