Maybe your project needs Fuzzy logic

[rtek1000]

This Issue is just a small suggestion for those who are having difficulties in starting the controller operation, with very high Overshoot (probably due to the integral term that will accumulate a lot, while the system is still far out of the operating range, for example a cold oven).

I once saw a group present a course conclusion work, about Fuzzy logic being present in a crockpot, in conjunction with PID. This helped me to avoid Overshoot on a gas heater control, which I mounted. There was a lot of Overshoot, so I remembered this Fuzzy logic and tried to implement something similar, so that Overshoot would not occur anymore, I did something like setting the Setpoint value of the PID control gradually, in order to go up automatically without OverShut.

https://en.wikipedia.org/wiki/Fuzzy_control_system

https://www.omega.com/en-us/resources/pid-fuzzy-logic-adaptive-control