Dynamic Modeling and Robust Active Control of Graphene-Piezoelectric Composite Missile Wings with Elastic Boundary Constraints

To improve the stability and vibration suppression capability of missile wings under complex aerodynamic conditions, this study develops a dynamic model and explores the active control strategy for a graphene-reinforced piezoelectric composite missile wing subjected to elastic boundary constraints. An electromechanically coupled dynamic model with elastic boundary conditions is constructed by employing CLPT, the geometric nonlinearity following the von Karman assumptions, and piezoelectric coupling theory. The system is discretized and solved numerically using characteristic orthogonal polynomials and the Galerkin method. The influences of graphene distribution configurations, material properties, and boundary flexibility on the linear natural frequencies and nonlinear hardening characteristics are investigated. Results show that the X-type graphene distribution significantly enhances the equivalent stiffness and reduces nonlinearity. Boundary flexibility markedly modulates the vibration characteristics; in particular, increased structural flexibility strengthens geometric nonlinearity, leading to noticeable changes in frequency characteristics and hardening degree. A robust state-feedback controller together with a full-order observer is developed using the Linear Matrix Inequality (LMI) framework, and their performance is verified under different parameter disturbances and uncertainties. The control strategy effectively suppresses vibrations while maintaining good robustness, with the best performance achieved under X-type graphene reinforcement combined with thin piezoelectric layers. This study reveals the coupling mechanisms among material distribution, boundary flexibility, and robust control, providing a theoretical basis for the structural optimization and active control design of smart missile wings.