Stabilization of Altitude Control for Multirotor Flying Vehicles with Respect to Propeller Actuator Dynamics

To design motion control system for drones and multirotor vehicles, the traditional approach has relied on the dynamical equations of the vehicle body. However, almost of the studies neglected the existence of the propeller actuators. Considering the altitude control problem, this paper shows that it is essential to address the following property of the actuator to properly ensure system stability. It is the nonlinear relationship between the thrust force and the rotational speed of the propeller. To reduce the complexity of stability analysis, this paper shows that the altitude control system can be generally represented by the feedback connection of two parts: (i) the linear part with rank-1 physical interaction; (ii) the nonlinear part which belongs to certain sector bound. Based on this modelling, this paper derives the condition for the controller to ensure the absolute stability of the control system. The condition is independent of the number of propeller actuator, and it allows graphical test which can be performed conveniently. Moreover, it can easily address the change of battery voltage in accordance with the state of charge. The effectiveness of the proposed approach is demonstrated via numerical simulation and experiments with a quadrotor vehicle.