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Invisible oscillation (sometimes D term oscillation or yaw oscillation) generally cannot be seen or heard. One way you know you have it is that all throttle stick positions can act as if they were closer to the middle. Another way you know is if you have two FMS positions that use different PID banks (and manual thrust), and one set of PIDs has significantly lower D terms (or a lower yaw PID) and you are hovering and switch from one to the other, you may notice that you need to add power to maintain altitude. Increased thrust from the high D term / high yaw PID is caused by the ESCs being commanded up and down and being quicker when increasing RPM than when decreasing it. You may find that motors tend to run hotter and batteries don't last as long as they should. Powerful copters (those that require less than 50% power to hover) will take off with much less throttle than expected. Weak copters (those that require more than 50% power to hover) will need more power than expected to take off, or will not take off even at full power. Try reducing your D terms (Stabilization -> Advanced), reducing your yaw PID, or increasing (doubling) GyroTau (GCS -> Configuration -> Stabilization -> Expert > Gyro Noise Filtering), but realize that increasing GyroTau requires rerunning the AutoTune flight and will make AutoTune create very slow smooth PIDs.Oscillation can cause AutoTune to fail.
If your multicopter is already tuned and you reduce performance by adding weight like a camera or larger battery (with same cell count); or reducing power (fewer cells in battery, different props) then you have created an oscillation.
On the other hand, if you remove a camera from a multicopter that is tuned to fly with the camera (or generally do something to increase performance), it wont' oscillate, it just won't be quite as quick reacting as it could be. It will fly a bit "like it has a camera mounted" even when it doesn't. That isn't so bad.
So if you are only going to do one tune, then do it with the camera on. You can fly this tune with or without the camera. Be aware that PID banks are excellent for storing different PIDs if you want different tunes for e.g. with / without a camera. You can use one PID bank for with camera and one PID bank for without camera.
Oscillation can cause AutoTune to fail and even to crash. If you have a problem with oscillation, it must be corrected before running AutoTune. This is especially true of invisible oscillations if only because they are not obvious. This is also especially true if you are adding a camera to a multicopter that is already tuned.
Ringing (Attitude mode) is when you move the stick suddenly and it doesn't immediately settle at the new bank angle. Instead it oscillates a few times, but the oscillations die out quickly.
Assume that stock PIDs may oscillate or ring, especially with small multicopters or adding cameras. Cutting your R/P/Y PI's in half will usually remove oscillation or ringing and make it safe to run AutoTune.
If AutoTune internal sanity checks fail, it won't write PIDs. It's also possible to get PIDs that don't fly well. If you have a problem with oscillation, it must be corrected before running AutoTune. This is especially true of invisible oscillationsThis was more true in earlier versions of AutoTune.
This version of AutoTune puts the copter into a special version of Attitude flight mode that shakes the copter and measures the motions. As a pilot, you should be able to confidently fly in Attitude mode because it will be a bit more difficult than normal to maintain control. Tuning also needs a larger area than simple hovering. As a point of reference, a good pilot should be able to do a tuning in a single car garage stall.
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