Objective functions in PID theory are used as a performance criteria.

The five most common ones are:

- ISE (Integral of the Square Error)

- IAE (Integral of Absolute Magnitude of Error)

- ITSE (Integral of Time multiplied by the Square Error)

- ITAE (Integral of Time multiplied by the Absolute Error)

- MSE (Mean of the Square Error)

As for the code, which program do you prefer?

In Python for instande, you have the easy-to-use "simple-pid" package - https://pypi.org/project/simple-pid/