[YZF]

I think the parent is saying something along the lines of "if you can look at your problem and determine there's no need for an integrator, or you can take the need out using feed forward, then you can remove the integrator" (or set your integral gain to zero). Keep in mind though the integral gain isn't simply acting to take out constant error, it changes the transfer function of the loop.

If you have a mathematical model for the thing you're controlling you can derive the PID parameters using that model. That's very rarely the case though and even with a model reality almost always differs.

The PID controller doesn't "care" about your knowledge. What it does "care" about is how the system responds to the control signal, specifically with linear systems the gain and phase for the different frequencies. If you're tuning a PID using some heuristics then the process of tuning includes the response of the system you're controlling. So at least intuitively I don't see an easy way to take some partial knowledge of the system and incorporate it into the tuning process. Maybe someone with experience can say something like "using less proportional gain and more integral gain results in better <something> for temperature control systems where there's a lot of energy loss due to gradient" but otherwise there's no easy way to tell IMO. If the integrator doesn't help you're probably going to discover that in the process of tuning anyways.

I think this knowledge is more useful in the context of a feed forward, i.e. if you have a good model of how your system behaves and you incorporate it into the feed forward part of your control loop then the residual error is going to be much smaller and you'll get better performance.