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It’s been years since I took controls classes.
Does this help? https://ctms.engin.umich.edu/CTMS/index.php?example=Introduction§ion=ControlPID
I’m not sure if your asking about the math or how to implement your k values into the controller.
I’m just passing by from the homepage of lemmy
Upvote just for that link I hand it out every time I get asked a controls question
But yea another guy drifting in from the homepage who normally works with physical systems where I can assume I'm in the continuous domain and can do the PID loop with a fast enough computer / sensors.
That said seems like the relationship poles / zeros and your physical components are given by the set of equations found in eq 4 of your second link.
Assuming you used, something like desired second order behavior (%OS, settling time etc), pole placement or lqr methods to pick where those poles should be for your desired system performance you should be able to plug those poles/ zeros in with one real component value to nail something to reality then solve for the rest.
Again you'll probably get values that are stupid specific and you'll round up or down to get things you actually can buy or have on hand and you'll recompute the poles and zeros and see how far off you are from your goal. Provided they aren't shifted tooff the right hand side of the plane you can test or simulate to make sure you meet your minimal performance requirements.
Edit shifted left to right damn I should do control theory rants at 11pm
Lol this is probably a major shot in the dark, because I have no idea what you're talking about. But incase it helps lol, I remember at uni, a lecturer talking about PID once, and they changed the time to 1 second, and since you don't need to multiply/divide by 1, it reduced the complexity of the algebra.
(You can also use a base of that like 0.001 or whatever and multiply it back out).
Again no idea if this has anything to do with it but yeah.