Boundary control for an unmanned aerial vehicle with a nonhomogeneous rigid–flexible coupling wing

With the rapid development of unmanned aerial vehicle technology and the continuous growth of requirements demanded in engineering applications, flapping-wing unmanned aerial vehicles are playing an increasingly important role in the national economy and livelihood because of their advantages such as good concealment, rapid maneuverability, high flexibility, and excellent economic performance. However, due to the limitations of the operating environment and their rapid maneuvering, the wings of flapping-wing unmanned aerial vehicles often have continuous high-frequency vibrations. These undesirable vibrations can affect the stability of the system and reduce its service life. In addition, flapping-wing unmanned aerial vehicles adjust their attitude rapidly and accurately during operation to accomplish assigned tasks. Therefore, this study focuses on the issues of vibration suppression and attitude control for flapping-wing unmanned aerial vehicles with rigid–flexible coupling wings. First, considering the impact of external disturbances on a flapping-wing unmanned aerial vehicle, using the Hamiltonian principle, the flapping-wing system comprising the homogeneous rigid link connected with the heterogeneous flexible link is modeled as an infinite dimensional distributed parameter system. The dynamic equations of the flapping-wing unmanned aerial vehicle are expressed as nonhomogeneous partial differential equations coupled with ordinary differential equations. Afterward, based on the original model with infinite-dimensional state space, two boundary control laws are designed to stabilize the system of the flapping-wing unmanned aerial vehicle by applying the back-stepping method. Different from the traditional modal control methods, the proposed control scheme can avoid overflow instability and control all system modals. An auxiliary input signal and disturbance adaptive law are constructed to cancel the impact of external disturbances via the robust control strategy. The developed disturbance rejection technique greatly relaxes the assumptions about external disturbances. By arranging the sensors and actuators at the body of the flapping-wing unmanned aerial vehicle and the connection point of the rigid–flexible coupling wing, the vibrations of the flexible wing are regulated into the vicinity around the original position and the attitude angle positions of the rigid and flexible wings are adjusted to the desired angular positions. It is worth noting that the proposed boundary control scheme exhibits great feasibility, cost-effectiveness, and robustness. Using the Lyapunov stability theory, it is rigorously proven that the closed-loop system is uniformly bounded stable. Finally, numerical simulations are conducted to demonstrate the effectiveness and performance of the designed control scheme.