## 1 Introduction  
Meteorological satellites play a vital role in our daily life. To send back high-quality images, satellites have to meet stringent demands related to attitude accuracy [1; 2; 3]. However, periodic disturbances from spaceborne equipment result in difficulty in retaining stability in the attitude of spacecraft. The application of spaceborne microwave imaging instruments has substantially improved the image definition, but poor effects on attitude accuracy are also brought about by their known-law rotating imbalance [4; 5; 6]. Furthermore, characteristics like flexibility and low weight make spacecraft vulnerable to vibrations caused by numerous sources [7]. In this paper, we focus on the compensation of known-law long-lasting periodic disturbances and attenuation of vibrations to improve the attitude accuracy of meteorological satellites. Many studies have been done on the attitude control of meteorological satellites. Mitigation of the periodic disturbances by compensating torques has been proposed by researchers over the course of the past years. [PERSON] et al. [8] presented a fault tolerant control for external disturbances and actuator failures. This controller is the combination and application of the free weighting matrices method and LMI (linear matrix inequality) technique. However, this simply designed controller has not been well verified for flexible spacecraft. [PERSON] et al. [9] presented an improved sliding mode attitude control algorithm with an exponential time-varying sliding surface. This controller enhanced the accuracy of maneuver in the presence of disturbances and parametric uncertainties. To reduce the dependence of estimate accuracy on a disturbance model, [PERSON] et al. [10] designed a sliding mode disturbance observer for the attitude control of a rigid spacecraft in the presence of disturbance and actuator saturation. The adaptive controller has also been adopted. Unfortunately, the studies neglected the flexibility of the structure. The attitude control and disturbance rejection have been studied for flexible spacecraft during attitude maneuvering by [PERSON] et al. [11]. An improved compensator is developed to achieve asymptotic disturbance rejection. Then, a new robust state feedback controller is presented for the attitude maneuver. The proposed strategy achieved the maneuver process in the presence of small amplitude disturbances. [PERSON] et al. [12] proposed a generalized-disturbance rejection (GDR) control for vibration suppression of flexible structures in the presence of unknown continuous disturbances. The unknown disturbances are estimated by a generalized-disturbance rejection which is defined by a refined state space model. [PERSON] et al. [13] focused on the disturbance observer-based control method to attenuate or reject disturbances for a spacecraft attitude control system. The disturbance observer is used to estimate the disturbances. Also, the feedforward compensation is given according to the corresponding results. [PERSON] et al. [14] developed an adaptive failure compensation approach for the attitude control of satellites in the presence of disturbance and uncertain failures of actuators. This research mainly focuses on the disturbances from actuator failures; external disturbances have not been sufficiently considered. [PERSON] et al. [15] improved the research on disturbance identification and rejection. The dipole-type disturbance rejection filter is adopted and applied in [15]. Subsequently, two simple close-loop system identification methods are introduced to improve the robustness of the rejection filter relative to frequency uncertainty. [PERSON] et al. [16] made contributions to the rejection of general multi-periodic disturbances. The multi-periodic disturbances are estimated by a new presented method. Based on the estimation results, a new adaptive control method is applied for disturbance rejection. The residual vibration can be controlled in a specified range under the provided strategy.