Abstract Large membrane diffraction space telescopes offer significant advantages for deep-space observation owing to their lightweight construction, high resolution, and cost-effective deployment. However, the dense low-frequency modal characteristics induced by parallel ultra-long support trusses pose substantial challenges for dynamic modeling and control. Traditional control strategies developed for solid mirror reflector telescopes are unsuitable for such highly flexible parallel structures. Existing research, primarily based on linear assumptions, relies on reduced-order modeling and frequency-domain decoupling for attitude-vibration control, which limits model accuracy and causes frequency-band coupling. To overcome these challenges, this study develops a high-fidelity rigid-flexible coupled dynamics model using the Absolute-Coordinate-Based (ACB) method. A novel reduced-gradient ANCF beam modeling technique is proposed to address gradient-discontinuous joints and reduce system variables. From a geometric perspective, the matrix null-space method is employed to eliminate algebraic constraints introduced by the parallel support trusses. Furthermore, a backstepping approach integrated with a relaxed quadratic optimization allocation algorithm is used to realize an attitude-vibration integrated controller within a unified ODE framework. To mitigate local modes excited by the controller, cable dampers are incorporated. Numerical simulations demonstrate that the proposed method effectively suppresses low-frequency vibrations and enhances pointing accuracy, thereby establishing a theoretical foundation for the dynamic modeling and control of ultra-large-aperture parallel space telescopes.
Yu et al. (2026) studied this question.