# Design and Analysis of the Composite Stability Control of the Reflective Optoelectronic Platform
## 2 Problem Description
### The Problem Description of the LOS Anti-Disturbance  
In general, the following assumptions can be made:  
* Previous research experience suggests that the coarse-stable framework is primarily designed to address low-frequency and high-angle velocity disturbances of the carrier [3; 4; 10; 11]. As a result, the closed-loop control bandwidth typically falls within the range of 20-100 Hz. To achieve inertial stability control of the coarse-stable two axes, a group of two-axis gyroscopes are installed on the coarse-stable driving frame, and the reflector uses the gyroscope measurement as the feedback signal.  
The fine-stable framework is specifically designed to address high-frequency and low-amplitude angle disturbances of the carrier, and therefore, its closed-loop control bandwidth is typically set above 500 Hz [3; 4; 10; 11]. The fast reflector in the fine-stable framework functions as a precision stabilized component and operates under the angular position closed-loop working mode. The bandwidth of the fast reflector is generally set to not less than 500 Hz accordingly, and the angular motion stroke typically does not exceed a few milliradians. Furthermore, the angular position accuracy of the fine-stable framework is generally high, and its closed-loop error can be neglected.
* Real-time angle measurements of each rotation axis are typically obtained through motor feedback values. In this study, the focus is on the transmission error of the mechanism with a 2-to-1 transmission ratio, and thus, the measurement error of each rotation axis angle can be disregarded when compared to this transmission error.
* The transmission error of the mechanism with a 2-to-1 transmission ratio is denoted as \(\theta_{err}\), and it can be calculated by the geometric relationship formula \(\theta_{E2}=\frac{\theta_{E1}}{\lambda}-\theta_{err}\), which is shown in Figures 3 and 5.  
The problem of resisting matrix disturbance for LOS and realizing inertial stability can be described as follows: How to use the coarse inertial velocity to stabilize the closed-loop subsystem under the action of disturbance torque and how to use the fine position closed-loop subsystem to make the inertial velocities of the apparent axes, namely \(\dot{\theta}_{a}\) and \(\dot{\theta}_{e}\) approach zero.  
The stability precision, calculated by measuring the error ranges of \(\dot{\theta}_{a}\) and \(\dot{\theta}_{e}\) under constant frequency disturbance are used as the performance evaluation criteria for stability methods, which is shown in Equation (7), where \(T\) denotes the total sampling time.  
\[\left\{\begin{array}{l}Error\_range_{azimuth}=\left[Max(\dot{\theta}_{a})- Min(\dot{\theta}_{a})\right]\mid_{t\leq T}\\ Error\_range_{pitch}=\left[Max(\dot{\theta}_{e})-Min(\dot{\theta}_{e}) \right]\mid_{t\leq T}\end{array}\right. \tag{7}\]  
Additionally, during the simulation verification process, the error ranges can be obtained from the final output signals of \(\dot{\theta}_{a}\) and \(\dot{\theta}_{e}\). During the experimental verification process, the error ranges can be measured by the stable precision data acquisition platform. The principle and construction process of the platform are shown in our previous studies [25; 26].