Model of effective thrust induced by propellers in hover mode for simulation and control of miniature quadrotors

Precision flight of quadrotors, the most popular rotary-wing UAV, requires of sophisticated controllers to control their complex dynamics of coupled forces and their sensitivity to environmental conditions. However, controllers are often designed without considering the dynamic behavior of the actuators; situation that leads to excessive controller actuation and diminishes the overall performance of the aircraft, including its energy consumption. In this paper, we discuss the dynamic effects of the airflow induced by a propeller, in hover mode, on the thrust produced, the dynamic response of the actuators, and we determine a thrust correction factor for the effective thrust as well as a bandwidth of the dynamic response, which can be used as designing parameters to improve the controller design. Using a mechanical analogy, we show the implicit assumption on the inertial frame of reference when the Conservation of Momentum Theory is used to calculate the thrust in a hovering propeller; assumption that modifies the perception of the produced thrust with respect to the effective thrust observed in an absolute frame of reference. This highlights the importance of the horizontal change of momentum of the incoming airflow, neglected in traditional approaches but responsible of the effective force of lift in the steady state of the propeller when an ideal fluid is assumed. Finally, we introduce a simple dynamic model of the airflow induced by the propeller and provide an estimation of the maximum bandwidth response to be expected from the actuators.