Design and Analysis of the Composite Stability Control of the Reflective Optoelectronic Platform

Abstract

To improve image object detection and tracking, researchers have been exploring methods to enhance the stability and precision of optoelectronic platforms’ line of sight (LOS). The innovation of stability mechanisms is the key driver of this breakthrough. This study presents a composite stability control system for reflective optoelectronic platforms using the integral composite stability principle. A platform kinematic model was established based on multi-body kinematic theory, and a composite stable control strategy was designed. The strategy includes coarse stability design and fine stability design based on residual error feed-forward correction. The performance of the control strategy was analyzed in terms of dynamics, current loop control effects, and loop structure. The proposed control strategy was simulated and experimentally verified for fixed-frequency angular velocity disturbance and translational disturbance. The stability accuracy index of the system was significantly improved after compensation, with improvement of more than 75 times for fixed-frequency angular velocity disturbance and more than 37% for translational disturbance. Comparative experimental results with traditional stable methods show that the proposed composite stable control strategy can significantly improve the system stability, with stability accuracy index improvement of one to two orders of magnitude in micro-radian units compared to traditional algorithms.

1. Introduction

The optoelectronic stability platform (OSP) is a versatile solution that has gained popularity in various fields, including military reconnaissance and astronomical topography, due to its exceptional disturbance isolation capacity and LOS stability [1]. The stability precision of an OSP is a critical technological parameter that significantly impacts the sharpness of images produced by the optoelectronic sensor in the system. As such, it plays a crucial role in enhancing the system’s ability to capture, identify, and precisely target objects [1,2].

In the technological development of OSP, the enhancement of stability precision is primarily achieved through the evolution of the system stability principle schemes. However, as stability precision indexes are influenced by working conditions, their definitions in various papers and product introductions can often be confusing for readers. To provide a more comprehensive analysis of the problem discussed in this research, the typical application of a certain type of air-plane will be used as a case study.

Previous studies such as [3,4] provide a detailed overview of the principle of OSP. The main application mode of optoelectronic pod products is frame stability, which is a type of direct stability where the inertial sensor directly detects the LOS. The two-axis two-framework application is an early and comparatively mature application mode. However, despite continuous efforts to update the key devices and optimize the control algorithm, it has been challenging to make significant breakthroughs after achieving stability precision at the $mrad$ level due to the sealing of the system, which results in a significant friction torque that restricts further improvement of the stability precision. Recent studies on the two-axis two-framework application are exploring ways to treat friction as a disturbing or unmodeled element and improve the precision ability through anti-interference control methods [5,6,7,8]. However, these improvements are often limited.

To completely eliminate the effects of friction, a two-axis four-framework application mode was developed, with two internal frameworks for stability control protected by two external frames. This eliminates the need for sealing treatments [3,9]. Though this principle scheme is more complex, it significantly improves stability precision, achieving a level within one hundred micro-arcs [3,4]. To further enhance performance, a fast reflector is placed in the optical channel of the two-axis four-framework system, using the high bandwidth and precision of the fast steering reflector to actively compensate loop errors. By optimizing the two-stage method of coarse and fine control, known as the composite stability principle scheme, stability precision is improved by nearly an order of magnitude, reaching a level of ten micro-arcs [4,10,11].

The reflector stability mode is an optoelectronic stability solution that is commonly applied to specific types of equipment [11,12]. This method involves placing a reflector in the LOS of a fixed optoelectronic detector and achieving inertial stability of the LOS by adjusting the reflector’s attitude. While this approach is an indirect stability method, the LOS of the detector is calculated using different sensors of inertial, angle, and angular velocity. To eliminate the double effect caused by reflection, a mechanism with a transmission ratio of 2 to 1 is introduced. However, the transmission precision and stiffness are limited, which restricts the improvement of stability precision. Although this approach is still necessary in certain situations, its stability precision is lower than overall stability methods.

The papers [13,14] propose the design of a fused reflector and fast reflector based on the principle of integrated composite stability. This design utilizes the stability of the reflector and error compensation of the fast reflector to establish a stability control system for reflective optoelectronic stability platforms. However, the simplicity of the theoretical model used in the research papers limits a comprehensive understanding of the error source and compensation principles.

Additionally, researchers have investigated design challenges related to tracking differentiators and expansion observers for photoelectric stabilized platforms, using active disturbance rejection control (ADRC) methods and the transition process to address the conflict between PID’s rapid response and overshoot [15,16]. Nevertheless, the effectiveness of these research improvements is constrained by the low-frequency phase lag issue caused by filters lacking a zero point. Some other researchers have used adaptive algorithms to enhance the stability error compensation process for optoelectronic platforms and validated their approach through simulations [15,17,18,19,20]. However, developing an adaptive algorithm model requires extensive empirical data and can be challenging to implement, raising questions about its practical utility in solving engineering problems.

In summary, previous research has only focused on single methods of using reflectors and has limited practical value. Therefore, this paper concentrates on how to utilize the advantages of overall stability combined with the reflector method to overcome complex and coupled interference. This approach will improve the overall performance and application prospects of the platform.

Specifically, this paper offers a comprehensive showcase of the theoretical approach to composite controller design, including an evaluation of design impacts and a complete solution framework for the reliable implementation of high precision reflectors. Through an exploration of the composite model, this study provides a more profound comprehension of the design principles and the origins of error, facilitating more efficient compensation and superior stability control. Compared to the ADRC control method and adaptive compensation method, the method proposed in this paper can provide a more practical solution for two-axis four-frame structures with complex manufacturing processes. The main reason is that the theoretical modeling and analysis process of the method proposed is relatively clear, does not require a large amount of sample data accumulation, and has been experimentally verified by real products under typical disturbances.

Furthermore, performance of the proposed method is compared with traditional reflector stabilization methods and other existing classic methods, such as methods of the disturbance observer combined with zero phase error tracker (ZPETC) [21], XPC real-time simulation [22], optimized adaptive Kalman filtering [23], high-speed target tracking [24], LuGre and ADRC [18], back-stepping control [19], and RBFNN and SMC [20]. The stability precision, calculated by measuring the error range under constant frequency disturbance, is used as the comparison index. The reasons for using the above methods as comparison objects are that their application background and parameters of validation experiments are similar to those of this paper, and the experimental data of these studies are available, which can serve as comparative references for the method proposed.

2. Problem Description

2.1. The Principle Assumption of the LOS Stability

This study utilizes the typical two-axis four-frame structure dynamics model [3,4,9] to ensure system stability. The basic principle assumption of the model is illustrated in Figure 1, where the detector and fixed reflector (Figure 1a) are fixed on the base, and the adjustable reflector can adjust its attitude relative to it. The imaging stability of the detector is maintained by adjusting the adjustable reflector when the base’s motion causes the inertial instability of the line of sight (LOS).

The adjustable reflector consists of two components: the traditional two-degree-of-freedom reflector and the fast steering reflector. As depicted in Figure 1b, the traditional reflector utilizes two frame axes to provide coarse-stable axes, while the fast steering reflector employs two motion axes as fine-stable axes. The coarse-stable pitch frame of the traditional reflector comprises a driving axis and a driven axis, which necessitates a mechanism with a 2-to-1 transmission ratio [4,10]. On the other hand, the fast steering reflector is mounted on the driven axis for improved efficiency.

2.2. The Preparation of System Motion

To simplify analysis, this study adopts a different approach than previous methods [3,4,9,10], setting x, y, and z to correspond to the rolling, pitch, and azimuth axes of the carrier, respectively. Physical quantities are denoted by subscripts b, A, $E_1$, $E_2$, a, and e, corresponding to the coordinate systems of the carrier, coarse-stable azimuth framework, coarse-stable pitch driving framework, coarse-stable pitch driven framework, fine-stable azimuth framework, and fine-stable pitch framework. The coordinate systems for each axis are defined as shown in Figure 2, and the motion transmission relationships between the frameworks are shown in Figure 3 and Figure 4.

The optical detector is fixed in the centre of the fine pitch framework, and the LOS motion is consistent with the mechanical axis on the azimuth axis due to controllable attitude reflection components in the optical path. However, due to the existence of an optical multiple, the motion transfer relation around the LOS is inconsistent with the mechanical frame, which can be shown in Figure 5 and Figure 6, with the optical multiple set to $\lambda$. A two-degree freedom gyro is installed on the active framework of the coarse-stable pitch, corresponding to the coordinate system $E_1$.

The notation ${\overline{\omega }}_b$ is used to represent the carrier’s angular velocity vector, with components ${\left[{\omega }_{bx},{\omega }_{by},{\omega }_{bz},1\right]}^T$. The coarse-stable azimuth frame’s angular velocity vector is denoted by ${\overline{\omega }}_A$, with components ${\left[{\omega }_{Ax},{\omega }_{Ay},{\omega }_{Az},1\right]}^T$. Similarly, the coarse-stable pitch driving frame’s angular velocity vector is denoted as ${\overline{\omega }}_{E1}$, with components ${\left[{\omega }_{E1x},{\omega }_{E1y},{\omega }_{E1z},1\right]}^T$, and that of the coarse-stable pitch driven frame as ${\overline{\omega }}_{E2}$, with components ${\left[{\omega }_{E2x},{\omega }_{E2y},{\omega }_{E2z},1\right]}^T$. The LOS coarse-stable azimuth frame’s angular velocity vector is ${\overline{\omega }}_{LA}$, with components ${\left[{\omega }_{ax},{\omega }_{ay},{\omega }_{az},1\right]}^T$, and that of the LOS fine-stable pitch frame is ${\overline{\omega }}_{Le}$, with components ${\left[{\omega }_{ex},{\omega }_{ey},{\omega }_{ez},1\right]}^T$.

Therefore, Equation (1) from references [11,12] can be used to describe the kinematic model of the line of sight (LOS), where ${\overline{\omega }}_{La}$ represents the angular velocity vector of the LOS fine-stable azimuth frame, and ${\overline{\omega }}_{LE}$ represents that of the LOS coarse-stable pitch frame.

$$\begin{array}{cc}\hfill {\overline{\omega }}_{Le}& =W_{ea}·{\overline{\omega }}_{La}=W_{ea}·W_{aE}·{\overline{\omega }}_{LE}\hfill \\ \hfill & =W_{ea}·W_{aE}·W_{EA}·{\overline{\omega }}_{LA}\hfill \end{array}$$

(1)

where

$$\begin{array}{cc}\hfill W_{ea}& =\left[\begin{array}{cccc}cos\left(\lambda {\theta }_e\right)& 0& -sin\left(\lambda {\theta }_e\right)& 0\\ 0& 1& 0& \lambda {\dot{\theta }}_e\\ sin\left(\lambda {\theta }_e\right)& 0& cos\left(\lambda {\theta }_e\right)& 0\\ 0& 0& 0& 1\end{array}\right],\hfill \\ \hfill W_{aE}& =\left[\begin{array}{cccc}cos\left({\theta }_a\right)& sin\left({\theta }_a\right)& 0& 0\\ -sin\left({\theta }_a\right)& cos\left({\theta }_a\right)& 0& 0\\ 0& 0& 1& {\dot{\theta }}_a\\ 0& 0& 0& 1\end{array}\right],\hfill \\ \hfill W_{EA}& =\left[\begin{array}{cccc}cos\left(\lambda {\theta }_{E2}\right)& 0& -sin\left(\lambda {\theta }_{E2}\right)& 0\\ 0& 1& 0& \lambda {\dot{\theta }}_{E2}\\ sin\left(\lambda {\theta }_{E2}\right)& 0& cos\left(\lambda {\theta }_{E2}\right)& 0\\ 0& 0& 0& 1\end{array}\right]\hfill \end{array}$$

(2)

Due to the limited range of motion in ${\theta }_a$ and ${\theta }_e$, representing the real-time angular velocities of the fine-stable azimuth frame and the fine-stable pitch frame, their sine and cosine values can be considered negligible, resulting in Equation (1) being simplified to Equation (3). Furthermore, the geometric relationship formula ${\theta }_{E2}=\frac{{\theta }_{E1}}{\lambda }-{\theta }_{err}$ can be utilized, where ${\theta }_{E1}$ and ${\theta }_{E2}$ denote the real-time angular velocities of the coarse-stable frames of driving and driven, respectively, $\lambda$ represents the transmission ratio, and ${\theta }_{err}$ represents the transmission angle error (which is also negligible). This simplifies Equations (3) and (4). Finally, Equations (5) and (6) were derived from Equation (4).

$${\overline{\omega }}_{Le}=\left[\begin{array}{cccc}cos\left(\lambda {\theta }_{E2}\right)& 0& -sin\left(\lambda {\theta }_{E2}\right)& 0\\ 0& 1& 0& \lambda {\dot{\theta }}_{E2}+\lambda {\dot{\theta }}_e\\ sin\left(\lambda {\theta }_{E2}\right)& 0& cos\left(\lambda {\theta }_{E2}\right)& {\dot{\theta }}_a\\ 0& 0& 0& 1\end{array}\right]·{\overline{\omega }}_{La}$$

(3)

$${\overline{\omega }}_{Le}=\left[\begin{array}{cccc}cos\left({\theta }_{E1}\right)& 0& -sin\left({\theta }_{E1}\right)& 0\\ 0& 1& 0& {\dot{\theta }}_{E1}+\lambda \left({\dot{\theta }}_e-{\dot{\theta }}_{err}\right)\\ sin\left({\theta }_{E1}\right)& 0& cos\left({\theta }_{E1}\right)& {\dot{\theta }}_a\\ 0& 0& 0& 1\end{array}\right]·{\overline{\omega }}_{La}$$

(4)

Furthermore, due to

$${\overline{\omega }}_{E1}=\left[\begin{array}{cccc}cos\left({\theta }_{E1}\right)& 0& -sin\left({\theta }_{E1}\right)& 0\\ 0& 1& 0& {\dot{\theta }}_{E1}\\ sin\left({\theta }_{E1}\right)& 0& cos\left({\theta }_{E1}\right)& 0\\ 0& 0& 0& 1\end{array}\right]·{\overline{\omega }}_A$$

(5)

The kinematic models of the line-of-sight (LOS) can be represented as follows:

$${\overline{\omega }}_{Le}=\left[\begin{array}{c}{\omega }_{ex}\\ {\omega }_{ey}\\ {\omega }_{ez}\\ 1\end{array}\right]=\left[\begin{array}{c}{\omega }_{E1x}\\ {\omega }_{E1y}\\ {\omega }_{E1z}\\ 1\end{array}\right]+\left[\begin{array}{c}0\\ \lambda ({\dot{\theta }}_e-{\dot{\theta }}_{err})\\ {\dot{\theta }}_a\\ 0\end{array}\right]$$

(6)

2.3. 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 Figure 3 and Figure 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.

$$\left\{\begin{array}{c}Error\_rang{e}_{azimuth}=[Max\left({\dot{\theta }}_a\right)-Min\left({\dot{\theta }}_a\right)]{\mid }_{t\le T}\\ Error\_rang{e}_{pithch}=[Max\left({\dot{\theta }}_e\right)-Min\left({\dot{\theta }}_e\right)]{\mid }_{t\le T}\end{array}\right.$$

(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].

3. Design and Analysis of Composite Stabilization Control System

3.1. Control Scheme Design and System Model

Figure 7 depicts the optimized combined stabilization control scheme. The coarse-stable part, located below the dotted line, achieves LOS stabilization through conventional control methods [13,14]. The unique feature in this study is the fine-stable part, located above the dotted line. This section employs a fast reflection operation under the position closed-loop mode to utilize the residual errors from the coarse-stable control loop as the input instruction for the fast reflector after feed-forward correction. The combined outputs from both coarse and fine circuits determine the inertial attitude of the LOS. The disturbance torques $T_{d1}$ and $T_{d2}$ correspond to the coarse and fine stabilization loops, respectively, while the optical coefficient is denoted by $\lambda$.

The system model shown in Figure 7 can be optimized to achieve the results seen in Figure 8:

• The coarse-stable channel and the current controller are controlled by $C_1$ and $C_2$. The driving magnification, torque coefficient, current sampling coefficient, and back electromotive force coefficient are represented by $K_1$, $K_2$, $K_3$, and $K_4$. The equivalent object of coarse-stable control and the gyro are represented by $G_1$ and $G_g$.
• The feed-forward correction, fine-stable channel position control, and current controller are controlled by $W_1$, $W_2$, and $W_3$, respectively. The driving magnification, torque coefficient, current sampling coefficient, and back electromotive force coefficient are represented by $M_1$, $M_2$, $M_3$, and $M_4$, respectively. The equivalent object of fine-stable control is represented by $G_2$, and the position sensor is represented by $G_p$.
• The optical coefficient is denoted by $\lambda$, and $T_{d1}$ and $T_{d2}$ represent the disturbance torque of the two channels. The motion of the base is represented by ${\omega }_b$. The dotted line separates the fine stabilization components.
• By using the coarse-stable control error as the input, error compensation control can be carried out through the feed-forward channel to achieve high precision control of the LOS. When the azimuth channel is selected, ${\theta }_A$ and $\lambda =1$ are represented by ${\theta }_A/¦{È}_{E2}$, and when the pitch channel is selected, ${\theta }_{E2}$ and $\lambda =2$ are represented.

This control strategy utilizes current closed-loop systems in the coarse and fine channels to decrease motor delay and enhance the response speed from voltage to current, optimizing motor performance.

3.2. The Proof of the Stabilization of Anti-Disturbance of the LOS

• Model simplification

The current loop’s control bandwidth can reach very high levels, causing $K_1{K}_2{C}_2$ to greatly surpass both R and L. The high-bandwidth current closed-loop system results in a proportional relationship between the control voltage and armature current, rendering the induced electromotive force insignificant. Consequently, Figure 8 is simplified as illustrated in Figure 9, where $W=M_2{W}_2/M_3$ and $C=K_2{C}_1/K_3$.

• Transfer function analysis

As shown in Figure 9, it can be inferred that

$$[(r-G_g·{\omega }_1)·C+T_{d1}]·G_1·\frac{1}{s}={\theta }_1$$

(8)

$$\begin{array}{cc}\hfill & \left\{[(r-G_g·{\omega }_1)·W_1-G_p·{\theta }_2]·W+T_{d2}\right\}\hfill \\ \hfill & ·G_2·\frac{1}{s}-{\theta }_1/\lambda ={\theta }_2\hfill \end{array}$$

(9)

$${\theta }_L=\lambda {\theta }_2+{\theta }_1$$

(10)

Hence, it can be deduced that Equation (11) represents the inertial instructions of the line of sight (LOS), with the first two terms being zero under stable mode. The third term represents the impact of the fast reflector subsystem disturbance on the LOS, which is negligible due to the high precision of the subsystem as per the aforementioned assumptions. Therefore, Equation (11) can be simplified to Equation (12).

$$\begin{array}{cc}\hfill & {\theta }_L=\frac{W{W}_1{G}_2\lambda r}{s+W{G}_p{G}_2}+\hfill \\ \hfill & \frac{[s+W{G}_p{G}_2-s(W{W}_1{G}_g{G}_2\lambda +1)·C{G}_1]r}{s+sC{G}_1{G}_g}+\hfill \\ \hfill & \frac{[[s+W{G}_p{G}_2-s(W{W}_1{G}_g{G}_2\lambda +1)]·G_1]}{(s+W{G}_p{G}_2)(s+sC{G}_1{G}_g)}·T_{d1}+\hfill \\ \hfill & \frac{G_2\lambda }{s+W{G}_p{G}_2}·T_{d2}\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill \frac{{\theta }_L}{T_{d1}}& =\frac{[s+W{G}_p{G}_2-s(W{W}_1{G}_g{G}_2\lambda +1)]·G_1}{(s+W{G}_p{G}_2)(s+sC{G}_1{G}_g)}\hfill \\ \hfill & =\frac{(G_p-s{W}_1{G}_g\lambda )W{G}_1{G}_2}{(s+W{G}_p{G}_2)(s+sC{G}_1{G}_g)}\hfill \end{array}$$

(12)

When satisfied,

$$G_p=s{W}_1{G}_g\lambda$$

(13)

Namely,

$$W_1=\frac{G_p}{G_g\lambda }·\frac{1}{s}$$

(14)

It can be deduced that

$$\frac{{\theta }_L}{T_{d1}}=0$$

(15)

3.3. The Design Process

The composite stabilization control system for reflectors is designed and derived in Section 3.1 and Section 3.2. The design specifications are as follows:

• The two-axis fast reflector is developed based on a high bandwidth position closed-loop control system that receives position instructions. Its motion range is five times greater than the coarse-stable zone and covers the maximum angle error of coarse stabilization. The angle control error is less than one tenth of the maximum angle error of the coarse stabilization.
• Two-axis velocity gyros are installed on the active axes of the coarse-stable framework and used as feedback signals to design the two-axis inertial stabilization controller.
• The gyro signals are adjusted using Equation (14) and treated as the position instruction input for the fast reflector.

4. Experiments and Analysis

4.1. The Design of Subsystem and Composite System

Figure 10 shows the construction of the validation experimental system for both traditional and fast reflector equipment, using a real product as a reference. The construction principles and key parameters of the experimental system are based on the overall simulation model presented in Figure 11.

Figure 12 displays the experiment results for the closed-loop bandwidths of the coarse and fine stabilizations of the pitch axis, which were the focus of this study.

The overall simulation model of the system, shown in Figure 11, was constructed based on the scheme depicted in Figure 7. The specific details of Figure 11 are as follows:

• On the far left are the inputs of linear and rotational disturbances, used to simulate the interference of carrier motion.
• The top row is the kinematics analysis of linear disturbances, including the coarse-stable azimuth and pitch frameworks, and the linear kinematics model of fine-stable azimuth and pitch frameworks.
• Below the kinematics analysis of linear disturbances is the kinematics analysis of rotation disturbances, including the coarse-stable azimuth framework, coarse-stable pitch driving framework and coarse-stable pitch driven framework, as well as the rotation motion model of fine-stable azimuth and pitch frameworks, corresponding to Equations (1) and (2).
• Other boxes represent the dynamic model analysis module, mainly the private server motor model used in the system, which is consistent with the dynamic analysis shown in Figure 8.
• The middle part of Figure 11 shows the mechanism implementation module with a transmission ratio of 2-to-1, and the rotational error is set to $0.1^{\circ }$ based on experience.

A sinusoidal command with a frequency of 1 Hz is applied to both channels, resulting in self-stabilization of the LOS motion. Figure 13 displays the experiment results, indicating that the LOS moved in a controlled manner, and both axes performed consistently well.

4.2. The Anti-Disturbance Comparison Experiment

4.2.1. The Comparative Experiment of Fixed-Frequency Angular Velocity Disturbance

The azimuth axis and pitch axis channels were subjected to a fixed frequency disturbance of 1 degree and 1 Hz, respectively. The motion response of the line of sight (LOS) for the traditional reflector stabilization and composite stabilization control systems is presented in Figure 14 and Figure 15. As evident from the figures, the traditional reflector has a two-axis stabilization error range of approximately 3.6 $\mathsf{\mu }$rad, whereas the composite stabilization mode has a range of only 0.048 $\mathsf{\mu }$rad. This represents a significant improvement of 75 times in stabilization precision.

4.2.2. The Comparative Experiment of Translational Disturbance with Traditional Reflector Stabilization

The LOS motion results of the traditional reflector stabilization and composite stabilization control systems under the influence of a flat vibration disturbance applied to the base can be observed in Figure 16 and Figure 17.

The traditional reflector stabilization exhibits an error range of approximately 3.7 $\mathsf{\mu }$rad in azimuth of the LOS and 3.0 $\mathsf{\mu }$rad in pitch, while the error range under composite stabilization control is about 2.2 $\mathsf{\mu }$rad in azimuth of the LOS and 1.9 $\mathsf{\mu }$rad in pitch, resulting in a 37% reduction in error.

In comparison to angular disturbance, composite stabilization mode demonstrates superior suppression effects. However, it is observed that the suppression effect is not as pronounced for flat vibration acceleration disturbance. This is largely due to the error induced by dynamic unbalance torque acting on the fast reflector assembly under flat vibration disturbance, which falls beyond the compensation mechanism. Hence, to effectively suppress the error, it is necessary to improve the precision of dynamic balance during the design and machining process while also enhancing the control stiffness of fine-stable components.

4.2.3. Comparative Analysis of Translational Disturbance against Existing Methods

To validate the proposed compensation method for the composite stability mechanism, its effectiveness was compared with existing research methods. Stability precision was evaluated using error range under constant frequency disturbance of 1 degree and 1 Hz, with methods such as ZPETC [21], XPC real-time simulation [22], optimized adaptive Kalman filtering (OAK) [23], high-speed target tracking (HT) [24], LuGre and ADRC (LA) [18], back-stepping control (BS) [19], and RBFNN and SMC (RS) [20] used as comparison indices.

The corresponding validation experiments for each method were all repeated five times, and the stability precisions based on the error ranges were calculated five times. The average values were calculated as the comparison standards for the final stability performances. All experimental results are listed in

Table 1. The stability precision of different methods under constant frequency disturbance.

Error Range ($\mathsf{\mu }$rad)		Proposed Method	ZPETC	XPC	OAK	HT	LA	BS	RS
Azimuth	No.1	0.056	3.854	1.983	7.342	102.5	0.632	0.029	0.285
	No.2	0.045	3.743	2.345	7.034	100.3	0.621	0.031	0.265
	No.3	0.043	3.767	2.123	6.874	96.3	0.547	0.032	0.279
	No.4	0.047	3.967	2.324	6.987	99.2	0.587	0.025	0.269
	No.5	0.049	4.139	1.885	6.663	103.7	0.683	0.023	0.279
	avg	0.048	3.874	2.132	6.980	100.4	0.614	0.028	0.279
Pitch	No.1	0.054	3.564	2.234	3.322	135.3	0.643	0.065	0.348
	No.2	0.053	3.521	2.145	3.435	136.3	0.623	0.066	0.356
	No.3	0.047	3.323	2.023	3.021	132.5	0.598	0.062	0.358
	No.4	0.045	3.412	1.987	3.123	132.8	0.599	0.061	0.338
	No.5	0.041	3.505	2.271	3.269	134.1	0.607	0.061	0.345
	avg	0.048	3.465	2.132	3.234	134.2	0.614	0.063	0.349

.

Based on the comparison results, the proposed composite stabilization method shows superior performance in enhancing stability precision under constant frequency disturbance, surpassing existing classic methods.

5. Conclusions

The proposed composite stability technology of global stability + reflector stability is a solution to the problem of high precision stability of the optical detector’s visual axis (LOS), which combines the large motion range of the coarse two-axis platform with the high bandwidth and accuracy of the fast reflector. This paper presents a theoretical study on the technology realization method and demonstrates through experiments that the composite stabilization mechanism can effectively improve the stability precision of the system, surpassing traditional reflector stabilization methods and other classical stabilization control methods. These research results provide a reference for the development of new products of high-precision photoelectric stabilization platforms.

6. Limitation and Future Work

This study has some limitations that need to be acknowledged, including (1) the study only considers error correction issues related to dynamics and current control loops, neglecting other crucial errors such as mechanical installation errors and gyroscope noise errors; (2) the study only focuses on correcting and compensating errors through control algorithms, without considering other methods such as error adaptive compensation; and (3) the validation conditions and experimental parameters used are relatively simple and ideal, which may differ from real-world engineering applications.

Future research will primarily concentrate on enhancing accuracy in more complex and practical engineering applications, such as developing more precise error compensation methods to deal with carrier motion interference. Advanced techniques such as machine learning will be employed to construct error correction based on neural network adaptive models.