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Old Aug 27, 2011, 11:28 PM
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PID coefficients

A collection of links about PIDs and tuning

1) http://www.rcgroups.com/forums/showp...postcount=7460

2) http://www.multiwii.com/software
PID controller involves three separate parameters: the term Proportional, the term Integral and the term Derivative. The variation of each of these parameters alters the effectiveness of the stabilization.

Applied to a multirotor, the coefficients of these parameters can be translated by their behaviour:

Proportional coefficient: alone, it may achieve stabilization. This coefficient determines the importance of action on the engines in relation with the values measured by the gyroscopes. The higher the coefficient, the higher the tricopter seems more “rigid” versus angular deviation. If it is too low, the multicopter will appear soft and will be harder to keep steady. One can “feel” this setting by handling the tricopter and trying to change its orientation: the higher the parameter, the higher the opposition is important. In practice, this parameter must be set alone and increased up to be the limit for obtaining small oscillations. If too high, the system becomes unstable by amplifying the oscillations.

Integral coefficient: this coefficient can increase the precision of the angular position. In practice, when the tricopter is disturbed and its angle changes, the term Integral remembers the disruption and apply a correction to the engines to get the right angle. We can see this term as an heading hold factor. Typically if you take handfuls the multicopter and try to force it into a position, the engines will continue for some time to counteract the action. Without this term, the opposition does not last as long. This way, the angular position can be steady and accurate even with irregular wind, or during ground effect. However, the increase of this ratio often involves a reaction speed decrease and a decrease of the Proportional coefficient as a consequence. Compared to the conventional PID algorithm, I decided to cancel this term in the presence of strong angular variations. This strategy allows a safer behaviour in case of looping or hard shaking.

Derivative coefficient: this coefficient allows the tricopter to reach more quickly the requested attitude. In practice it will amplify the reaction speed of the system, and in certain cases an increase of the Proportional term. By cons, this parameters induces more noise.
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