Rigid-flexible coupling dynamic modeling and vibration control for flexible spacecraft based on its global analytical modes

In this study, we used global analytical modeswfny(GAMs) to develop a rigid-flexible dynamic modeling approach for spacecraft with large flexible appendages(SwLFA). This approach enables the convenient and precise calculation of the natural characteristics for designing an attitude control law for the spacecraft while simultaneously suppressing the active vibration of its flexible appendages. We simplify the flexible spacecraft as a rigid-flexible coupling hub-beam system with tip mass and derive the system's governing equations of motion based on Hamilton's principle. By solving the linearized form of those equations with their associated boundary conditions, we obtain the frequencies as well as the corresponding GAMs of flexible spacecraft,which we use to discretize the equations of motion. Using this approach, we performed numerical simulations to investigate the system's global modes and assess the performance of the controller based on the GAM model. The results reveal that the GAM model can be used to directly calculate the exact global modes of SwLFAs and that the controller based on the discrete GAM model can achieve a control-index for a SwLFA in a shorter time with less input energy than other methods.