A fast steering mirror sliding mode control method and related devices

Abstract

This application belongs to the field of optical device control technology and discloses a sliding mode control method and related equipment for a fast reflector. The method includes: establishing a closed-loop error model of the fast reflector; the closed-loop error model includes a lumped disturbance term composed of external disturbances and system parameter measurement deviations; setting a fixed-time RBF disturbance observer; the fixed-time RBF disturbance observer is used to estimate the lumped disturbance term to output a lumped disturbance estimate, and the fixed-time RBF disturbance observer is configured with a weight update law that makes the estimation error converge within a fixed time independent of the initial state; based on the lumped disturbance estimate output by the fixed-time RBF disturbance observer and the closed-loop error model, a sliding mode controller is constructed; the sliding mode controller is used to control the fast reflector; thereby improving control accuracy and anti-interference capability, while avoiding the problems of controller dependence on the upper bound of the disturbance and disturbance estimation convergence time dependence on the initial state.

Description

Technical Field

[0001] This application relates to the field of optical device control technology, and more specifically, to a fast mirror sliding mode control method and related equipment. Background Technology

[0002] Fast reflectors, as precision beam pointing adjustment devices, play a crucial role in high-precision optical systems such as space-to-ground laser communication and optical tracking due to their excellent dynamic performance. These systems have extremely stringent requirements for beam pointing accuracy and stability, typically needing to achieve micro-radian or even sub-micro-radian levels. However, in practical applications, fast reflector systems face multiple technical challenges: First, the inherent nonlinear characteristics of the system make it difficult to achieve ideal control effects using traditional linear control methods; second, external disturbances such as atmospheric turbulence and mechanical vibration significantly affect control accuracy; and third, system parameters drift due to factors such as temperature changes and mechanical wear during actual operation, leading to model mismatch problems.

[0003] Currently, the control of fast reflectors mainly employs PID control and its improved algorithms. While these methods are simple in structure and have a fast response, they suffer from significant shortcomings in terms of anti-interference capability and parameter robustness. Although sliding mode control has been introduced into this field due to its strong robustness, existing solutions still have significant drawbacks: most sliding mode controllers fail to simultaneously handle external disturbances and system parameter uncertainties, limiting their practical applications; control algorithms typically require prior knowledge of the upper bound of the disturbance, forcing designers to use excessively large control gains, which wastes energy and may excite unmodeled dynamics; existing disturbance observers mostly employ finite-time convergence mechanisms, whose convergence speed heavily depends on the initial state, making it difficult to guarantee stable dynamic performance. These problems severely restrict the control accuracy and reliability of fast reflectors in extreme environments.

[0004] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0005] The purpose of this application is to provide a fast mirror sliding mode control method and related equipment, which improves control accuracy and anti-interference ability, while avoiding the problems of controller dependence on upper bound of disturbance and disturbance estimation convergence time dependence on initial state.

[0006] In a first aspect, this application provides a fast sliding mode control method for a reflective mirror, the method comprising the following steps:

[0007] A1. Establish a closed-loop error model for the fast reflector; the closed-loop error model includes a lumped disturbance term composed of external disturbances and system parameter measurement deviations;

[0008] A2. Set up a fixed-time RBF perturbation observer; the fixed-time RBF perturbation observer is used to estimate the lumped perturbation term to output the lumped perturbation estimate, and the fixed-time RBF perturbation observer is configured with a weight update law that makes the estimation error converge within a fixed time independent of the initial state;

[0009] A3. Based on the lumped disturbance estimate output by the fixed-time RBF disturbance observer and the closed-loop error model, construct a sliding mode controller;

[0010] A4. Use the sliding mode controller to control the fast reflector.

[0011] Secondly, this application provides an electronic device including a processor and a memory, the memory storing a computer program executable by the processor, wherein when the processor executes the computer program, it performs the steps of the fast-reflecting mirror sliding mode control method described above.

[0012] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the fast mirror sliding mode control method described above.

[0013] Beneficial effects: The sliding mode control method and related equipment for a fast reflector provided in this application improve control accuracy and anti-interference ability by establishing a closed-loop error model, setting a fixed-time RBF disturbance observer, constructing a sliding mode controller and controlling the fast reflector, while avoiding the problems of controller dependence on the upper bound of disturbance and disturbance estimation convergence time dependence on the initial state. Attached Figure Description

[0014] Figure 1 A flowchart of a fast-sliding mirror sliding mode control method provided in this application.

[0015] Figure 2 A schematic diagram of the structure of the electronic device provided in this application.

[0016] Labeling explanations: 301, processor; 302, memory; 303, communication bus. Detailed Implementation

[0017] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0018] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this application, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0019] Please refer to Figure 1 A fast-reflecting mirror sliding mode control method in some embodiments of this application includes the following steps:

[0020] A1. Establish a closed-loop error model for the fast reflector; the closed-loop error model includes a lumped disturbance term composed of external disturbances and system parameter measurement deviations;

[0021] A2. Set up a fixed-time RBF perturbation observer; the fixed-time RBF perturbation observer is used to estimate the lumped perturbation term to output the lumped perturbation estimate, and the fixed-time RBF perturbation observer is configured with a weight update law that makes the estimation error converge in a fixed time independent of the initial state.

[0022] A3. Based on the lumped disturbance estimate and closed-loop error model output by the fixed-time RBF disturbance observer, a sliding mode controller is constructed;

[0023] A4. Use a sliding mode controller to control the fast reflector.

[0024] A fast reflector is a precision opto-electromechanical device used to adjust the beam direction between a light source and a receiver. It is characterized by its small size, low inertia, fast response speed, and high compensation accuracy, and is widely used in high-precision opto-electromechanical systems such as space / ground-based laser communication, image stabilization optics, adaptive optics, and optical tracking.

[0025] The closed-loop error model is a mathematical model used to describe the error dynamics of a fast reflector in a control system. This model typically includes angular error, angular velocity error, and a lumped disturbance term composed of external disturbances and deviations in system parameter measurements. It forms the basis for designing controllers and observers.

[0026] In the closed-loop error model of the fast reflector, the lumped disturbance term combines external disturbances (such as atmospheric turbulence and optical-electromechanical carrier jitter) and system parameter measurement deviations (such as model parameter uncertainties) into a single comprehensive disturbance term. This approach simplifies the modeling and compensation of complex disturbance sources.

[0027] The fixed-time RBF perturbation observer is a perturbation observer based on a radial basis function (RBF) neural network. Its design goal is to accurately estimate the lumped perturbation term within a fixed time independent of the initial state. This observer ensures rapid convergence of the estimation error by configuring a specific weight update law.

[0028] Sliding mode controllers are nonlinear controllers that achieve robust control of a system by designing a sliding surface and allowing the system state to move along that surface. Sliding mode control has a strong ability to suppress changes in system parameters and external disturbances.

[0029] This embodiment provides a sliding mode control method for a fast reflector. The method aims to achieve high-precision angle control of the fast reflector under the influence of external disturbances and uncertainties in system parameter measurement, and to ensure that the disturbance estimation converges within a fixed time independent of the initial state.

[0030] Specifically:

[0031] First, in step A1, a closed-loop error model for the fast reflector is established. This closed-loop error model includes a lumped disturbance term composed of external disturbances and measurement deviations of system parameters. In practical applications, there are several ways to establish a closed-loop error model. For example, a dynamic model containing disturbance terms can be obtained by fitting the input and output data of the fast reflector using system identification methods. Another approach is to analyze the mechanical structure and electrical characteristics of the fast reflector based on physical principles, derive its equations of motion, and then introduce disturbance terms. For example, parameters such as inertia, damping, and stiffness of the fast reflector can be considered and combined with external environmental factors (such as wind and vibration) and sensor noise to form a comprehensive error model.

[0032] Secondly, in step A2, a fixed-time RBF perturbation observer is set up. This fixed-time RBF perturbation observer is used to estimate the lumped perturbation term to output the lumped perturbation estimate, and it is configured with a weight update law that ensures the estimation error converges within a fixed time independent of the initial state. In practice, different RBF neural network structures and weight update strategies can be used. For example, the center and width parameters of the RBF neural network can be preset or adjusted using an adaptive algorithm. The design of the weight update law is crucial to ensuring fixed-time convergence, and it can be derived using a method based on Lyapunov stability theory to guarantee that the estimation error converges to zero within a finite time, and that the convergence time is independent of the initial state.

[0033] Next, in step A3, a sliding mode controller is constructed based on the lumped disturbance estimate output by the fixed-time RBF disturbance observer and the closed-loop error model. When constructing the sliding mode controller, different sliding surfaces and control laws can be selected according to different control objectives and system characteristics. For example, the sliding surface can be designed as a linear combination of system state errors, or it can be a more complex nonlinear function. The design of the control law typically includes an equivalent control term and a switching control term. The equivalent control term is used to cancel system dynamics, while the switching control term is used to compensate for disturbances and drive the system state to the sliding surface. The introduction of the lumped disturbance estimate eliminates the need for the controller to rely on upper bound information about the disturbance, thereby improving the controller's practicality.

[0034] Finally, in step A4, a sliding mode controller is used to control the fast reflector. During actual control, the control output of the sliding mode controller acts on the actuator of the fast reflector, such as a drive motor, thereby adjusting the deflection angle and angular velocity of the fast reflector. The calculation and output of the control input need to be performed in real time to ensure that the fast reflector can accurately track the desired trajectory and effectively suppress disturbances.

[0035] Compared to traditional PID controllers, the proposed solution more effectively suppresses nonlinear disturbances and parameter uncertainties, significantly improving control accuracy and robustness. Compared to existing sliding mode controllers, the fixed-time RBF disturbance observer overcomes the drawback of traditional observers where convergence time depends on the initial state, ensuring fast and deterministic disturbance estimation. Furthermore, it eliminates the need to predict the upper bound of the disturbance, reducing control gain and effectively avoiding chattering. This integrated design enables the fast reflector to maintain excellent performance even in the face of complex and variable external environments and internal system uncertainties, thus possessing significant engineering value in high-precision applications such as spaceborne laser communication and adaptive optics.

[0036] In some implementations, step A1 includes:

[0037] A101. Based on external disturbances and uncertainties in system parameter measurements, a fast reflector motion model including a lumped disturbance term is established; the lumped disturbance term is composed of both external disturbances and system parameter measurement deviations.

[0038] A102. Based on the motion model of the fast reflector, establish a closed-loop error model for angle error and angular velocity error; the angle error is the error between the actual deflection angle and the desired deflection angle of the fast reflector, and the angular velocity error is the error between the actual deflection angular velocity and the desired deflection angular velocity of the fast reflector.

[0039] In step A101, establishing a fast-reflecting mirror motion model that includes a lumped disturbance term refers to mathematically describing the dynamic behavior of the fast-reflecting mirror and explicitly introducing a lumped disturbance term into this model. This lumped disturbance term aims to comprehensively reflect all unmodeled dynamic characteristics, external disturbances, and variations in internal system parameters. For example, a second-order linear differential equation can be used to describe the mirror's angular position and angular velocity, with a term representing the lumped disturbance added to this equation. This term can encompass external environmental factors (such as vibration and airflow disturbances) and internal system uncertainties (such as deviations in stiffness, damping, or motor constants). Alternatively, for mirror systems with significant nonlinear characteristics, a more complex nonlinear motion model can be constructed, similarly using a lumped disturbance term to uniformly handle unmodeled dynamics and various uncertainties.

[0040] The lumped disturbance term is composed of both external disturbances and system parameter measurement deviations, meaning that this disturbance term includes not only the influence of the external environment on the system but also the inaccuracies of the system's own parameters. External disturbances refer to all external forces or influences acting on the fast reflector system that are not controlled inputs, such as changes in ambient temperature, air pressure fluctuations, or mechanical vibrations. System parameter measurement deviations refer to the differences between the actual values ​​and design or measured values ​​of the system's physical parameters (such as parameters related to mass, inertia, stiffness, damping, and natural oscillation frequency).

[0041] For example, the angular motion of a fast-reflecting mirror can be simplified to a second-order underdamped element, whose open-loop transfer function can be described as:

[0042] (1);

[0043] in, For open-loop transfer functions, For open-loop gain, For the system damping ratio, The natural oscillation frequency of the system. It is a complex variable.

[0044] Considering external disturbances, the above open-loop transfer function can be rewritten in the form of the following state equation:

[0045] (2);

[0046] (3);

[0047] in, This represents the actual deflection angle of the fast-reflecting mirror. This represents the actual deflection angular velocity of the fast-reflecting mirror. for The first derivative with respect to time, for The first derivative with respect to time, To control the quantity, Due to external disturbances, , and These are the actual values ​​of the system parameters, and , , .

[0048] Based on the above state equations, we further consider the measurement uncertainty of system parameters, which manifests as the deviation between the measured and actual values ​​of the system parameters. Let... , and These are measured values ​​of system parameters. , and For the system parameter measurement deviation, the measured value of the system parameter, the actual value of the system parameter, and the system parameter measurement deviation satisfy the following relationship:

[0049] , , ;

[0050] Substituting the above relationships into formulas (2) and (3), we can obtain the following fast-reflecting mirror motion model:

[0051] (4);

[0052] (5);

[0053] (6);

[0054] in, This is the lumped disturbance term.

[0055] In step A102, establishing a closed-loop error model for angular and angular velocity errors based on the fast-reflecting mirror motion model involves deriving a mathematical model describing the dynamic behavior of system errors by introducing the desired trajectory and defining error variables, based on the established fast-reflecting mirror motion model. This process transforms the control objective from tracking an absolute trajectory to driving the error to zero, thus simplifying controller design. For example, the angular error can be defined as the difference between the actual deflection angle and the desired deflection angle, and the angular velocity error as the difference between the actual and desired deflection angular velocities. Then, these error definitions are substituted into the motion model and combined with the dynamic characteristics of the desired trajectory to obtain a system of differential equations for the angular and angular velocity errors.

[0056] Angular error is the error between the actual deflection angle and the desired deflection angle of the fast reflector. It is a direct measure of the deviation between the current angular position and the target angular position of the fast reflector, quantifying the positioning accuracy of the system. In practical applications, this error can be obtained by subtracting the commanded angle from the actual angle measured by the encoder or position sensor in the control unit. Angular velocity error is the error between the actual deflection angular velocity and the desired deflection angular velocity of the fast reflector. It is a measure of the deviation between the current angular velocity and the target angular velocity of the fast reflector, quantifying the system's performance in velocity tracking. In practical applications, this error can be obtained by subtracting the desired angular velocity (usually obtained from the derivative of the desired angle) from the actual angular velocity derived from the gyroscope or position sensor data.

[0057] For example, angular error and angular velocity error are defined as follows:

[0058] (7);

[0059] (8);

[0060] in, For angular error, For angular velocity error, For the desired deflection angle of the fast-reflecting mirror, for The first derivative with respect to time, and represents the desired deflection angular velocity of the fast-reflecting mirror;

[0061] Substituting equations (7) and (8) into equations (4) and (5), we can obtain the following closed-loop error model:

[0062] (9);

[0063] (10);

[0064] in, for The first derivative with respect to time, for The first derivative with respect to time, for The second derivative with respect to time.

[0065] This application's solution first establishes a fast reflector motion model incorporating a lumped disturbance term based on external disturbances and system parameter measurement uncertainties. It clarifies that the lumped disturbance term is jointly composed of external disturbances and system parameter measurement deviations, thus comprehensively and accurately capturing all uncertainties affecting the fast reflector's performance. This comprehensive modeling approach avoids the inaccuracy problems caused by neglecting some disturbance sources in traditional methods. Based on this motion model, a closed-loop error model for angle and angular velocity errors is established, and these errors are clearly defined. This application provides a clear and accurate dynamic description of the error for subsequent controller design. The construction of this error model allows the controller to directly optimize for system deviations, thereby improving control accuracy and response speed. This precise modeling provides accurate disturbance source information for the fixed-time RBF disturbance observer, enabling the observer to more effectively estimate lumped disturbances. Furthermore, the sliding mode controller can achieve high-precision and robust control of the fast reflector based on these accurate disturbance estimates and the error model, significantly improving the system's performance in complex disturbance environments.

[0066] In some implementations, the fixed-time RBF perturbation observer is an RBF neural network model, which is as follows:

[0067] (11);

[0068] in, For the lumped disturbance estimate (i.e., for) (estimated value) This is the estimated weight matrix of the RBF neural network model. for The transpose of the matrix, Let be the Gaussian matrix of the RBF neural network model, and , for The n radial basis functions are:

[0069] , (12);

[0070] in, Let j be the radial basis function. This is the input vector for the RBF neural network model. Let j be the center vector of the j-th radial basis function. Let be the width of the j-th radial basis function;

[0071] The RBF neural network model is configured with a weight update law that makes the estimation error converge in a fixed time independent of the initial state.

[0072] The RBF neural network model is a type of feedforward neural network where the hidden layer neurons use radial basis functions as activation functions, and the output layer linearly combines the outputs of the hidden layers. This model exhibits good nonlinear approximation and generalization capabilities, and is commonly used in function approximation, pattern recognition, and control. (Estimation of the weight matrix...) It is the set of weight parameters connecting the hidden and output layers in an RBF neural network model. These weights are adjusted during training to optimize the network's output. It can accurately approximate the actual lumped disturbance term D. It can be a column vector or a matrix, the dimension of which depends on the number of neurons in the hidden layer and the dimension of the output. It can be initialized with random small values ​​or with a zero matrix. (Gaussian matrix) It is the set of outputs of the hidden layer neurons in the RBF neural network model, each element This corresponds to a radial basis function. The calculation of the Gaussian matrix depends on the input vector. The center vector of the radial basis functions and width The Gaussian matrix can be generated by pre-setting the number of radial basis functions n and based on the input vector. This is obtained by calculating the output value of each radial basis function. Radial basis functions It is the activation function of the hidden layer neurons in the RBF neural network model, characterized by the output value depending only on the distance between the input and the center. In this application, a Gaussian function is used, i.e., formula (12). This function form makes the network responsive to local regions of the input space, thereby enhancing the model's local approximation ability. Other forms of radial basis functions can also be chosen, such as quadratic functions or thin-plate spline functions, but the Gaussian function is widely used due to its smoothness and locality. Input vector This is the input data received by the RBF neural network model, used to calculate the output of the radial basis function. In the context of perturbation observations, the input vector... This is typically included in system state errors, such as angle errors. Angular velocity error Or a combination thereof. The dimensions and specific content of the input vector need to be designed according to the actual application scenario and perturbation characteristics. Center vector The center position of each radial basis function (RBF) in the input space is defined. The choice of these center vectors is crucial to the performance of the RBF neural network, as they determine which regions of the input space the network responds to most strongly. Various methods can be used to determine the center vectors, such as using the K-means clustering algorithm to cluster the training data and using the cluster centers as the center vectors. Alternatively, randomly selected training samples can be used as... Alternatively, the width can be preset in the input space using a uniform distribution method. The response range, or "width," of each radial basis function is defined. A larger width results in a wider response range and lower sensitivity to input variations; a smaller width results in a narrower response range and higher sensitivity. Width The weights can be determined heuristically, for example, by setting them as a proportion of the maximum distance between adjacent centers; or they can be adjusted using optimization algorithms, such as genetic algorithms or particle swarm optimization algorithms. The rules.

[0073] This fixed-time RBF perturbation observer combines fixed-time convergence characteristics with a radial basis function (RBF) neural network. Its main function is to estimate the lumped perturbation term in a fast reflector system in real time, ensuring that the estimation error converges within a fixed time independent of the system's initial state. In some preferred embodiments, the weight update law of the RBF neural network model is:

[0074] (13);

[0075] (14);

[0076] (15);

[0077] in, This is the estimated value of the angular velocity error. for The first derivative with respect to time, , , and It is a positive number, and , , for rate of change, To estimate the error, It is a positive number.

[0078] The observer dynamic equation (15) defines the dynamic behavior of a fixed-time RBF disturbance observer. It models the system state and disturbance by using the derivative of the angular velocity error estimate z. This dynamic equation includes known terms from the closed-loop error model. It reflects the nominal dynamics of the system; it includes the lumped perturbation estimate obtained by the RBF neural network model. It is used to compensate for unknown disturbances in the system; and contains key nonlinear terms to achieve fixed-time convergence. The dynamic equation can be discretized using a digital controller (such as a microcontroller, DSP, or FPGA), and calculated in each control cycle based on the current system state and control input. , and update z.

[0079] Where z is the estimated angular velocity error, which is the actual angular velocity error of the fast-reflecting mirror. The estimation of z is achieved by gradually approximating the true angular velocity error through the evolution of the observer's dynamic equations, providing accurate state information for subsequent disturbance estimation and controller design. z can be obtained by integrating the observer's dynamic equations; for example, in digital implementations, iterative updates can be performed using numerical integration methods such as the Euler method or the Runge-Kutta method.

[0080] parameter , , and It is a positive number, and , These are the design parameters in the fixed-time convergence term. By carefully selecting these parameters, the observation error (or estimation error) can be ensured. It converges to a small neighborhood near zero in a fixed time independent of the initial state. This ensures fast convergence even with large errors, while This ensures that the convergence rate is maintained even when the error is small, working together to achieve fixed-time convergence. One approach is to theoretically derive and design these parameters using Lyapunov stability theory to meet the conditions for fixed-time convergence. Another approach is to optimize these parameters through simulation experiments, selecting appropriate values ​​while satisfying the requirements for system stability and convergence rate.

[0081] The RBF neural network model is configured with a weight update law that ensures the estimation error converges within a fixed time independent of the initial state. This weight update law is the algorithm used in the RBF neural network model to adjust its internal weights. This law ensures that the estimation error of the lumped disturbance by the RBF neural network converges within a fixed time, and this convergence time does not depend on the initial values ​​of the neural network weights or the initial state of the disturbance, thereby improving the robustness and real-time performance of the disturbance estimation. One implementation approach is to design the weight update law based on Lyapunov stability theory, introducing specific nonlinear terms or saturation functions to guarantee the fixed-time convergence of the weight error. Another implementation approach is to combine the weight update law with adaptive control theory, adjusting the weights through online learning while ensuring convergence characteristics.

[0082] The fixed-time RBF perturbation observer proposed in this application achieves accurate, fixed-time convergent estimation of lumped perturbations in a fast-reflecting mirror system by introducing specific nonlinear terms and an RBF neural network model. In the above implementation, firstly, based on the motion model and closed-loop error model of the fast-reflecting mirror, a system dynamic equation including lumped perturbation terms is constructed. Based on this, the observer estimates the angular velocity error using its dynamic equation. This dynamic equation cleverly combines the known dynamic information of the system with the lumped disturbance estimate output by the RBF neural network model. And, crucially, the fixed-time convergence term. Within the fixed-time convergence term, This represents the estimation error of the angular velocity error, which is determined by design parameters. , , and This allows the estimation error to converge to a small neighborhood near zero within a fixed time independent of the system's initial state. Simultaneously, the lumped disturbance estimate... Instead of being preset, the disturbance estimation is generated in real-time by an RBF neural network model. This RBF neural network model leverages its powerful nonlinear approximation capabilities to learn and compensate for complex disturbances in the system online. More importantly, this RBF neural network model is configured with a special weight update law, which is also designed to ensure that the estimation error of the neural network converges within a fixed time independent of the initial state. This dual fixed-time convergence mechanism (fixed-time convergence of the observer state estimation and fixed-time convergence of the RBF neural network weight estimation) works together to give the entire disturbance estimation process extremely high robustness and real-time performance. Through the above mechanism, this fixed-time RBF disturbance observer overcomes the limitation of traditional disturbance observers whose convergence time depends on the initial state. Regardless of the initial state of the system, it can provide accurate lumped disturbance estimates within a predictable fixed time. These accurate disturbance estimates are then used in the sliding mode controller, effectively compensating for external disturbances and system parameter measurement deviations, significantly improving the angle control accuracy of the fast reflector and its ability to suppress disturbances. This design enables the entire control system to maintain high performance and high stability in the face of uncertainties and disturbances.

[0083] The update law of formula (13) used in this application is an adaptive law based on the idea of ​​gradient descent, which is based on the estimation error. and Gaussian matrix To adjust in real time To reduce the estimation error due to perturbation, this update law ensures that the estimation error converges within a fixed time, independent of the initial state. Besides this form, other adaptive algorithms such as least squares or Kalman filtering can also be used for the weight update law, but the update law in this application has advantages in terms of fixed-time convergence. (Estimation error) It is an important feedback signal used by the RBF neural network model to adjust the weights; it represents the angular velocity error. The difference between the estimated angular velocity z and the actual angular velocity error. This error directly reflects the accuracy of the disturbance observer's estimation of the system state. When As the value approaches zero, it indicates that the observer's estimation of angular velocity error is more accurate, and consequently, the estimation of lumped disturbance is also more accurate. (Positive constant) It is a learning rate parameter in the weight update law, which controls the estimation of the weight matrix. Adjustment speed. The larger the value, the slower the weight adjustment, which may make the system more stable but the convergence speed is slower. The smaller the value, the faster the weights are adjusted, potentially leading to faster convergence but also causing system oscillations or instability. Therefore, The selection of a metric requires a trade-off between convergence speed and system stability, and is usually optimized through simulation or experimentation.

[0084] Through the aforementioned weight update law, the fixed-time RBF disturbance observer of this application can accurately estimate the lumped disturbance term. Crucially, the convergence time of this estimation error is fixed and independent of the system's initial state. Compared to traditional disturbance observers, this significantly improves the efficiency and robustness of disturbance estimation, providing more reliable disturbance compensation information for the subsequent sliding mode controller. This fixed-time convergence characteristic enables the entire control system to reach a steady state more quickly when facing unknown disturbances and parameter uncertainties, thereby ensuring high-precision angle control of the fast reflector.

[0085] Specifically, step A3 includes:

[0086] Design a sliding mode surface, and based on the lumped disturbance estimate and closed-loop error model output by a fixed-time RBF disturbance observer, combine the sliding mode surface, Use class functions and symbolic functions to construct a sliding mode controller.

[0087] In constructing a sliding mode controller, this application first requires the design of a sliding surface. The sliding surface is a core concept in sliding mode control theory; it defines a hyperplane or manifold in the system's state space. When the system state reaches and remains on this surface, the system will exhibit the desired dynamic characteristics, such as insensitivity to disturbances and fast convergence. By rationally designing the sliding surface, the system state can be guided to move along this surface, thereby achieving precise control over the system's performance.

[0088] When constructing a sliding mode controller, it is also necessary to use the lumped disturbance estimate and closed-loop error model based on the output of a fixed-time RBF disturbance observer. The lumped disturbance estimate provided by the fixed-time RBF disturbance observer... This can reflect the external disturbances and internal parameter uncertainties experienced by the system in real time, providing feedforward compensation information for the controller. This lumped disturbance estimate... This can be directly obtained from the output of a fixed-time RBF disturbance observer, which estimates the disturbance using an RBF neural network model. Meanwhile, the closed-loop error model provides information on the current state error of the system. , The state variables in the closed-loop error model (such as...) form the basis for feedback control in the controller. , The actual deflection angle and angular velocity of the fast reflector can be measured by sensors and compared with the expected value.

[0089] In addition, when constructing a sliding mode controller, it is also necessary to combine the sliding surface, Class functions and symbolic functions. As mentioned earlier, the sliding surface defines the desired dynamic trajectory of the system. Class functions are typically used for switching terms in smooth control laws to reduce or eliminate chattering inherent in sliding mode control. The class function (existing technology) is a continuous, monotonically increasing function with a small slope near the origin, gradually increasing in slope away from the origin. Examples include saturation functions or hyperbolic tangent functions. The sign function is a key component in sliding mode control for implementing the switching control law. It determines the direction of the control quantity based on the sign of the sliding surface variable, thus pushing the system state toward the sliding surface. This can be directly implemented in the controller. By combining the above elements, a sliding mode controller is finally constructed. This controller generates control quantities based on input information and mathematical tools. This is to drive the fast reflector to move along the desired trajectory and suppress disturbances.

[0090] Through the above technical solution, this application effectively solves the problems of insufficient robustness, slow convergence speed, and chattering in existing sliding mode controllers when handling external disturbances and system parameter uncertainties. Specifically, by designing a reasonable sliding surface, the system state can be guided to the desired trajectory and converge quickly. The lumped disturbance estimate output by the fixed-time RBF disturbance observer is directly integrated into the controller, enabling the controller to compensate for external disturbances and system parameter measurement deviations in real time and accurately, greatly enhancing the system's disturbance rejection capability and robustness. Furthermore, the introduction of… The function smooths the switching terms in the control law, significantly suppressing the chattering inherent in sliding mode control. This avoids wear on the fast reflector actuator, extends equipment life, and improves the smoothness of the control output. Ultimately, these improvements work synergistically to significantly enhance the angle tracking accuracy and stability of the fast reflector, meeting the stringent beam pointing requirements of high-precision opto-electromechanical systems.

[0091] For example, the sliding surface can be designed as follows:

[0092] (16);

[0093] in, For sliding surface, It is a positive number;

[0094] Therefore, the sliding mode controller can be designed as follows:

[0095] (17);

[0096] in, for Class function, For symbolic functions, These are controller parameters that are greater than zero.

[0097] Among them, positive numbers It is an adjustable parameter in sliding surface design, whose main function is to adjust the slope and convergence speed of the sliding surface. By selecting a suitable... This value can balance the system's response to angular errors. and angular velocity error The response weights are used to optimize the dynamic characteristics of the system converging to the sliding surface. For example, larger... A higher value may allow the system to eliminate angular errors more quickly, while a smaller value... The value may place more emphasis on smooth angular velocity tracking.

[0098] Control quantity This is the input signal applied to the fast-reflecting mirror system to drive the fast-reflecting mirror to move along the desired trajectory. Its function is to generate appropriate torque or voltage based on the current system state and control strategy to correct system errors and suppress disturbances. Controller parameters greater than zero. The switching gain used to adjust the sliding mode controller directly affects the system's convergence speed to the sliding surface and its ability to suppress disturbances. A larger gain... A higher value usually means stronger control and faster convergence, but it may also increase chattering in the system. The purpose of the class function is to provide a smooth switching characteristic, replacing the potentially severe chattering that may occur in traditional sliding mode control. The sign function provides a switching control signal based on the sign of the sliding surface 's', driving the system state onto the sliding surface. The sign function is typically defined as outputting 1 when the input is greater than zero, -1 when it is less than zero, and 0 when it equals zero. This is introduced into the sliding mode controller. This allows for feedforward compensation of these disturbances, thereby significantly improving the system's anti-disturbance capability and control accuracy. , , , , , These terms are constructed based on the closed-loop error model and the desired trajectory information, and together they constitute the equivalent control part of the sliding mode controller. The role of these terms is to compensate for the known dynamic characteristics of the system and the kinematics of the desired trajectory, ensuring that the system can accurately track the desired trajectory under undisturbed conditions, and assisting the system state to converge to the sliding surface.

[0099] Through this design, the sliding mode controller can ensure that the system state asymptotically converges to the sliding surface, and due to the lumped disturbance estimate... The compensation process, particularly the convergence process, is more independent of the system's initial state and disturbance characteristics. Overall, this scheme combines a precisely designed sliding surface with a sliding mode controller that incorporates disturbance estimation, dynamic system compensation, and a smooth switching mechanism, forming an efficient and robust control closed loop. The fixed-time RBF disturbance observer provides accurate estimates of unknown disturbances, enabling the sliding mode controller to perform feedforward compensation. This allows for high-precision angle control of the fast reflector even in the presence of external disturbances and system uncertainties. The ingenious combination of class functions and symbolic functions further optimizes the controller's performance, effectively suppressing chattering while ensuring fast convergence and strong robustness, thus enhancing the practical application value of the control system.

[0100] To verify the convergence of the fast-reflecting mirror control system under the action of the sliding mode controller, the following Lyapunov function can be constructed:

[0101] (18);

[0102] in, The value of the Lyapunov function. Let be the trace function of the matrix. For the weight estimation error, and , The ideal estimated weight matrix for the RBF neural network model. for The transpose of the matrix;

[0103] The time derivative of the Lyapunov function is:

[0104] (19);

[0105] in, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time, for The first derivative with respect to time;

[0106] The above formula (18) satisfies the following inequality:

[0107] (20);

[0108] in, It is a positive number;

[0109] According to the above inequality (20), under the action of the sliding mode controller in formula (17), the fast reflector control system gradually converges.

[0110] Through the above design, this invention eliminates the need for prior knowledge of the upper bound of the lumped disturbance term constituted by external interference and system model measurement deviations, enabling estimation of the system's lumped disturbance within a fixed time range. Furthermore, the controller designed based on a fixed-time RBF disturbance observer exhibits high control accuracy and robustness in fast mirror angle tracking tasks with external interference and uncertainties in system parameter measurements.

[0111] Please refer to Figure 2 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device includes a processor 301 and a memory 302. The processor 301 and the memory 302 are interconnected and communicate with each other via a communication bus 303 and / or other forms of connection mechanisms (not shown). The memory 302 stores a computer program executable by the processor 301. When the electronic device is running, the processor 301 executes the computer program to perform the fast mirror sliding mode control method in any optional implementation of the above embodiments, to achieve the following functions: establishing a fast... A closed-loop error model for the reflector is established. This model includes a lumped disturbance term composed of external disturbances and system parameter measurement deviations. A fixed-time RBF disturbance observer is set up. This observer estimates the lumped disturbance term and outputs a lumped disturbance estimate. The observer is configured with a weight update law that ensures the estimation error converges within a fixed time independent of the initial state. Based on the lumped disturbance estimate output by the fixed-time RBF disturbance observer and the closed-loop error model, a sliding mode controller is constructed. The sliding mode controller is used to control the fast reflector.

[0112] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it performs the fast reflector sliding mode control method in any optional implementation of the above embodiments to achieve the following functions: establishing a closed-loop error model of the fast reflector; the closed-loop error model includes a lumped disturbance term composed of external disturbances and system parameter measurement deviations; setting a fixed-time RBF disturbance observer; the fixed-time RBF disturbance observer is used to estimate the lumped disturbance term to output a lumped disturbance estimate, and the fixed-time RBF disturbance observer is configured with a weight update law that makes the estimation error converge within a fixed time independent of the initial state; constructing a sliding mode controller based on the lumped disturbance estimate output by the fixed-time RBF disturbance observer and the closed-loop error model; and using the sliding mode controller to control the fast reflector. The computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0113] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A fast steering mirror sliding mode control method, characterized in that, The method comprises the following steps: A1. establishing a closed-loop error model of the fast steering mirror; the closed-loop error model comprises a lumped disturbance term composed of external disturbances and system parameter measurement deviations; A2. setting a fixed-time RBF disturbance observer; the fixed-time RBF disturbance observer is used for estimating the lumped disturbance term to output a lumped disturbance estimation value, and the fixed-time RBF disturbance observer is configured with a weight update law that makes the estimation error converge within a fixed time regardless of the initial state; A3. constructing a sliding mode controller based on the lumped disturbance estimation value output by the fixed-time RBF disturbance observer and the closed-loop error model; A4. using the sliding mode controller to control the fast steering mirror; Step A3 comprises: design a sliding surface, and based on the lumped disturbance estimation value output by the fixed-time RBF disturbance observer and the closed-loop error model, combine the sliding surface, a sign function, and construct a sliding mode controller The sliding surface is: ； wherein is a slide surface, is a normal number, is an angle error, is an angular velocity error; The sliding mode controller is: ； wherein is a step function, is a sign function, is a controller parameter greater than zero, is a control quantity, , and is a system parameter measurement, is an aggregate disturbance estimate, is a desired deflection angle of the fast steering mirror, is a first derivative with respect to time and represents a desired deflection angular velocity of the fast steering mirror, is a second derivative with respect to time.

2. The fast steering mirror sliding mode control method of claim 1, wherein, Step A1 comprises: A101. establishing a fast steering mirror motion model comprising a lumped disturbance term based on external disturbances and system parameter measurement uncertainties; the lumped disturbance term is composed of external disturbances and system parameter measurement deviations; A102. establishing a closed-loop error model about angle error and angular velocity error according to the fast steering mirror motion model; the angle error is the error between the actual deflection angle and the expected deflection angle of the fast steering mirror, and the angular velocity error is the error between the actual deflection angular velocity and the expected deflection angular velocity of the fast steering mirror.

3. The fast steering mirror sliding mode control method of claim 2, wherein, The fast steering mirror motion model is: ； ； ； wherein is the actual deflection angle of the fast steering mirror, is the actual deflection angular velocity of the fast steering mirror, is the is the first derivative with respect to time, is the is the first derivative with respect to time, is the lumped disturbance term, , and is the measurement error of the system parameters, is the external disturbance.

4. The fast steering mirror sliding mode control method of claim 3, wherein, The closed-loop error model is: ； ； wherein is the first derivative with respect to time, is the first derivative with respect to time.

5. The fast steering mirror sliding mode control method of claim 4, wherein, The fixed-time RBF disturbance observer is an RBF neural network model, and the RBF neural network model is: ； wherein is an estimated weight matrix of the RBF neural network model, is is a transpose matrix of is a Gaussian matrix of the RBF neural network model, and , is is n radial basis functions in , wherein the radial basis functions are ， ； wherein, is the jth radial basis function, is an input vector of the RBF neural network model, is a center vector of the jth radial basis function, is a width of the jth radial basis function; The RBF neural network model is configured with a weight update law that makes the estimation error converge within a fixed time regardless of the initial state.

6. The fast steering mirror sliding mode control method of claim 5, wherein, The weight update law of the RBF neural network model is: ； ； ； wherein is an angular velocity error estimate, is a first derivative with respect to time, , , and are normal numbers, and , , is a rate of change of is an estimation error, is a normal number.

7. An electronic device, comprising: The computer program is executed by the processor to run the steps of the fast steering mirror sliding mode control method according to any one of claims 1-6.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to run the steps of the fast steering mirror sliding mode control method according to any one of claims 1-6.

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