Searched several topics, but in particular have not found how I'm thinking about this.

Intuition suggests:

- Each P, I, D should be minimized to tighten the control.

No, you tune the values for good performance, ie _maximizing_ without bounds set by unstability and noise

- P (proportional gain - potential height of oscillations) should require a minimum multiple of the precision of measurement (if input measurement has 1 decimal of precision eg- 35.3°c, then P could be +/- 2.0°c or something, but if precision is no decimal eg- 35°c, then 2° P would not be reasonable and should be bigger. Of course P would also need a minimum based on the potential rate of change and ability to control the set point.

Have you played with PID control and seen how each parameter works in reality? I'm struggling to understand

this posting.

Typical approach is start P only, increase till marginally stable, backoff. Add D until noise becomes an issue,

backoff. Repeat till P+D are maximized without those constraints. Add I to improve accuracy and settling

(but this affects stability so P and D need re-tweaking to control oscillation).

With a non-linear system like heater control, everything is a big compromise because cooling response is not

the same as heating response. More advanced modelling of state can improve things, but your basic way to get things to work is to turn down the overall gain to regain stability at the expense of settling time - so long as

you have some I-term the system's steady state will converge.

For simple linear control like with a servomotor, tuning is pretty intuitive once you understand what each term

does.

You soon discover using PIDs that you have to handle integral-windup intelligently if there are step

changes of setpoint - the I term is only useful in settling performance and works against you when

out of equilibrium. Either have special handling to cancel integral windup, or prevent step changes

in setpoint (ie turn them into slew-rate limited ramps that don't generate unlimited wind-up).