# Do you have to have a rate controller for a Quadcopter?

Most academic papers characterise the rate of rotation along the x axis as φ"=(1/Jx)τφ. As far as I cant tell, this characterises the rate and not the actual angle φ itself and yet the PID controllers academics use to control this takes φsetpoint-φmeasured as its error signal. Should the error signal not be φ"setpoint-φ"measured (using gyro values) instead. Why are they using the euler angle instead of its second derivative to control the rate?

Is it possible to stabilise a quadcopter using euler angles only?