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What do the PID gains do?
This helped scratch the surface of what's going on >>
I know it is a bit confusing, but in the context of pypilot since it is commanding the rate of change of rudder, the P, D, DD gains would translate to I, P, D gains for absolute movement.
This also explains why the I gain is typically zero, but it is useful if you want to avoid average error always slightly port or starboard (but you can also compensate this factor by commanding a slightly different course)

The absolute pilot is different as it commands absolute rudder position, but this actually uses nested PID filters as one is needed just to set the position of the rudder, and the other to determine what the position should be. This could in theory give slightly better performance assuming everything is correctly tuned as it makes use of rudder feedback to eliminate integration error, but this is only a small factor (perhaps 10%) of the error the pilot must correct for in normal use which is why most autopilots do not require rudder feedback as the potential performance improvement is difficult to notice.

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