## 1 Introduction  
The resolution of optical remote sensing satellites has now mostly reached the sub-meter level. With the increase in resolution level, more requirements have been posted on the stable mechanical environment of satellites. One of the main factors affecting the stability of satellites is the micro-vibration of flywheels. The flywheel is the actuator of the control subsystem; due to its small manufacturing errors and defects, it will produce small amplitude and wide-band disturbance forces or torques, which will lead to an instability of sensitive components. While this small vibration will not cause structural damage, it will significantly affect imaging resolution [1]. It is particularly significant to establish an accurate analysis model for research on the micro-vibration of high-resolution optical remote sensing satellites flywheels. The influencing characteristics of micro-vibration are the results of the interactions of vibration source, structural, control, and optical subsystems. Since the interaction characteristics are complex, it is difficult to reflect its true responses if models only consider one subsystem. At present, an integrated modeling method is widely adopted for micro-vibration analysis, which uses the tools of different disciplines to establish an integrated micro-vibrationanalysis mathematical model. The model includes various subsystem models and their interaction processes, and it finally obtains the transfer characteristics of micro-vibration [2; 3]. In early 1990s, Jet Propulsion Laboratory (JPL) was the first to adopt an integrated modeling that mainly integrated optical, control, structural and vibration source subsystems and proved the effectiveness of the method [4]. [PERSON] et al. of the Space Systems Laboratory (SSL) of the Massachusetts Institute of Technology (MIT), USA, established a more detailed integrated modeling work based on the theory of linear time-invariant systems for Space Interferometry Mission (SIM), and they developed an integrated analysis software--DOCS (Dynamics Optics Controls Structures). DOCS integrated various subsystems and employed the Micro-Precision Interferometer Testbed (MPI) developed by [PERSON] et al. for SIM to obtain experimental data. By comparing measured and predicted closed-loop transfer functions, the reliability of the methodology was verified [5; 6; 7; 8]. [PERSON] et al. from NASA developed the Integrated Modeling Environment (IME) for the James Webb Space Telescope (JWST). IME is able to perform micro-vibration analysis and structural-thermal-optical analysis to obtain dynamic wave front error and pointing error; another optical analysis software is also programed to obtain indicators of micro-vibration affecting the imaging performance of an optical subsystem according to the movement of optical components [9; 10; 11]. The two integrated software, IME and DOCS, fully considered the transmission mechanism of micro-vibration in each subsystem, effectively integrated the subsystem models, and developed a more various assessment of micro-vibration disturbance impact on optical indicators. The overall model input of the two kinds of software is micro-vibration disturbance source in the form of power spectral density (PSD), which has the advantages of simple calculation and wide coverage of frequency, but researchers did not analyze time-domain response characteristics. [PERSON] et al. conducted an in-depth investigation and analysis on micro-vibration integrated modeling technology, and they drafted an overall framework of an integrated analysis system [12; 13]. [PERSON] et al. and [PERSON] et al. proposed a time-domain analysis method based on time-domain calculations, which can better distinguish the effects of rigid-body low-frequency drift and elastic transient deformation, thereby contributing to obtain a steady time-domain response [14; 15]. However, the real in-orbit control strategy of the control subsystem was not fully considered; the control subsystem was approximated as a second-order filter.