Although theoretically a drone could be controlled based on mathematical  methods, in reality, multiple elements could lead to a theory-based control system failure.
Different status of motors, balancing of the frame, battery voltage or weather, all of these could be a reason of control system failure. Thus a control system that could surveillance the system and give out a corrective value simultaneously is needed for this task.

As angular acceleration is the most direct parameter that effects the gesture of the quadcopter,  and is determined by the rotational speed of the motors,  the best PID subject is estimated gesture, angular speed, and output that could effect the rotational speed of motors. Under this circumstance the quadcopter could balance it self pretty well as long as a gesture error value is inputed. However, to take control of the drone, the first parameter that you would like to control from the quadcopter will be the anticipated gesture angle, which is not angular speed as mentioned above. In this case, another PID controller that links estimated gesture angle and angular speed output should be introduced to the system. With these two control systems, the quadcopter should be well controlled one Kp, Ki, and Kd is set to a correct value.