It is definitely true for a few simple cases where the model producing simulated gain values can get pretty close, but there's an entire sub-discipline of contr

It is definitely true for a few simple cases where the model producing simulated gain values can get pretty close, but there's an entire sub-discipline of controls theory dedicated to the trade-offs of the various tuning methodologies [1][2] because for most real-world situations, you can't predict the system response for any given set of values accurately enough to be useful. You can get the initial values set from first principles by checking your poles to avoid clear regions of instability, but once you're past that point, I believe that it's mathematically true that you can't truly find the correct gains only from first principles. If I'm missing something in the formal background, though, I'd love to hear it. My own implementation of digital PID controllers have been based on using Ziegler-Nichols for tuning bc I was under the impression above. Any literature or methods contrary to that would definitely be welcome! (Edited because my first line didn't make any sense) [1] https://pages.mtu.edu/~tbco/cm416/tuning_methods.pdf https://pages.mtu.edu/~tbco/cm416/tuning_methods.pdf [2] https://en.wikipedia.org/wiki/PID_controller#Loop_tuning https://en.wikipedia.org/wiki/PID_controller#Loop_tuning