## 1 Introduction
[11] designed a frequency-divided controller that coordinates the spacecraft attitude control loop and the telescope attitude control loop, improving the overall performance and pointing stability of the system. [PERSON] et al. [12] proposed a closed-loop control method for a fine stabilization system based on dual-port adaptive internal model control, enabling the disturbance compensation of the space telescope's fine stabilization system with lower steady-state error and a broader frequency range. In addition, for robust control in space applications, [PERSON] et al. [13] proposed an attitude controller of a mini-SSAR with a deployable reflector antenna, which ensures robustness against unmodeled dynamics and frequency variations. [PERSON] et al. [14] proposed a layered sliding mode fault-tolerant tracking control method based on a zero-sum game, which improved the response speed and robustness of the system. [PERSON] et al. [15] proposed a low-computation two-level triggering adaptive control strategy to achieve accurate trajectory tracking and maintain the boundedness of closed-loop signals. However, the aforementioned studies mainly focus on the coordinated control between spacecraft attitude and telescope pointing, with relatively simple disturbance noise. This may lead to a decline in control performance in the presence of multiple disturbances, making it challenging for traditional control methods to ensure high-precision pointing requirements. In terms of robust tracking control, the provided controller is not specifically designed for multiple disturbances, and thus, such control methods may be insufficient in suppressing these disturbances. To improve the system's disturbance rejection capability, tracking accuracy, and pointing stability, a composite tracking control method that guarantees the system's robust stability and dynamics while attenuating and suppressing multi-frequency disturbances has been proposed. This method has already been applied in several engineering fields [16; 17]. In this paper, the problem of trajectory tracking in a telescope pointing system with ultra-high precision and ultra-high pointing stability under multiple disturbances is investigated. A composite tracking control method is designed by introducing an \(H_{\infty}\) controller in the outer loop of the control system and integrating a robust disturbance observer in the inner loop. This method aims to improve the disturbance rejection capability of the system and ensure that the tracking accuracy and pointing stability of the telescope pointing system meet the requirements of gravitational wave detection tasks. The main contributions of this paper are summarized as follows:  
1. Disturbance analysis: Based on the mechanism research, this paper systematically analyzes the multiple disturbance noises of the telescope pointing system and establishes a specific disturbance mathematical model. This lays a solid foundation for suppressing multiple disturbances and improving system pointing stability. 2. Controller design: Based on the dynamic model of the telescope pointing mechanism and the multiple disturbance model, this paper designs a composite control controller. By designing an \(H_{\infty}\) controller, stability is ensured while suppressing external disturbance noise. To relax the constraints of the feedback controller and enhance the anti-interference capability of the telescope pointing system, an HODOB method is proposed. By combining the \(H_{\infty}\) controller and HODOB, it not only suppresses and attenuates multiple interferences but also achieves satisfactory tracking accuracy and pointing stability level, compensating for the respiratory angle changes in gravitational wave detection. The paper is organized as follows: Section 2 establishes the dynamic models of the telescope pointing mechanism and analyzes the models of the primary disturbance noises. Section 3 is dedicated to presenting the primary contributions, where a composite control scheme is proposed.