Lol. There is an entire field dedicated to this question. It's called Automatic Control. Yes, you can do all of the above. You need to model it with a multivariable system. Google control systems and systems theory.
Usually in a physical control system (that is driven by a PID controller) your limiting factors are the execution element (how fast can you change the input) and your sensors (the resolution of the transducers/sensors dictate the resolution of what you can achieve). A lot of times the PID controller will have a way that it can autotune itself as it's extremely rare to be able to measure the properties of the physical system precisely and for those properties to not vary with temperature and with wear and tear.
Well, you kind of prove my point, because you made me jump from a 5 minute lecture about PIDs to a study about control systems.
Yes, probably there are all kinds of systems to control and autotune a PID. But that's the problem. In gamedev, PID's get constantly recommended for so many things, but when you play around with them you soon realize, that they are quite hard to get right. So then there's two ways: you dive into control systems or you just lerp the value and call it a day.
yup. i get it. it's a steep learning curve. and it's hard to grok if you don't understand what the theory behind them is.
My bigger point is that the articles like the one linked here just barely scratch the surface and you cannot really jump into it and get an intuitive understanding by just looking at it. that being said, if you want to learn more you can and they can be applied to a large range of problems.
Control theorist here. The articles are pretty good. There is nothing wrong with them.
What you are insinuating is not always correct that if you model stuff you'll get a better result. Sometimes PID is more then enough and in fact better since your model can get arbitrarily complex and you don't have any tools to deal with that behavior. It's a bit snobbish that you need to have math and all the shenanigans. The rest of the manufacturing world disagrees with your premise that is very common in academic circles.
Usually in a physical control system (that is driven by a PID controller) your limiting factors are the execution element (how fast can you change the input) and your sensors (the resolution of the transducers/sensors dictate the resolution of what you can achieve). A lot of times the PID controller will have a way that it can autotune itself as it's extremely rare to be able to measure the properties of the physical system precisely and for those properties to not vary with temperature and with wear and tear.