A Proportional Closed-loop Control for Equivalent Vertical Dynamics of Flapping-Wing Flying Robot

The closed-loop position control of a flapping-wing flying robot (FWFR) is a challenging task. A complete six-degree-of-freedom (DoF) modeling and control design is preferable though that imposes complexity on the procedure and analysis of the oscillations in the trajectory. Another approach could be studying independent state variables of the system and designing a controller for them. This will provide the possibility of a better understanding of the dynamic, comparing to experimental data, then use this information for moving forward to complete 6-DoF modeling. In this work, a simple linear proportional closed-loop controller is proposed and analyzed for an equivalent dynamic model of the flapping-wing flying robot. The equivalent dynamic modeling considers the flapping motion as a base excitation that disturbs the system in oscillatory behavior. The frequency of the oscillation and data of the motion was obtained from previous experimental results and used in the modeling. The designed controller performed the regulation task easily and regulated the system to a series of set-point control successfully. The motivation for the selection of a proportional control is to keep the design as simple as possible to analyze the excitation and behavior of the flapping more precisely. A discussion on the transient and steady-state flight and the role of control design on them have been presented in this work.