Finite Element Dynamic Modeling of Smart Structures and Adaptive Backstepping Control

Smart structures with topological configurations that integrate perception and actuation have complex geometric features. The simplification of these features can lead to deviations in dynamic characteristics, making it difficult to establish an accurate dynamic model. Uncertainties, such as material nonlinearity, hysteresis in elastic deformation, and external disturbances, affect the trajectory tracking accuracy of the smart structure’s actuation function. This paper proposes a modeling method that combines finite element unit bodies and orthogonal characteristic mode reduction to construct an accurate dynamic model of the smart structure and design an adaptive backstepping controller. Nonlinear dynamic equations are derived through a finite element analysis of the structure, and the orthogonal characteristic mode reduction method is employed to reduce computational complexity while ensuring model accuracy. An adaptive backstepping controller is designed to mitigate model uncertainties and achieve precise trajectory tracking control. Simulation and experimental results demonstrate that the proposed method can effectively handle the nonlinearity and modeling errors of smart structures, achieving high-precision trajectory tracking and verifying the accuracy of the dynamic model as well as the robustness of the controller.