Dynamic modeling, linearization and characteristic analysis of Taiji drag-free attitude and control system

This study investigates on the Drag-Free and Attitude Control System (DFACS) for the Taiji space-based gravitational wave detection mission. A comprehensive effort has been undertaken to develop the system’s dynamic modeling, model linearization, accuracy validation, and stability analysis. In response to mission requirements, a novel formation coordinate system with clear physical interpretation and geometric intuitiveness is proposed. Based on this framework, a complete nonlinear dynamic model is established, capturing the coupling relationships among the spacecraft, optical assembly, and proof mass. A high-fidelity nonlinear simulation system is subsequently developed to support dynamic behavior analysis. Utilizing perturbation matrix techniques, a linearized dynamic model suitable for short-duration analysis is derived, along with an efficient linear simulation system. Comparative analysis with the nonlinear model demonstrates that the linear model maintains high accuracy and computational efficiency over a 10-day timescale. Furthermore, system-level analyses based on the linear model reveals critical insights into the DFACS, including coupling characteristics, stability, and robustness. The results reveal complex inter-degree-of-freedom couplings, weak stability in certain modes, and an uneven distribution of control authority. These findings lay a solid theoretical foundation for the future development of high-precision control laws and the optimization of system performance. The methodologies and results presented in this work represent significant advancements in dynamic modeling, simulation system development, and characteristics analysis, offering strong technical support for the engineering implementation of the DFACS in the Taiji mission.