A fast mirror precise control method based on super-spiral sliding mode disturbance observation

Abstract

This invention relates to a precision control method for a fast-reflecting mirror based on superspiral sliding mode disturbance observation, belonging to the field of photoelectric system tracking control. The method includes the following steps: Step 1, modeling the voice coil motor fast-reflecting mirror system; Step 2, obtaining a superspiral sliding mode control algorithm based on the constructed model; Step 3, designing a superspiral disturbance observer based on the superspiral sliding mode control algorithm; Step 4, the superspiral disturbance observer calculates the system control quantity, and a digital-to-analog converter performs digital-to-analog conversion, sending the analog voltage signal as an input command to the power driver; Step 5, the power driver outputs a corresponding drive current to the voice coil motor coil winding, causing the mirror surface of the fast-reflecting mirror to generate a precise angular displacement; Step 6, an angle measurement sensor detects the mirror deflection angle in real time and feeds it back to the main control module. This invention can both perform real-time online observation and compensation for the total disturbance of the fast-reflecting mirror system and improve the response speed and tracking accuracy of the fast-reflecting mirror system.

Description

Technical Field

[0001] This invention relates to the field of tracking control of photoelectric systems, and in particular to a precision control method for fast-reflecting mirrors based on super-spiral sliding mode perturbation observation. Background Technology

[0002] Optical-electric tracking systems are high-precision dynamic target tracking devices based on photoelectric detection and servo control technology. By acquiring the target's spatial position information in real time and implementing closed-loop control, they have been widely used in various fields such as military reconnaissance, laser communication, astronomical observation, and traffic monitoring. Fast steering mirror (FSM) systems are an indispensable and crucial component of most optical-electric tracking systems. To achieve precise system control, FSM systems require excellent tracking accuracy and anti-interference performance. Although traditional PID controllers have been used in optical-electric tracking, they exhibit significant limitations in handling nonlinear disturbances, making it difficult to meet the stringent high-precision control requirements of FSM systems.

[0003] To improve the control accuracy and anti-interference capability of photoelectric tracking systems, scholars both domestically and internationally have conducted in-depth research on the precision control technology of fast-reflecting mirror systems, and have successively proposed a variety of advanced control strategies, such as fuzzy control, active disturbance rejection control, neural network adaptive control, and sliding mode control. Among these methods, sliding mode control (SMC) has gained some application due to its insensitivity to changes in system parameters and external disturbances, as well as its rapid response, simple implementation, and high robustness. However, traditional sliding mode control typically satisfies the sliding mode reachability condition by setting a large upper limit for disturbances. This conservative design leads to frequent system state crossings of the sliding surface, resulting in significant chattering, and it cannot perform online estimation and compensation for internal and external disturbances, thus limiting its further application in the field of precision control for photoelectric tracking. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for precise control of fast-reflecting mirrors based on super-helical sliding mode perturbation observation.

[0005] A precision control method for fast-reflecting mirrors based on superspiral sliding mode perturbation observation includes the following steps:

[0006] Step 1: Model the voice coil motor fast-reflecting mirror system;

[0007] Step 2: Obtain the superspiral sliding mode control algorithm based on the constructed model;

[0008] Step 3: Design the superhelical disturbance observer based on the superhelical sliding mode control algorithm;

[0009] Step 4: The superspiral disturbance observer calculates the system control quantity, and after amplitude limiting, transmits it to the digital-to-analog conversion module for digital-to-analog conversion to obtain the corresponding analog voltage signal. The analog voltage signal is then sent to the power driver as an input command.

[0010] Step 5: The power driver outputs the corresponding drive current to the coil winding of the voice coil motor according to the input command, thereby driving the mirror surface of the fast reflector to produce a precise angular displacement around its rotation center.

[0011] Step 6: The rotation angle measurement sensor detects the actual deflection angle of the mirror in real time and feeds it back to the main control module to form a closed-loop control circuit.

[0012] Furthermore, step 1 specifically includes:

[0013] The equivalent mathematical model of the two-axis voice coil motor fast-reflector system is a second-order mass-spring-damped system, and its open-loop transfer function is:

[0014] ,

[0015] Where t is the sampling time; then Let represent the angular displacement, angular velocity, and angular acceleration of the fast-reflection mirror system, respectively; u(t) is the system control input to the fast-reflection mirror system; a, b, and c are the angular displacement matching parameters, angular velocity matching parameters, and system matching parameters of the model, respectively.

[0016] make The system control variable u = u(t) is expressed as the state equation of the fast-reflecting mirror system as follows:

[0017] ,

[0018] Where d represents the total disturbance received by the system. , , , This represents angular displacement, angular velocity, and the system's fluctuation range coefficient. y represents the interference introduced by the external environment; y is the actual output signal of the system.

[0019] Furthermore, step 2 specifically includes:

[0020] The control objective of the fast-reflecting mirror system is: The sliding mode variable s is: ,in, , Indicates controller parameters, These are the desired tracking angle and desired tracking angular velocity values ​​for the fast-reflection mirror system, respectively. For the angle tracking error of the fast-reflecting mirror system; For the angular velocity tracking error of the fast-reflection mirror system; differentiate with respect to the sliding mode variable:

[0021] u is the system control variable; , denoted as angular displacement and angular velocity of the fast-reflection mirror system; a, b, and c are the angular displacement matching parameters, angular velocity matching parameters, and system matching parameters of the model, respectively; d represents the total disturbance experienced by the system.

[0022] The design of the superspiral sliding mode control algorithm is as follows:

[0023] ,

[0024] in, and These are the sliding mode control coefficient and the intermediate switch control coefficient, respectively; s is the sliding mode variable; L is the intermediate variable; when the system satisfies the super-helical sliding mode control algorithm, the sliding mode variable s and its derivative are... It will converge to zero in a finite amount of time; sign(s) is the switching function;

[0025] Based on sliding mode variables The formula for calculating the system control quantity is:

[0026] ,

[0027] in, This represents the desired angular velocity of the fast-reflecting mirror system;

[0028] Substituting the system control law formula into the calculation, and transferring the original disturbance term d to the derivative term of the intermediate variable L, the reconstructed super-helical sliding mode control algorithm is obtained as follows:

[0029] .

[0030] Furthermore, step 3 specifically involves:

[0031] Based on the state equation of the fast-reflecting mirror system, and taking the total disturbance d of the system as a new state variable, the extended state equation of the fast-reflecting mirror system is obtained as follows:

[0032] ,

[0033] Where g(t) is the derivative of the total interference of the fast-reflection mirror system;

[0034] Based on the extended state equation of the fast-reflection mirror system, the extended state observer is designed as follows:

[0035] ,

[0036] in, and These are the observed values ​​of the polarization angular velocity and disturbance of the fast-reflection mirror system. For the observation error of velocity, To perturb the observation error, and The coefficients to be designed for the observer;

[0037] Perturbed observations By performing feedforward compensation, the formula for the superspiral perturbation observer is obtained:

[0038] .

[0039] The beneficial effects of this invention are as follows: This invention proposes a super-helical sliding mode control method based on disturbance observation to improve the tracking performance of fast mirror. Compared with the traditional sliding mode controller, the super-helical sliding mode algorithm proposed in this invention can not only perform online observation and compensation for the total disturbance of the fast mirror system in real time, but also improve the response speed and tracking accuracy of the fast mirror system. At the same time, it effectively weakens the chattering phenomenon of traditional sliding mode control and enhances the robustness of the fast mirror system under parameter perturbation and external disturbance, which has certain application prospects and research value. Attached Figure Description

[0040] Figure 1 This is a control block diagram of a fast-reflecting mirror precision control method based on super-spiral sliding mode disturbance observation, as proposed in this application.

[0041] Figure 2 This is a schematic diagram of a two-axis voice coil motor fast mirror structure in a fast mirror precision control method based on super-helical sliding mode disturbance observation in this application;

[0042] Figure 3 This is a diagram showing the sinusoidal signal tracking in a fast-reflecting mirror precision control method based on super-helical sliding mode perturbation observation, as described in this application.

[0043] Figure 4 This is a diagram of the perturbation observer in a fast-reflecting mirror precision control method based on super-helical sliding mode perturbation observation, as described in this application.

[0044] Figure 5 This is the controller input diagram in a fast-reflecting mirror precision control method based on super-helical sliding mode disturbance observation, as described in this application.

[0045] Figure descriptions: 1. Reflector; 2. Reflector support structure; 3. Voice coil motor; 4. Angle measurement sensor; 5. Flexible support structure; 6. Fast-reflecting mirror base; 7. Main control module. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] In this embodiment: A method for precise control of a fast-reflecting mirror based on superspiral sliding mode perturbation observation according to an embodiment of the present invention includes:

[0048] Step 1: Model the voice coil motor fast-reflector system.

[0049] Step 2: Using the voice coil motor fast-reflecting mirror system model established in Step 1, design a super-helical sliding mode controller.

[0050] Step 3: Design a superspiral perturbation observer;

[0051] After obtaining the superhelical perturbation observer, as Figure 1 As shown, the system control quantity u(t) is calculated and, after being limited, is transmitted to the digital-to-analog converter module to be converted into a corresponding analog voltage signal. This analog voltage signal is sent as an input command to the power driver. The power driver outputs the corresponding drive current to the coil winding of the voice coil motor according to the input command. The working principle of the voice coil motor is based on the Lorentz force law: the energized coil experiences an electromagnetic force proportional to the current in the magnetic field generated by the permanent magnet. This electromagnetic force drives the flexible hinge mechanism of the fast reflector, thereby causing the mirror surface of the fast reflector to produce a precise angular displacement around its rotation center. At the same time, the rotation angle measurement sensor installed on the back of the mirror surface detects the actual deflection angle of the mirror surface in real time and feeds it back to the main control module, forming a closed-loop control circuit.

[0052] Step 1: Model the voice coil motor fast-reflecting mirror system. This will be implemented according to the following steps:

[0053] The equivalent mathematical model of a two-axis voice coil motor with a fast-reflecting mirror is a second-order mass-spring-damped system, and its open-loop transfer function is as follows:

[0054] (1)

[0055] Where t is the sampling time; then Let represent the angular displacement, angular velocity, and angular acceleration of the fast-reflecting mirror system, respectively; u(t) is the system control input of the fast-reflecting mirror system; a, b, and c are the angular displacement matching parameters, angular velocity matching parameters, and system matching parameters of the model, respectively.

[0056] make The system control variable u = u(t) is expressed as the state equation of the fast-reflecting mirror system as follows:

[0057] (2)

[0058] Equation (2) incorporates a comprehensive consideration of the uncertainties in the parameters of the fast-reflecting mirror system and external disturbances, namely... Represents the total disturbance received by the system. , , This reflects the fluctuation range of the fast-reflection mirror system parameters (angular displacement, angular velocity, and system parameters), while This represents interference introduced by the external environment. Furthermore, y represents the actual output signal of the system. , For the angular displacement and angular velocity of the fast-reflecting mirror system.

[0059] Step 2 specifically involves designing a super-spiral sliding mode controller using the voice coil motor fast-reflection mirror system model established in Step 1, and implementing it according to the following steps:

[0060] The control objective of the fast-reflecting mirror system is: The sliding mode variable s is designed as follows:

[0061] (3)

[0062] in, , Indicates controller parameters, These are the desired tracking angle and desired tracking angular velocity values ​​for the fast-reflection mirror system, respectively. For the angle tracking error of the fast-reflecting mirror system; To determine the angular velocity tracking error of the fast-reflection mirror system; differentiate with respect to the sliding mode variable s:

[0063] (4)

[0064] The design of the superspiral sliding mode control algorithm is as follows:

[0065] (5)

[0066] in, and These are the sliding mode adjustment coefficient and the intermediate switch adjustment coefficient, respectively; s is the sliding mode variable; when the system satisfies this super-helical sliding mode control algorithm, it can ensure that the sliding mode variable s and its derivative are... It converges to zero in a finite time. It is worth noting that although the superspiral algorithm model includes two switching functions sign(s), they do not affect the system's second-order sliding mode properties. Specifically, regarding... Switching function, parameters The system approaches zero near the sliding surface, effectively suppressing the step characteristics of this part. Meanwhile, the switching function sign(s) in the intermediate variable L is transformed into a continuous signal through integration, and the discontinuous nature of its derivative is hidden during the integration process. This ingenious design ensures that the first derivative of the sliding variable remains continuous in the neighborhood of the sliding surface, thereby ensuring that the system satisfies the continuous stability condition on the sliding surface. This algorithm exhibits second-order sliding mode characteristics, effectively suppressing chattering phenomena commonly found in traditional sliding mode control from a control principle perspective.

[0067] The sliding mode variable function for designing a fast-reflecting mirror is: The system control quantity is then set as shown in equation (6):

[0068] (6)

[0069] in, This represents the desired angular velocity of the fast-reflecting mirror system;

[0070] Substituting the equation into equation (4), we get:

[0071] (7)

[0072] In equation (7), the dynamic characteristics of the sliding mode variable are affected by the external disturbance term d. The original disturbance term d can be transferred to the derivative term of the intermediate variable L, thereby realizing the reconstruction of the super-helical sliding mode control algorithm:

[0073] (8)

[0074] As shown in equation (8), under the control law equation (6), the sliding mode variable equation of the system satisfies the structure of a superspiral system with perturbation. Now, stability verification is carried out for the superspiral system with perturbation. That is, by selecting an appropriate matrix to construct a Lyapunov candidate function, if the selected function satisfies the positive definite condition and its derivative is negative definite, it indicates that the total energy of the system continues to decay, thereby ensuring the asymptotic stability of the system.

[0075] Choose the state variable as:

[0076] (9)

[0077] Choose the Lyapunov function as follows:

[0078] (10)

[0079] in Let be a matrix, denoted as:

[0080] (11)

[0081] It is not difficult to see when hour, It is a positive definite matrix. It satisfies the positive definite quadratic form condition. Assume the derivative of the perturbation... Bounded, that is Then, when the coefficients λ and α satisfy the following equation:

[0082] (12)

[0083] The derivative of the Lyapunov function of the system satisfies the negative definite condition, at which point the system exhibits global asymptotic stability, and the system state variable X will converge to the sliding surface in finite time. This also indicates that the sliding variable s and its first derivative of the superspiral sliding system are... All of them converge to zero within a finite amount of time.

[0084] Step 3: Design the superspiral perturbation observer, specifically following these steps:

[0085] Based on the dynamic equation of the fast-reflecting mirror system given by equation (2), we can consider adding the disturbance term. d Also considered as a new state variable, the following extended state equation for the fast-reflecting mirror system can be obtained:

[0086] (13)

[0087] in g(t) To obtain the derivatives of all perturbations in the fast-reflection mirror system, the extended state observer is further designed as follows:

[0088] (14)

[0089] in, and These are the observed values ​​of the polarization angular velocity and disturbance of the fast-reflection mirror system. For the observation error of velocity, To perturb the observation error, and Let be the coefficients to be designed for the observer. Subtracting equation (13) from equation (14) yields the observation error dynamic equation of the fast-reflecting mirror system:

[0090] (15)

[0091] Equation (15) shows that the error dynamic equation of the extended state observer satisfies the form of a perturbation-containing second-order superspiral sliding mode structure. The stability of this perturbation-containing superspiral system has been demonstrated previously, when the coefficients... and When certain conditions are met and the derivative of the perturbation is bounded, the observer's error variable... and Asymptotic convergence to zero ensures the effectiveness of the superspiral sliding mode observer.

[0092] The observed disturbance value After performing feedforward compensation, the formula for the superspiral perturbation observer is obtained as follows:

[0093] (16)

[0094] Then the sliding mode state equation of the system under the control law (16) will become:

[0095] (17)

[0096] When the observation results stabilize, the observed values ​​will tend to the actual values, that is... Therefore, provided the observer's observations are accurate, it can effectively compensate for the effects of disturbances on the system, and significantly suppress and mitigate chattering. The control block diagram is shown below. Figure 1 .

[0097] To facilitate quantitative comparison of the control effect of the fast-reflecting mirror precision control method based on super-spiral sliding mode perturbation observation proposed in this invention, the root mean square error is defined. for:

[0098] (18)

[0099] in N The number of sampling points is given. The desired tracking signal given in the experiment is a sinusoidal signal with an amplitude of 0.5 mrad and a frequency of 10 Hz. The fast-reflecting mirror system is simulated and verified using a traditional sliding mode (SMC) controller and a perturbation observation-based super-spiral sliding mode controller (STA) proposed in this paper.

[0100] The voltage-position open-loop transfer function of the fast-reflecting mirror during simulation is:

[0101] (19).

[0102] In a preferred embodiment, such as Figure 2As shown, the two-axis voice coil motor fast-reflecting mirror structure in the precision control method based on super-spiral sliding mode disturbance observation includes: a reflector 1, a reflector support structure 2, a voice coil motor 3, an angle measurement sensor 4, a flexible support structure 5, a fast-reflecting mirror base 6, and a main control module 7. The main control module 7 calculates, processes, and performs digital-to-analog conversion of the system control quantities, and inputs commands to the power driver of the voice coil motor 3. The power driver outputs a corresponding drive current to its coil windings. The working principle of the voice coil motor 3 is based on the Lorentz force law: a current-carrying coil experiences an electromagnetic force proportional to the current in the magnetic field generated by a permanent magnet. This electromagnetic force pushes the flexible support structure (hinge) of the fast-reflecting mirror 1, thereby causing the mirror surface of the reflector 1 to produce a precise angular displacement around its rotation center. Simultaneously, the angle measurement sensor 4, installed on the back of the mirror surface, detects the actual deflection angle of the mirror surface in real time and feeds it back to the main control module 7, forming a closed-loop control circuit.

[0103] Figure 3 The results show the tracking performance of the traditional sliding mode controller and the proposed superspiral sliding mode controller for sinusoidal signals. After adding a disturbance, the proposed superspiral sliding mode controller can track the system state more quickly and accurately, and its output curve is closer to the input sinusoidal signal curve. Initially, the convergence speed of the traditional sliding mode controller is lower than that of the superspiral sliding mode controller. After stable tracking (0.017s~1s), the RMS error of the traditional sliding mode controller is approximately 16.40 μrad, while the RMS error of the controller proposed in this paper is approximately 5.38 μrad, demonstrating a significant improvement in accuracy. The peak error of the traditional sliding mode controller is approximately 23.41 μrad, while the peak error of the superspiral sliding mode controller is approximately 8.04 μrad (reduced to 34.3% of the traditional sliding mode algorithm). Figure 4 The disturbance estimation curves of the super-helical sliding mode observer (Equations (14) to (15)) proposed in this invention are shown. The red line and the blue line represent the actual disturbance value and the disturbance estimation value, respectively. It can be seen that the trends of the disturbance estimation value and the actual disturbance value are basically consistent. The disturbance observer has a certain estimation effect on the total disturbance (external disturbance and parameter uncertainty), which provides a good feedforward effect for the high-precision control of the fast mirror system.

[0104] Figure 5 The control input simulation curves of the two controllers were recorded. It can be seen from the enlarged part of the figure that the super-helical sliding mode controller based on disturbance observation proposed in this invention significantly reduces chattering compared with the traditional sliding mode control.

[0105] In the description of embodiments of the present invention, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first," "second," "third," or "fourth" may explicitly or implicitly include one or more of that feature. In the description of the present invention, unless otherwise stated, "a plurality of" means two or more.

[0106] In the description of embodiments of the present invention, the term "and / or" is used only to describe the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " generally indicates that the preceding and following associated objects are in an "or" relationship.

[0107] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A precise control method for a fast-reflecting mirror based on superspiral sliding mode perturbation observation, characterized in that, Includes the following steps: Step 1: Model the voice coil motor fast-reflecting mirror system; Step 2: Obtain the superspiral sliding mode control algorithm based on the constructed model; Step 2 specifically involves: The control objective of the fast-reflecting mirror system is: The sliding mode variable s is: ,in, , Indicates controller parameters, These are the desired tracking angle and desired tracking angular velocity values ​​for the fast-reflection mirror system, respectively. For the angle tracking error of the fast-reflecting mirror system; For the angular velocity tracking error of the fast-reflection mirror system; differentiate with respect to the sliding mode variable: u is the system control variable; , denoted as angular displacement and angular velocity of the fast-reflection mirror system; a, b, and c are the angular displacement matching parameters, angular velocity matching parameters, and fast-reflection mirror system matching parameters, respectively; d represents the total disturbance experienced by the fast-reflection mirror system. The design of the superspiral sliding mode control algorithm is as follows: ， in, and These are the sliding mode control coefficient and the intermediate switch control coefficient, respectively; s is the sliding mode variable; L is the intermediate variable; when the fast-reflecting mirror system satisfies the super-helical sliding mode control algorithm, the sliding mode variable s and its derivative are... It will converge to zero in a finite amount of time; sign(s) is the switching function; Based on sliding mode variables The formula for calculating the system control quantity is: ， in, This represents the desired angular velocity of the fast-reflecting mirror system; Substituting the system control formula into the calculation, and transferring the original disturbance term d to the derivative term of the intermediate variable L, the reconstructed super-helical sliding mode control algorithm is obtained as follows: ； Step 3: Design the superhelical disturbance observer based on the superhelical sliding mode control algorithm; Step 4: The super-helical disturbance observer calculates the control quantity of the fast-reflecting mirror system, and after amplitude limiting, it is transmitted to the digital-to-analog conversion module for digital-to-analog conversion to obtain the corresponding analog voltage signal. The analog voltage signal is then sent to the power driver as an input command. Step 5: The power driver outputs the corresponding drive current to the coil winding of the voice coil motor according to the input command, thereby driving the mirror of the fast-reflecting mirror system to produce a precise angular displacement around its rotation center. Step 6: The rotation angle measurement sensor detects the actual deflection angle of the mirror in real time and feeds it back to the main control module to form a closed-loop control circuit.

2. The method for precise control of a fast-reflecting mirror based on superspiral sliding mode perturbation observation as described in claim 1, characterized in that, Step 1 specifically involves: The equivalent mathematical model of the two-axis voice coil motor fast-reflector system is a second-order mass-spring-damped system, and its open-loop transfer function is: ， Where t is the sampling time; then Let represent the angular displacement, angular velocity, and angular acceleration of the fast-reflecting mirror system, respectively; u(t) is the system control input of the fast-reflecting mirror system; a, b, and c are the angular displacement matching parameter, angular velocity matching parameter, and system matching parameter, respectively. make The system control variable u = u(t) is expressed by the state equation of the fast-reflecting mirror system as follows: ， Where d represents the total interference experienced by the fast-reflection mirror system. , , , These represent the angular displacement, angular velocity, and fluctuation range coefficient of the fast-reflecting mirror system, respectively. y represents interference introduced by the external environment; y is the actual output signal of the fast-reflecting mirror system.

3. The method for precise control of a fast-reflecting mirror based on super-helical sliding mode perturbation observation as described in claim 1, characterized in that, Step 3 specifically involves: Based on the state equation of the fast-reflecting mirror system, taking the total disturbance d experienced by the fast-reflecting mirror system as a new state variable, the extended state equation of the fast-reflecting mirror system is obtained as follows: ， Where g(t) is the derivative of the total interference of the fast-reflection mirror system; Based on the extended state equation of the fast-reflection mirror system, the extended state observer is designed as follows: ， in, and These are the observed values ​​of the polarization angular velocity and disturbance of the fast-reflection mirror system. For the observation error of velocity, To perturb the observation error, and The coefficients to be designed for the extended state observer; Perturbed observations By performing feedforward compensation, the formula for the superspiral perturbation observer is obtained: 。

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