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Abstract
The pointing and tracking performance of laser beams in free space optical communication (FSOC) systems and other precision laser systems is severely limited by beam jitter. This research proposes an adaptive control method to suppress beam jitter by adjusting the deflection angle of the beam by controlling the fast steering mirror (FSM) driven by piezoelectric ceramics. In order to verify the effectiveness of the control method, we have established an experimental platform. First, the internal controller of the FSM is adjusted to an approximately linear system, aiming to turn the input and output control signals into a linear relationship. Based on the adaptive filter, a filtered-x variable step-size normalized least mean square (FxVSNLMS) algorithm is proposed. To further improve the robustness of the controller, a Proportion Integral Differential (PID) controller and an adaptive controller which work in parallel are then added to the control loop. Finally, experimental results are provided and compare with the traditional controller and other adaptive control methods. Experimental results show that for more complex narrow-band and broad-band mixed beam disturbances, the control scheme developed in this research is significantly improved. This conclusion has also been verified on the ground experimental platform of FSOC.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser transmission over long-distance and precise target aiming have long been a question of great interest in a wide range of laser orientation systems such as free space optical communication (FSOC) systems [1–3]. In practical applications, there are two main types of disturbances that seriously degrade system performance. The former comes from atmosphere turbulence, which causes changes in the density of the laser propagation medium, and light is then refracted [4,5]. Atmospheric turbulence is usually broad-band, affecting the terrestrial system in the atmosphere, or the communication link between the satellite and the ground [6,7]. The latter comes from mechanical vibration, which is usually an natural frequency generated by the platform equipped with the laser emission source or due to the movement of other mechanical parts [8,9]. Mechanical vibration disturbance is generally narrow-band and is not affected by the use environment. It has been observed that these disturbances will cause the laser beam to fluctuate or even deviate from the target position, which will have a very negative impact on free space optical communication (FSOC) and other laser aiming systems.
The purpose of the beam jitter control is to suppress the broad-band and narrow-band jitter discussed above through the control scheme and stabilize the position of the beam at the target point [10–12]. There is a variety of disturbances causes beam jitter, which is usually expressed as an angle measured in radians in the optical path. But when the light beam falls on the photodetector, such as quadrant detector (QD) or charge coupled device (CCD) camera, the jitter will appear as errors in the horizontal and pitch directions. Therefore it can be measured in the form of displacement or the number of pixels.
Beam jitter control uses a fast steering mirror (FSM) to accurately point the laser beam to the target point. The jitter control schame requires an fast convergent adaptive controller for optimal control. To date, most of the adaptive control research for beam jitter suppression has adopted the least mean square (LMS) and the recursive least square (RLS) adaptive filtering algorithm [13–15]. The adaptive controllers based on LMS are numerically stable and effective, but they usually converge slowly. Those based on RLS provide significant and high-speed adaptive capabilities, but the high-order lattice adaptive RLS filter algorithm is more complicated [16]. Therefore, in the application of FSOC systems, we need to weigh the convergence speed and the computational complexity of the control algorithm.
Inspired by the adaptive controller used in [17], this paper proposes a filtered-x variable step-size normalized least mean square (FxVSNLMS) control algorithm, which is mainly used to suppress the disturbance with lower frequency than the control fast steering mirror (CFSM) control bandwidth. At present, there are many adaptive control methods used to control FSM driven by piezoelectric ceramics [18–20]. It has been proved that the adaptive control algorithm based on the least mean square adaptive filter has higher requirements on the calculation [21]. Filtered-x least mean square (FxLMS) and filtered-x normalized least mean square (FxNLMS) algorithms were first proposed for active noise control [15,22,23]. Then expanded in vibration suppression and chatter control [24,25]. FxLMS and FxNLMS adaptive filters are simple and robust as an improved LMS adaptive filter. They are considered to be easier to obtain controller parameters. Because of the excellent performance of these algorithms in jitter control, they have been widely used in laser beam jitter control of the FSOC systems [12,10]. However, the traditional FxLMS algorithm is limited by slow convergence speed, and the mean square error and convergence speed are not proportional to the step-size. Compared with the standard FxLMS algorithm, the FxNLMS algorithm has adjustable controller parameters but one of its defects is that the step-size is fixed.
The importance and originality of this study is to utilize variable step-size to accelerate the convergence of the adaptive filter. Compared with the RLS filter, the LMS filter also has a simpler structure and less computational complexity. In addition, we introduce Proportion Integral Differential (PID) control into the control system to further improve the system robustness. This is because the disturbance signal is unknown and changes with time, a sudden increase in amplitude will cause the adaptive controller unable to adjust. It must be mentioned that the beam jitter control system built in this article has a more complex jitter, no vibration isolation measures have been taken between our experimental platform and the building, so the system is exposed to an external mechanical vibration environment. This phenomenon will be explained in more detail in Section 4.
2. Experimental system description
In order to explore the experimental verification of the adaptive control algorithm in the beam jitter control system, we built an experimental platform for beam jitter control. Schematic diagrams and pictures of the experimental platform are shown in Fig. 1 and Fig. 2 respectively.
The experimental platform contains a laser source, a laser attenuator to attenuate the laser power to the same magnitude as the communication optical power in the FSOC system, and a collimator to transform the single-mode laser beam into collimated parallel light, a coupling lens to focus the beam on the detector, a spot position detection sensor (QD), and two FSM: disturbance fast steering mirror (DFSM) and control fast steering mirror (CFSM). These devices are installed on the optical floating platform, for isolating the components from external vibrations, but in this research, to simulate a more complex beam jitter environment, we turned off the air flotation device, so the platform is inevitably affected by the vibration of the external environment. By applying different disturbance signals to the DFSM, the beam in the optical path jitter accordingly, which is manifested in the position shift of the light spot on the surface of the detector. The effects of mechanical vibration and atmospheric turbulence to be dealt with by the FSOC platform are simulated through narrow-band and broad-band disturbances of different frequencies [26].
The laser beam emitted from the laser passes through the fiber collimator and first propagates to the DFSM, which is used to add narrow-band disturbance to the beam and to simulate the broad-band disturbance of atmospheric turbulence. Immediately, the beam is passed to the CFSM, where the computer control signal is input for correcting the beam jitter. Finally, the corrected beam is focused on the surface of the spot position detection sensor through the coupling lens. The QD feeds back an error signal to the computer. So far, the experimental platform simulates the jitter control system in the receiver of the FSOC system. Table 1 provides the device name and specific parameter information in the beam jitter control system.
Table 1. Equipment list and parameters provided by the test bench
From the control system block diagram shown in Fig. 3, it can be seen that the jitter signal ${d_1}(n)$ generated by the disturbance source and the narrow-band jitter signal ${d_2}(n)$ generated by the vibration source have a response of ${d_{in}}(n)$ through the DFSM. The response of the control signal ${u_{in}}(n)$ and the narrow-band jitter signal ${d_2}(n)$ input to the CFSM is ${y_{out}}(n)$. The error signal is then obtained by subtracting ${y_{out}}(n)$ from ${d_{in}}(n)$, which is detected by a photoelectric sensor and fed back to the jitter controller that outputs a control signal ${u_{in}}(n)$. In this beam jitter control system, the CFSM is closed-loop, and completed by the internal controller.
3. Control system
3.1 Fast steering mirror feedback control
The CFSM is the actuator that corrects the beam in the beam jitter control system. There is an analog control loop in the actuator, and the resistance strain gauge inside the CFSM is installed on the surface of the piezoelectric ceramic to feedback the internal measurement value of the CFSM position. The internal control loop can be selected as open-loop or closed-loop through an analog switch. The goal of this work is to show that the adaptive controller can improve the control performance of the existing stable feedback controller. Therefore, the CFSM in the beam jitter control system is closed-loop by default.
In the feedback control loop, a proportional integral controller is used to adjust the output accuracy of the CFSM. Figure 4 shows the output response of the closed-loop CFSM, with the transfer function $P(z)$ is determined by system identification. In order to suppress noise to the greatest extent and increase the control bandwidth without amplifying high-frequency disturbance, the proportional integral link is selected. It can be seen from the closed-loop frequency characteristic curve that the closed-loop bandwidth of the system is 1010 Hz. In addition, considering that the CFSM is in a closed-loop state, and there is no coupling between the x-axis and the y-axis, thus the control voltage applied to the CFSM and the elongation of the piezoelectric ceramic (the deflection angle of the mirror) have a linear relationship.
3.2 Adaptive control algorithm
The core of the adaptive filter control system for beam jitter is the adaptive filter and the corresponding adaptive algorithm. The adaptive filter can automatically adjust its own transfer function according to a certain criterion to achieve the required output. Because the transverse structure Finite Impulse Response (FIR) filter is easy to implement and the LMS algorithm’s simplicity, the transverse adaptive filter based on the LMS algorithm has been widely used in the field of signal processing. The FxLMS algorithm refers to a version of the LMS algorithm applied to the modeling shown in Fig. 5. It was first proposed for active noise control. The open-loop transfer function between the jitter signal and the output signal of the point position sensor is denoted as $P(z)$, and its gain is determined by the spot position sensor and the length of the laser transmission path. The two channels of the dual input of the DFSM and the dual output of the spot position sensor are uncoupled. Therefore, in the subsequent discussion and controller design in this article, $P(z)$ has two uncoupled channels.
In the beam jitter control system, we need to use a filter x adaptive algorithm. $d(n)$ represents the response of the primary jitter error source $x(n)$ in the DFSM. The input of the adaptive algorithm is filtered by the secondary path $S(z)$. In the block diagram of the adaptive control algorithm shown in Fig. 5, $S(z)$ represents the secondary path formed by the secondary source $y(n)$ being detected from the photoelectric sensor and then subjected to pre-amplification, primary filtering, and A/D sampling. $\hat{S}(z)$ represents the estimation model of the secondary path. $x^{\prime}(n)$ is the primary jitter error source $x(n)$ filtered by $\hat{S}(z)$, that is, the estimation of the primary jitter error source by the filter. $e(n)$ is the system error that has the same meaning as the residual beam jitter error.
In applications such as FSOC and adaptive optics, the dynamic model of an FSM as a beam steering device is either known or can be determined through a one-time system identification. However, due to the changes in the atmospheric conditions in the optical path, the structure of the optical system and the excited vibration mode, the disturbance characteristics usually change during the operation of the beam control system. In the previous work, we determined the transfer function $P(z)$ of the primary path and the transfer function $G(z)$ of the CFSM through system identification. But the dynamic model of the disturbance is unknown, which is represented by the transfer function $W(z)$ in the control loop. Assuming $\hat{S}(z) = S(z)$, $W(z)$ can be solved, such that
Therefore, the weight of the filter is approximated by an FIR filter, which is adjusted by using the variable step-size normalized LMS algorithm proposed in this paper.
3.3 FxVSNLMS algorithm
The normalized LMS algorithm can be described as a strategy considering the change of the signal at the input of the filter. Considering the recurrence of the LMS algorithm:
where the step-size parameter is time-varying, therefore, we call it the variable step-size NLMS algorithm. By choosing an appropriate $\mu (n)$ to minimize the magnitude of the posterior error, we can getSo far, we have obtained the update equation of the tap weight coefficient vector of the variable step-size NLMS algorithm:
Then we evaluate the complexity of the algorithm based on the number of operations required for one iteration of the algorithm. Assume that W(z) and P(z) are FIR filters of length L and M respectively. Taking the FxLMS algorithm as an example, one iteration requires addition/subtraction of L + M-1 and multiplication/division of L + M. As the limit of asymptotic complexity, the complexity of all algorithms is O(L) level for each sample. Table 2 briefly summarizes the algorithm proposed in this paper, namely the FxVSNLMS (filtered-x variable step-size normalized least mean square) algorithm. FxLMS, FxNLMS and FxVSNLMS algorithm control the addition/subtraction required in one iteration of the filter, and the times of multiplication/division are summarized in Table 3.
Table 2. The FxVSNLMS algorithm
Table 3. Computational Complexity of different algorithms.
3.4 PID parallel control
During the operation of beam jitter control systems such as FSOC and adaptive optics, the disturbance caused by mechanical vibration and atmospheric turbulence changes. Therefore, adaptive feedback control is applied to suppress such disturbances. However, the sudden increase of the amplitude of some frequency components and sudden mechanical vibration will reduce the robustness of the control system, resulting in a decrease in the convergence speed of the adaptive controller or even failure to converge. In order to solve this problem, we introduce PID control and adaptive controller in parallel into the control loop. It can be seen from the control block diagram in Fig. 6 that the PID controller works in parallel with the FxVSNLMS controller proposed in this article.
The control scheme of the PID control loop is as follows:
4. Experimental results and analysis
In the experimental system introduced in Section 2, the CFSM is used not only to compensate the beam jitter influence of the DFSM, but also to deal with the interferences caused by instruments’ vibrations in the experimental environment. The impacts of satellite platform vibration and atmospheric turbulence on the laser beam are simulated by applying different narrow-band and broad-band random disturbance signals to the DFSM. Many research institutions have measured the vibration characteristics of satellite platforms by launching on-orbit test satellites [9]. They use triaxial stability sensors to measure the spectrum of satellite disturbance power spectral density (PSD). It has previously been observed that the resonance frequency of vibration mainly occurs within 500 Hz.
Firstly, we analyzed the influence of experimental device vibration and building vibration on the beam. In the process of collecting the beam jitter signal caused by environmental factors, we did not power up the CFSM, which can eliminate the influence of micro-vibration under zero position voltage of the CFSM. It can be seen from Fig. 7 that the CFSM is equivalent to a fixed-angle mirror in the optical path, so the center of spot mass is not in the center of the detector. From the PSD spectrum of the beam jitter signal in Fig. 8, it can be seen that the resonant frequencies of the x-axis and the y-axis are 100 Hz and 200 Hz.
In order to verify the effectiveness of the control method proposed in this paper, we conducted experiments on the beam jitter control experimental platform mentioned in Section 2. First, we apply several fixed-frequency sinusoidal disturbances on the DFSM to obtain the corresponding beam position deviation on the QD and show them in Fig. 9, Fig. 10, and Fig. 11. The deviation of the spot position of the x-axis and y-axis on the surface of the detector can be expressed as the deviation of the beam's azimuth and pitch angle.
We compared the classic PID control method with other adaptive control methods. It is obvious that for the fixed-frequency sinusoidal disturbance, with increases in frequencies of the disturbances, the PID control method gradually reduces the control effect. The other three adaptive control methods all show satisfactory control effects. It can be seen from Table 4 that the method proposed in this paper has the smallest root mean square error (RMSE) value of the control residual error for the fixed-frequency disturbances, indicating that its control effect is better than the other two adaptive control methods. In addition, we show the PSDs of the jitter before and after control in Table 5.
Table 4. RMSE of control results of fixed frequency beam disturbance
Table 5. PSD of the jitter before and after control
The beam disturbance caused by mechanical vibration is usually a mixture of multiple narrow-band vibration disturbance signals. In the second set of experiments, we input three sets of mixed jitter signals to the DFSM, which are composed of 20 Hz, 50 Hz, and 100 Hz narrow-band jitter signals and 0-500 Hz broad-band white noise signals. In addition, the experimental platform is exposed to the vibration environment caused by buildings and other instruments in the laboratory, causing more severe jitter on the QD. We compared our method with the traditional PID, FxLMS and FxNLMS control method. The results are shown in Fig. 12, and the position error of the light spot on the QD is shown in Fig. 13.
In addition, we compared the convergence speed and stability of the three control algorithms through the influence of a set of step signals on the three control algorithms. We verify the convergence speed of several control methods through a step signal with an amplitude of 0.2 mm. It can be seen from the comparison results in Fig. 14, that the method proposed in this paper can complete convergence and reach a steady state in 0.003 seconds. The convergence time of FxLMS adaptive control and FxNLMS adaptive control are both longer than FxVSNLMS.
The experimental results show that for application scenarios with multi-band beam jitter, the traditional PID control method cannot meet high-precision control requirements. Due to the introduction of variable step-size parameters and the addition of parallel PID control, our control method significantly improves not only the robustness of the system, but also the convergence speed and algorithm stability. Numerically, the RMSE of multi-band beam jitter on the x-axis control results is reduced by 65.2% and 52.2% compared with FxLMS control and FxNLMS control methods.
To further verify the effectiveness of the control method proposed in this paper in practical applications, we apply it to the “XingGuang01(XG01)” low-orbit inter-satellite FSOC terminal ground experimental platform, which is mainly used to verify the target Pointing, Acquisition, and Tracking (PAT) of the FSOC terminal. The “XG01” terminal has the capabilities of automatic scanning, coarse tracking and fine tracking, as well as tracking and maintenance. It’s can carry out two-way laser beam alignment through remote control commands. The designed communication distance is 3000km-5000 km, and the communication rate is 1.25Gbps. The beacon laser has a wavelength of 800 nm, and the communication signal laser has a wavelength of 1550 nm. Coarse tracking accuracy is required to be less than 60urad, fine tracking accuracy is required to be less than 5urad, and precision tracking interference suppression bandwidth is greater than 200 Hz. The schematic diagram of the experimental platform is shown in Fig. 15.
The communication laser is emitted by a laser. First, it passes through the DFSM to introduce a disturbance signal to the beam for simulating the beam jitter caused by mechanical vibration on the satellite platform. Then the laser passes through the optical system to simulate the long-distance transmission of the laser in the space environment. Finally, it passes through a three-meter-long collimator to adjust the beam to parallel light. The optical system of the receiving telescope, the laser fine tracking control system, the spot coarse tracking and fine tracking position detection system are all installed in the PAT terminal. The spot position detector adopts a CCD camera, and the spot position change is represented by pixels in the camera. In the platform, one pixel in the direction of the azimuth and pitch angle corresponds to the deflection of the beam for $4.4\mu rad$. The PAT terminal is installed on the turntable with a L-shaped folding shaft structure, which is used to provide coarse tracking requirements.
First, we apply a disturbance signal with amplitude of 4 pixels, frequency of 20 Hz and offset of 1.2 pixels on the DFSM. The coarse tracking control is closed-loop, and the spot jitter phenomenon is observed in the fine tracking spot detector. By analyzing the disturbance without control in the fine tracking link, we found that, due to the vibration of the instrument and the influence of environmental factors, the disturbance signal is not an ideal 20 Hz sinusoidal disturbance signal with 1.2 pixels offset. Therefore, the requirements for the controller are more stringent.
In this set of experiments, we turned on the controller at 12.5s to get the compensated spot error. It can be seen from Fig. 16 that the three adaptive controllers have obvious advantages over traditional PID control. However, the control effect of the FxLMS controller with a filter length of $N = 24$ gradually decreases over time when dealing with the disturbance signal. Compared with the other two adaptive controllers, our method has a more obvious control effect. This conclusion can also be further confirmed from the RMSE of the beam jitter control in Table 6.
Table 6. RMSE of the 20 Hz disturbance control results on the “XG01” test platform
Subsequently, for verifying the anti-disturbance performance of the “XG01” test platform, we added a set of multi-band disturbance signals to the beam by DFSM. The disturbances contain seven components, all of which are generated by passing white noise through different filters. The bandwidths of these disturbance components are listed in Table 7. Compared with the first five components, the amplitude of the latter two jitter components is smaller. In most applications, beam jitter caused by mechanical vibration and atmospheric turbulence will bring errors in both the horizontal direction and the pitch direction. Therefore, we applied almost the same jitter signal on the horizontal axis and the pitch axis.
Table 7. Jitter bandwidths
Figure 17 shows the comparison of the spot scatter diagram detected on the CCD detector and the control effect of the three adaptive control algorithms. The point in the figure represents the position of the light spot mass center on the surface of the detector. The spot position shown in the figure is the statistics of the spot position after 5 seconds in the time series shown in Fig. 18.
It can be seen from the results of multi-band beam jitter control in Fig. 18 and Fig. 19, that the control effect of FxLMS and FxNLMS control algorithm gradually decreases with the increase of beam signal complexity. The FxNLMS has a certain improvement in convergence speed and stability compared to the FxLMS due to the normalized step-size parameter. The control method proposed in this paper can better deal with complex jitter signals due to the introduction of variable step-size parameters and the addition of PID control in the control loop. It can be easily concluded that our method has a significant improvement in convergence speed and control stability.
5. Conclusion
Aiming at the problem of beam jitter suppression in precise beam pointing and tracking, this paper has developed an experimental platform for researching beam jitter control schemes, and proposed an adaptive controller to effectively suppress laser beam jitter. For further improving the control system robustness, a PID controller and an adaptive controller are added to the control loop to work in parallel. The control method is verified by the beam jitter control platform built in this paper. The experimental results show that the control scheme has greatly improved the effect of suppressing the beam jitter compared with the traditional control method. In addition, compared with FxLMS and FxNLMS adaptive controllers, it has better performance in narrow-band jitter and more complex narrow-band and broad-band hybrid jitter control. This control method has also been applied to the “XG01” FSOC terminal ground experimental platform. Through the multi-band beam jitter environment test, the results show that the control scheme has better performance in control performance and stability.
Funding
National Natural Science Foundation of China (61875257).
Acknowledgments
The authors express sincere thanks for the experiments provided by the Photoelectric Tracking and Measurement Technology Laboratory, Xi'an Institute of Optics and Precision Mechanics, CAS. The authors are very grateful to Dr. Zengxin Liu for polishing the language of the paper.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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