my question is: in a lot of cases it is possible to find in Internet PD (instead PID) to control the euler angles of quadcopter? Why the integral part is often neglected in this kind of applications? thanks
Because the P term calculates a proportional response to the error, for example if the quad is tilted a little bit then you only correct a little bit o you do not overshoot your target value, the I controller will ramp up the response if it has not lowered fast enough, which in some cases can be good for example if there is wind and the proportional term is not correcting enough, but that too can cause problems with overshooting the error (requiring a negative error for the same time as there was a positive error), the D controller will dampen the P and I controllers as you get closer to the set point by measuring the rate of change of the system and slowing it as it approaches the set point.
Using only the P and D controllers can sometimes give better results especially in less demanding environments and can be easier to tune, In my experience this approach works great for multicopters expected to make less aggressive maneuvers where a well tuned PID controller can perform better with very aggressive environments.