An accurate system-level nonlinear order-reduction for the flexible solar array system using global modes

Dynamic analysis of solar array structures is a challenging job due to their complexity and nonlinearity. In this paper, an accurate and efficient reduced-order model of the solar array system is developed. The reduced model is derived by using the system-level nonlinear reduction strategy, where the global flexible modes and their corresponding modal derivatives are adopted to describe large deformations of the system. The system-level approach is superior to other component-level reduction methods in terms of computational efficiency. For the case of linear constraints, the proposed approach can reduce the high-dimensional differential algebraic equations (DAEs) system to a low-dimensional ordinary differential equations (ODEs) system. The reduced nonlinear elastic forces are polynomials of modal coordinates with constant coefficients, and these coefficients can be evaluated in advance to further improve efficiency. This is convenient for both equation solving and controller design. The nonlinear dynamic responses of the solar array during the orbit modification and attitude maneuver are simulated. The numerical results show that the current system-level reduction method can achieve high efficiency and accuracy in the dynamic analysis of the solar array structures. The present work also provides some guidance for the vibration control and real-time simulation of the flexible spacecraft.