Working with INDI
Actuators don't react instantly. Motors need time to spin up, and servos can only move so many degrees per second. This means that if the input is suddenly changed, the angular acceleration is not immediately expected to change. If there is actuator feedback available, we know exactly how much the actuator has moved and at what moment how much angular acceleration we should expect. If actuator feedback is not available, an estimate of the actuator position has to be made.
For electric motors, a first order system can be an accurate model. This can be written as: act(i+1) = act(i) + alpha*(input - act(i)), where alpha is the value that can be specified in the airframe file. There are a few vehicles for which this value has been determined, such as the ARDrone, Bebop and AscTec Hummingbird. It can be obtained with a step response of the motors, using for instance a logic analyzer and a light sensor to record the spinup profile.