Rigid–Flexible Coupled Modeling and Flexoelectric Control for Flexible Rotating Structures

The pursuit of lightweight structures has propelled spacecraft with large flexible appendages to the forefront of modern aerospace engineering. Flexoelectric actuators, with their inherent self-sensing and self-actuating capabilities, perfectly align with the demand for lightweight structures. This paper presents a dynamic model and a flexoelectric vibration control method tailored for spacecraft equipped with single-sided flexible appendages. The spacecraft system is a central rigid hub with flexible cantilever beam appendages that allow for single-axis rotation. The flexible beam has a flexoelectric element attached to it. Leveraging Hamilton’s principle, the equations of motion are derived, accounting for flexoelectric effects, the centrifugal stiffening effect, and the coupling between rigid body attitude and flexible beam vibration. A closed-loop proportional–derivative controller is crafted for attitude control of the system. Additionally, a flexoelectric patch is employed as an actuator for active vibration control of the flexible beam. The precision and efficacy of the proposed model and control scheme are meticulously validated through numerical simulation. The results indicate that the flexoelectric patch can effectively manage the vibration of the flexible beam, consequently impacting the attitude control performance of the system. Furthermore, the flexoelectric effect of the system under static conditions is scrutinized, and the influence of the flexoelectric actuator on the rigid–flexible coupling characteristics of the system is thoroughly analyzed. These analyses not only confirm the feasibility of flexoelectricity in rigid–flexible coupled systems, but also open avenues for applications and optimizations in intelligent control methods for flexible appendages.