High-precision positioning control method and system for linear modules

Abstract

This invention relates to the field of high-precision positioning technology and discloses a high-precision positioning control method and system for a linear module. The method includes: extracting and tracking feature points from a motion image sequence of the linear module to obtain displacement measurement data and vibration feature data; performing nonlinear compensation on the linear module based on the displacement measurement data and the vibration feature data to construct a standard linear state equation; designing a sliding mode surface and calculating gain parameters based on the standard linear state equation to obtain initial sliding mode controller parameters; performing trajectory interpolation and motion feedback on the linear module based on the initial sliding mode controller parameters to obtain real-time position deviation data; and iteratively optimizing the initial sliding mode controller parameters based on the real-time position deviation data to obtain target sliding mode controller parameters. This invention reduces the impact during acceleration and deceleration, effectively reduces system vibration, and improves positioning accuracy.

Description

Technical Field

[0001] This invention relates to the field of high-precision positioning technology, and in particular to a high-precision positioning control method and system for linear modules. Background Technology

[0002] Traditional linear module control methods face numerous challenges in high-speed, high-precision positioning. Due to the nonlinear characteristics of the mechanical structure, environmental interference, and load variations, linear modules are prone to vibration, friction, and temperature drift during operation, which severely restricts further improvements in positioning accuracy.

[0003] Currently, mainstream linear module control methods mainly rely on traditional sensors such as optical and magnetic scales for position feedback. These sensors are not only costly but also struggle to simultaneously acquire multi-dimensional information such as displacement and vibration. Furthermore, most existing control algorithms employ linear control theory, which has limitations in handling system nonlinearity and external disturbances, making it difficult to meet sub-micron level positioning accuracy requirements. Summary of the Invention

[0004] This invention provides a high-precision positioning control method and system for linear modules. This invention reduces the impact during acceleration and deceleration, effectively reduces system vibration, and improves positioning accuracy.

[0005] In a first aspect, the present invention provides a high-precision positioning control method for a linear module, the high-precision positioning control method for a linear module comprising:

[0006] Feature point extraction and feature point tracking are performed on the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data;

[0007] Based on the displacement measurement data and the vibration characteristic data, nonlinear compensation is performed on the linear module to construct a standard linear state equation;

[0008] Based on the standard linear state equation, the sliding surface is designed and the gain parameters are calculated to obtain the initial sliding controller parameters.

[0009] Based on the initial sliding mode controller parameters, trajectory interpolation and motion feedback are performed on the linear module to obtain real-time position deviation data;

[0010] The initial sliding mode controller parameters are iteratively optimized based on the real-time position deviation data to obtain the target sliding mode controller parameters.

[0011] Secondly, the present invention provides a high-precision positioning control system for a linear module, the high-precision positioning control system for a linear module comprising:

[0012] The feature point tracking module is used to extract and track feature points from the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data.

[0013] The nonlinear compensation module is used to perform nonlinear compensation on the linear module based on the displacement measurement data and the vibration characteristic data, and to construct a standard linear state equation.

[0014] The calculation module is used to design the sliding surface and calculate the gain parameters based on the standard linear state equation to obtain the initial sliding controller parameters;

[0015] The feedback module is used to perform trajectory interpolation and motion feedback on the linear module based on the initial sliding mode controller parameters to obtain real-time position deviation data;

[0016] The optimization module is used to iteratively optimize the initial sliding mode controller parameters based on the real-time position deviation data to obtain the target sliding mode controller parameters.

[0017] The technical solution provided by this invention employs a combination of visual measurement and dual-matching tracking to achieve high-precision measurement of the motion state of a linear module. By using feature point array design and sub-pixel feature extraction algorithms, the limitations of traditional sensors are overcome, simultaneously acquiring displacement and vibration information and improving measurement accuracy. Based on nonlinear dynamic modeling and feedback linearization methods, the nonlinear characteristics of the system are effectively compensated. By establishing a complete dynamic model, considering the influence of various factors such as inertial force, Coriolis force, and friction, the system maintains good linearity even during large-scale motion. An adaptive gain sliding mode controller is designed to enhance the system's anti-interference capability. Using a continuous reaching law instead of the traditional sign function effectively suppresses chattering caused by control switching, while the adaptive gain mechanism enables the controller to automatically adapt to load changes. A parameter optimization method based on multi-dimensional performance indicators is proposed, realizing automatic optimization of controller parameters. Through innovative designs such as hierarchical weight calculation, dynamic step size adjustment, and decoupling compensation, the coupling problem in the parameter optimization process is solved, ensuring continuous improvement in system performance. The use of seventh-order polynomial trajectory planning and third-order continuity processing ensures the smoothness of the motion trajectory. By designing a reasonable trajectory, the impact during acceleration and deceleration is reduced, effectively reducing system vibration and improving positioning accuracy.

[0018] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of one embodiment of the high-precision positioning control method for linear modules in this invention;

[0021] Figure 2 This is a schematic diagram of one embodiment of the high-precision positioning control system for linear modules in this invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions 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, 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.

[0023] The terms "comprising" and "having," and any variations thereof, used in the embodiments of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the steps or units listed, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0024] To facilitate understanding of this embodiment, a high-precision positioning control method for a linear module disclosed in this invention will first be described in detail. For example... Figure 1 As shown, this method includes the following steps:

[0025] 101. Extract and track feature points from the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data;

[0026] It is understood that the executing entity of this invention can be a high-precision positioning control system for linear modules, or it can be a terminal or a server; no specific limitation is made here. This embodiment of the invention will be described using a server as the executing entity as an example.

[0027] Specifically, Gaussian filtering is applied to a 5×5 feature point array pre-placed on the surface of the moving parts in the linear module to effectively remove high-frequency noise from the image and reduce the impact of noise on the accuracy of subsequent feature point extraction, resulting in filtered image data. For the filtered image data, Hough transform is used to detect circular contours. Hough transform is an image processing method that effectively identifies and extracts circular features in an image. In this process, the circular contour of each feature point in the image is located using Hough transform, thus determining the specific position of these feature points. Through this step, the contour data of the feature points is obtained. The contour data is then refined. Two-dimensional Gaussian curve fitting technology is used to fit the contour data, more accurately determining the center coordinates of each feature point. Gaussian curve fitting can eliminate errors caused by image edge blurring or noise, obtaining the center coordinate data of the feature points. The center coordinate data of the feature points is then transformed to convert the local coordinate data to the global coordinate system. By introducing a global coordinate system transformation matrix, the local coordinates of the feature points are converted into displacement coordinate data in the global coordinate system, ensuring that the obtained motion data matches the global motion state of the linear module. Time-series differentiation is performed on the displacement coordinate data to calculate the instantaneous velocity and acceleration data of the linear module. The displacement coordinate data, velocity and acceleration data are then fused with the linear module's motor torque, load mass, and ambient temperature. Motor torque is a crucial factor affecting the linear module's motion state, load mass influences acceleration and stability, and ambient temperature affects motor performance and the module's frictional characteristics. By fusing these various data sources, a motion state dataset is obtained. Based on this dataset, feature point tracking and analysis are performed. Using time-series kinematic models or Kalman filtering methods, the motion trajectory of each feature point is tracked and corrected, yielding real-time displacement measurement data and vibration characteristic data of the linear module.

[0028] 102. Based on displacement measurement data and vibration characteristic data, perform nonlinear compensation on the linear module and construct a standard linear state equation;

[0029] Specifically, the motion state dataset is input into the spatial matching layer. By calculating the affine transformation matrix of the feature point array in adjacent image frames, the spatial variation relationship between various feature points in the image is captured. The calculation of the affine transformation matrix is ​​based on keypoint matching in the image. By comparing the relative positions of the same feature points in the current frame and the previous frame, the spatial transformation is determined. To improve tracking accuracy, the optimal matching pairs are selected, i.e., the feature point combinations with the smallest transformation error. These matching pairs reflect the precise displacement of the module in adjacent time steps. Through this step, spatial matching displacement data is obtained, reflecting the positional changes of the module in actual motion. The spatial matching displacement data is input into the temporal matching layer for state vector construction. The temporal matching layer combines the spatial matching displacement data with temporal information to construct a state vector containing two important components: displacement and velocity. This state vector describes the motion state of the linear module at any given time. In this way, the motion trajectory of the module is updated and tracked in real time. Based on the state vector, a filter state model is constructed. The filter processes these state vectors to remove noise and errors, optimizes the accuracy of the data, and ensures accurate displacement and velocity estimation in real-time control. Trajectory prediction and smoothing are performed based on spatially matched displacement data and a filter state model. Trajectory prediction uses known kinematic models and historical displacement data to predict future motion trajectories, while smoothing helps reduce deviations caused by measurement noise or other uncertainties. By combining spatially matched displacement data and a filter state model, trajectory prediction can provide future displacement estimates for the system, and smoothing reduces transient fluctuations generated in a short period of time, yielding displacement measurement data. Vibration amplitude is calculated from the displacement measurement data to obtain vibration intensity information. Vibration amplitude reflects the mechanical vibration or instability that occurs during module movement. Frequency features of the vibration are extracted to analyze the dynamic response characteristics of the system. Frequency feature extraction employs frequency domain analysis methods such as Fast Fourier Transform to transform the displacement data from the time domain to the frequency domain, obtaining vibration frequency data, revealing the vibration modes of the module at different frequencies, which helps identify potential faults or instabilities in the system. Vibration amplitude data and vibration frequency data are fused to obtain vibration feature data.

[0030] Displacement measurement data is used to identify motion equation parameters and perform dynamic modeling to obtain the mapping relationship between displacement and external force. In the dynamic system, the motion of the linear module is affected by inertial force, as well as friction, gravity, and other external disturbances. The displacement-force mapping relationship is obtained through experimental measurement or data analysis, describing the dynamic response of the module under different force conditions. Simultaneously, to characterize the nonlinear characteristics of the system, frequency domain analysis is performed on the vibration characteristic data to extract the system's damping characteristics. Damping characteristics are an important parameter for measuring the vibration attenuation capability of the system. The damping coefficient is identified from the vibration spectrum using methods such as Fourier transform or wavelet transform, and combined with the previously obtained displacement-force mapping relationship, a complete nonlinear dynamic model is constructed. Through mathematical modeling, a nonlinear dynamic equation incorporating inertia, Coriolis force, gravity, friction, and external disturbances is established. The basic form of this equation is:

[0031] ;

[0032] in, The inertia matrix describes the mass-inertia characteristics of the system. Let be the displacement vector, representing the position state of the system. This is the Coriolis force matrix, used to describe the Coriolis force effect caused by the non-inertial motion of the system. This is the gravity term, which reflects the gravitational influence on the system at different locations. Representing the friction term, friction typically depends on velocity and manifests in different forms such as Coulomb friction and viscous friction. The external disturbance term represents the external impact force or environmental disturbance that the system may experience during actual operation, while u is the control input, representing the control force applied by the system. To construct the standard linear state equations, state variables are defined for this nonlinear dynamic model. This is achieved by introducing a state vector:

[0033] ;

[0034] The system's state variables are expressed as a combination of displacement and velocity, transforming the original second-order dynamic equations into first-order state equations. Since the original dynamic equations contain nonlinear terms, these nonlinear terms are compensated for to achieve effective control, thus converting the system into a linear form. Using feedback linearization techniques, a nonlinear compensation control law is designed, ensuring that the system's dynamic behavior exhibits linearity in the control coordinate system. The expression for the control law is:

[0035] ;

[0036] in, This is the new control input, whose function is to compensate for the nonlinear components of the original system, transforming the system's input-output relationship into a linear one. When this control law is substituted into the original nonlinear dynamic equations, the system's dynamic equations are rewritten as:

[0037] ;

[0038] in, and These are the system matrix and the input matrix, respectively. This form of expression is a standard linear state equation. To ensure the integrity of this linearized system, its system matrix is ​​constructed, ultimately yielding the standard linear state equation:

[0039] ;

[0040] in, The vector representing the derivatives of the state variables. yes A 3D system matrix describes the internal dynamic characteristics of a system. It is the input matrix, which reflects the influence of control inputs on the system state, and It is a disturbance vector that contains all unmodeled external disturbances or system uncertainties. Through this series of nonlinear compensation and linearization steps, a linear state equation conforming to the standard form is finally constructed.

[0041] 103. Based on the standard linear state equation, design the sliding surface and calculate the gain parameters to obtain the initial sliding controller parameters;

[0042] Specifically, the displacement tracking error equation is defined. The tracking error describes the deviation between the current state and the desired state of the system; therefore, it is determined by setting an error vector. Quantify this bias, among which Let be the current state vector of the system, and Let be the desired state vector. A sliding surface is constructed based on the tracking error equation. The sliding surface is a key component of sliding mode control; its design determines how the system approximates the target state and remains stable under disturbances. The sliding surface is defined by... To define, where Let the sliding surface vector be... The sliding surface coefficient matrix is ​​a positive definite diagonal matrix, and This represents the derivative term of the error. The purpose of this sliding surface expression is to construct a hyperplane for error convergence, enabling the system to maintain steady-state tracking on this hyperplane, unaffected by small disturbances. Through appropriate selection... and The value of is used to adjust the dynamic characteristics of sliding mode control, such as convergence speed and stability. To ensure rapid convergence and maintain sliding motion, a continuous reaching law is designed to control the evolution of sliding variables when constructing the sliding surface. The purpose of the reaching law is to guide the system state into the sliding surface and maintain stable motion there. Therefore, the reaching law is defined as... ,in Let be the derivative vector of the sliding surface. It is a positive definite diagonal matrix of approach velocity coefficients, controlling the rate at which the system approaches the sliding surface. The integral coefficient matrix, being a positive definite diagonal matrix, determines the influence of the accumulated error during the approach process, while The sliding mode surface integral vector represents the cumulative change of the sliding mode state over time. This reaching law ensures that the system can quickly approach the sliding surface and maintain stable tracking behavior on the sliding surface, while also guaranteeing strong robustness to external disturbances. After defining the reaching law, it is substituted into the standard linear state equations for solution, yielding the specific sliding mode control law. The purpose of the sliding mode control law is to design the control input so that the system state can remain stable on the sliding surface and overcome external disturbances. Therefore, the control input vector is represented as... ,in It is the equivalent control term vector, used to compensate for known system dynamics, thereby ensuring that the system moves according to the expected trajectory. The switching control term vector is used to suppress unknown disturbances and enhance the system's robustness. The equivalent control term is determined by the system dynamics model, while the switching control term is defined by the sliding mode control strategy, using a sign function or saturation function to suppress the influence of external noise on the control system. An adaptive gain update law is designed based on the sliding mode control law, allowing the controller to adjust the control gain according to the real-time error. The dynamic equation for the gain parameter is defined. ,in The derivative representing the gain matrix, The learning rate coefficient matrix is ​​a positive definite diagonal matrix, which determines the adjustment speed of the gain. The absolute value vector of the sliding surface is used to guide the gain update process. The gain update law allows the sliding mode control system to dynamically adjust the gain parameters according to the actual error level. This increases the control gain when the error is large, improving the convergence speed, while decreasing the gain when the error is small, reducing control chattering. The initial sliding mode controller parameters are obtained by combining the sliding mode control law with the dynamic equation of the gain parameters.

[0043] 104. Based on the initial sliding mode controller parameters, perform trajectory interpolation and motion feedback on the linear module to obtain real-time position deviation data;

[0044] Specifically, trajectory planning is performed for the positioning task of the linear module to ensure its stability throughout the entire motion process and to meet constraints on position, velocity, and acceleration. In the trajectory generation stage, a seventh-order polynomial programming method is employed to guarantee the smoothness and executability of the trajectory, while ensuring that the module does not experience abrupt changes or drastic velocity and acceleration variations during motion. By setting the start and end points and corresponding motion boundary conditions, an ideal trajectory is generated, enabling the system to perform high-precision motion control along a predetermined path and satisfy dynamic constraints throughout the entire motion process, ensuring smooth operation. Based on the initial sliding mode controller parameters, the desired trajectory data undergoes third-order continuity processing, ensuring continuity in position, velocity, and acceleration. The purpose of continuity processing is to reduce trajectory uncertainty and prevent shocks and oscillations caused by trajectory non-smoothness, thereby improving the dynamic performance of the system. In actual calculations, methods such as high-order spline interpolation or Bézier curve interpolation are used to ensure smooth transitions at each time point in the trajectory, conforming to the physical characteristics of the linear module, and obtaining smooth trajectory interpolation data. Meanwhile, to ensure the system's control effectiveness, the actual motion state of the linear module is monitored in real time. High-precision sensors, such as grating rulers, laser rangefinders, or inertial measurement units, collect the module's position information during operation, and combine this with speed sensors or other calculation methods to obtain real-time speed data. This real-time motion feedback data provides the control system with current state information, enabling the controller to make necessary adjustments based on the actual situation, ensuring the module operates strictly according to the planned trajectory and can quickly correct motion errors when subjected to external disturbances. The smooth trajectory interpolation data is compared with the real-time motion feedback data to calculate the real-time position deviation. The position deviation reflects the difference between the current system state and the ideal state, obtained by comparing the measured real-time position with the target position in the trajectory interpolation. Simultaneously, the speed deviation is determined by comparing the actual speed with the desired speed. The calculation results of the position and speed deviations directly reflect the module's current motion error and provide them to the control system for further adjustment and optimization. The real-time position deviation data is used as feedback input to the sliding mode controller to optimize the control strategy and dynamically adjust control parameters, ensuring the linear module maintains high-precision positioning even under external disturbances and changes in system parameters.

[0045] 105. The initial sliding mode controller parameters are iteratively optimized based on real-time position deviation data to obtain the target sliding mode controller parameters.

[0046] Specifically, positioning accuracy calculations and response time statistics are performed on real-time position deviation data to evaluate the system's dynamic performance, and performance evaluation indicators are obtained through data analysis. Positioning accuracy calculations primarily focus on the error between the actual and desired positions of the module when performing motion control tasks, including instantaneous and cumulative errors. Response time statistics measure the time it takes for the system to reach the target position and stabilize after receiving a control command. These data collectively constitute performance evaluation indicators, reflecting the quality of the control system. Based on these performance evaluation indicators, comparisons are made with preset thresholds to determine the optimization direction of the system's current parameters, identifying which parameters need adjustment to improve the overall control effect. After determining the parameter optimization direction, the adjustment magnitude of each control parameter is quantified, constructing a weight allocation matrix. This matrix is ​​used to weight key control parameters in the optimization direction data, including sliding surface coefficients, approach velocity coefficients, and integral coefficients. Since different parameters have varying degrees of impact on system performance, a hierarchical weight calculation method is adopted, that is, different optimization weights are set according to the contribution of each parameter to positioning accuracy and response speed. The weight calculation process yields an optimized weight matrix, ensuring a reasonable allocation of the relative influence between different variables during parameter adjustment. This prevents some parameters from being adjusted too large or too small, thus affecting system stability. The optimized weight matrix is ​​then multiplied with the parameter optimization direction data to calculate the initial gradient vector. The gradient vector indicates the direction and magnitude of the current control parameter adjustment. Weighting the gradient vector with the optimized weight matrix allows for a more accurate reflection of the system's optimization requirements. Dynamic step size calculations are performed on the initial gradient vector. The initial gradient vector is grouped according to different error types, including displacement error, velocity error, and acceleration error, and the maximum allowable step size for each error group is calculated to obtain adaptive step size data. During optimization, the adjustment magnitude of different parameters is dynamically adjusted based on the specific error situation, ensuring both efficiency and stability. A piecewise linear mapping is applied to the initial gradient vector based on the adaptive step size data to achieve adaptive optimization. Different mapping functions are used to adjust the gradient calculation results across different error ranges, resulting in larger adjustments when the error is large and smaller adjustments when the error is small. By employing piecewise linear mapping, the optimization process is ensured to converge quickly without causing over-adjustment that could lead to system instability, resulting in the optimized mapped gradient vector. This vector is then orthogonally decomposed to extract the coupling components between control parameters, and a decoupling compensation matrix is ​​constructed. The decoupling compensation matrix eliminates the mutual influence between different parameters, allowing each parameter to be optimized independently, thus improving optimization efficiency and accuracy. Through decoupling, a decoupled gradient vector is obtained, which enables more precise optimization adjustments while reducing parameter interference.To ensure the stability and convergence of the optimization process, the decoupled gradient vector undergoes dynamic decay processing. This prevents excessive parameter adjustments from causing system instability. The decay coefficient is dynamically adjusted based on the historical iteration count, resulting in larger parameter adjustments in the early stages of optimization to accelerate convergence, and gradually decreasing the adjustment magnitude in the later stages to improve system stability. Through this decay process, the final parameter adjustment data is obtained and iteratively calculated with the initial sliding mode controller parameters to obtain the final target sliding mode controller parameters.

[0047] In this embodiment of the invention, a method combining visual measurement and dual-matching tracking is employed to achieve high-precision measurement of the motion state of a linear module. By using feature point array design and sub-pixel feature extraction algorithms, the limitations of traditional sensors are overcome, simultaneously acquiring displacement and vibration information and improving measurement accuracy. Based on nonlinear dynamic modeling and feedback linearization methods, the nonlinear characteristics of the system are effectively compensated. By establishing a complete dynamic model, considering the influence of various factors such as inertial force, Coriolis force, and friction, the system maintains good linearity even during large-scale motion. An adaptive gain sliding mode controller is designed to enhance the system's anti-interference capability. Using a continuous reaching law instead of the traditional sign function effectively suppresses chattering caused by control switching, while an adaptive gain mechanism enables the controller to automatically adapt to load changes. A parameter optimization method based on multi-dimensional performance indicators is proposed, achieving automatic optimization of controller parameters. Through innovative designs such as hierarchical weight calculation, dynamic step size adjustment, and decoupling compensation, the coupling problem in the parameter optimization process is solved, ensuring continuous improvement in system performance. The use of seventh-order polynomial trajectory planning and third-order continuity processing ensures the smoothness of the motion trajectory. By designing a reasonable trajectory, the impact during acceleration and deceleration is reduced, effectively reducing system vibration and improving positioning accuracy.

[0048] In one specific embodiment, the process of performing step 101 may specifically include the following steps:

[0049] Gaussian filtering is applied to a 5×5 feature point array pre-set on the surface of the moving parts in the linear module to reduce noise, resulting in filtered image data.

[0050] Hough transform is performed on the filtered image data to detect circular contours, and feature point contour data is obtained by fitting a two-dimensional Gaussian curve to the feature point contour data to obtain the center coordinate data of the feature points.

[0051] The coordinates of the feature point center are input into the global coordinate system transformation matrix to perform coordinate transformation and obtain the displacement coordinate data;

[0052] Perform time series differentiation on the displacement coordinate data to obtain velocity and acceleration data;

[0053] The displacement coordinate data, velocity and acceleration data are fused with the motor torque, load mass and ambient temperature of the linear module to obtain the motion state dataset;

[0054] Feature point tracking is performed on the motion state dataset to obtain displacement measurement data and vibration characteristic data of the linear module.

[0055] Specifically, image data is preprocessed to improve the accuracy of subsequent feature point extraction. Gaussian filtering is used for image noise reduction. The mathematical expression for Gaussian filtering is:

[0056] ;

[0057] in, Represents the pixel values ​​of the filtered image. and These are the pixel coordinates of the image. The standard deviation of the Gaussian filter determines the smoothness of the filter. This filtering operation removes high-frequency noise from the image, making the edges of feature points smoother. Feature point detection is then performed on the image data. Since the feature points are circular markers, the Hough transform is used for circular contour detection. The Hough transform transforms the circular edge points in the image into voting points in the parameter space through a parameterized space transformation, and identifies the most likely circular contour through cumulative voting. The formula for circular detection using the Hough transform is as follows:

[0058] ;

[0059] in, Let the coordinates be the center of the circle. Let be the radius of the circle, and These are the coordinates of the detected edge points. This is achieved by traversing different... The value is calculated, and the point with the highest number of votes is found in the cumulative space to identify the feature point contour in the image. After completing the circular contour detection, a two-dimensional Gaussian curve fitting is performed to improve the accuracy of the feature point center coordinates. Since the gray-level distribution of the circular feature points in the image is approximately a two-dimensional Gaussian distribution in the local area, a two-dimensional Gaussian function is used for fitting, and its mathematical expression is:

[0060] ;

[0061] in, The grayscale value of a pixel. Represents peak intensity. For the precise center coordinates of the feature points, These are the standard deviations in the horizontal and vertical directions, respectively. This represents the background noise intensity. The parameters are solved using the least squares method. The precise center coordinates of the feature points are obtained. These center coordinates are then transformed into the global coordinate system of the linear module to match its motion data. It is assumed that a rotation matrix exists between the camera's imaging coordinate system and the module's global coordinate system. Translation vector Then global coordinates Calculated using the following transformation formula:

[0062] ;

[0063] in, The coordinates of the feature point in the camera coordinate system. for Rotation matrix, for Translation vector. Obtained by calibrating the camera parameters. and This allows for coordinate transformation. After obtaining the global coordinates of the feature points, the motion parameters of the module are calculated. The velocity and acceleration of the module are obtained through time series differentiation. Velocity calculation uses first-order backward difference:

[0064] ;

[0065] Acceleration calculations are performed using second-order backward difference:

[0066] ;

[0067] in, For the module in time Displacement at any moment The sampling time interval, and These are instantaneous velocity and acceleration, respectively. Displacement, velocity, and acceleration data are fused with external factors such as motor torque, load mass, and ambient temperature. Motor torque... Measured by a current sensor, while the load mass and ambient temperature Obtained through sensors. The final motion state dataset is represented as:

[0068] ;

[0069] in, A complete motion state dataset is provided, containing all key variables affecting the module's motion. To obtain displacement measurement data and vibration characteristic data for the linear module, feature point tracking is performed on the motion state dataset. Kalman filtering or particle filtering methods are used for feature point tracking to improve the stability of displacement measurements. Vibration features are extracted through frequency domain analysis, such as using Fast Fourier Transform to calculate the spectrum of the vibration signal and obtain the main vibration frequencies. and amplitude Vibration characteristic data are represented as follows:

[0070] ;

[0071] in, Representative module in time Vibration characteristic data at any given time.

[0072] In one specific embodiment, the process of performing feature point tracking on the motion state dataset to obtain displacement measurement data and vibration characteristic data of the linear module can specifically include the following steps:

[0073] The motion state dataset is input into the spatial matching layer, the affine transformation matrix of the feature point array in adjacent image frames is calculated, and the optimal matching pair is selected to obtain the spatial matching displacement data.

[0074] Spatial matching displacement data is input into the time matching layer to construct a state vector, resulting in a filter state model. The state vector contains position and velocity components.

[0075] Trajectory prediction and smoothing are performed based on spatial matching displacement data and filter state model to obtain displacement measurement data;

[0076] The vibration amplitude is calculated from the displacement measurement data to obtain the vibration amplitude data, and the frequency characteristics are extracted from the displacement measurement data to obtain the vibration frequency data.

[0077] Vibration amplitude data and vibration frequency data are fused to obtain vibration characteristic data.

[0078] Specifically, the motion state dataset is input into the spatial matching layer to calculate the affine transformation matrix of the feature point array in adjacent image frames. Since the coordinates of the feature points of the straight line module change in consecutive image frames during motion, these changes are described by calculating the affine transformation matrix. The basic form of the affine transformation matrix is:

[0079] ;

[0080] in, and These represent the coordinates of a feature point in the previous frame and the current frame, respectively. yes The transformation matrix describes the effects of rotation and scaling, while yes The translation vector represents the global displacement of the feature point. To solve for the affine transformation matrix, a system of linear equations is established using multiple matching point pairs based on the least squares method, and then solved. and After obtaining the affine transformation matrices of all feature points, to improve matching accuracy, the RANSAC (Random Sample Consensus) algorithm is used to select the optimal matching pair. This involves iteratively randomly sampling feature point pairs and calculating their affine transformation errors, selecting the pair with the smallest error to obtain the final spatial matching displacement data. This spatial matching displacement data is then input into the time-matching layer to construct the filter state model. The purpose of time matching is to establish a stable state estimation model using time-series data, making motion estimation more accurate. State vectors are then constructed. ,in, It is a state vector containing positions. and speed There are two components, and the velocity is obtained by differentiating the position data over time, i.e.:

[0081] ;

[0082] This state vector is input to a Kalman filter for filtering to eliminate measurement noise and improve estimation accuracy. The prediction equation for the Kalman filter is:

[0083] ;

[0084] in, This is the current state. Here is the state transition matrix. For the input matrix, To control the input, This represents process noise. The measurement update equation is:

[0085] ;

[0086] in, For measured values, For the measurement matrix, To mitigate noise, Kalman filtering is employed to obtain smoother and more stable displacement data in noisy environments. Based on spatially matched displacement data and a filter state model, trajectory prediction and smoothing are performed. Trajectory prediction estimates future motion trends based on the current state, while smoothing reduces short-term fluctuations and improves the continuity of measurement data. Trajectory prediction utilizes a kinematic model:

[0087] ;

[0088] in, It is acceleration, calculated by the difference in velocity:

[0089] ;

[0090] To reduce jitter in trajectory prediction, a Savitzky-Golay filter is used for smoothing. This method eliminates high-frequency noise by performing polynomial fitting on the data within a local window, obtaining smooth displacement measurement data. Vibration amplitude is then calculated from the displacement measurement data. The vibration amplitude is obtained by calculating the root mean square value of the displacement.

[0091] ;

[0092] in, Represents the vibration amplitude. For the first The displacement value at each moment. This represents the average displacement. This represents the total number of sampling points. This value reflects the vibration intensity of the module during its movement. Frequency features are extracted from the displacement measurement data to analyze the main frequency components of the module's vibration. A Fast Fourier Transform is used to convert the displacement signal from the time domain to the frequency domain, and the dominant frequency of the vibration is calculated. :

[0093] ;

[0094] in, The frequency corresponding to the maximum value of the displacement signal is taken as the dominant vibration frequency. This value reflects the main vibration mode of the module and helps to determine whether resonance or external interference exists. Vibration amplitude and frequency data are fused to obtain vibration characteristic data. By comprehensively considering different dimensions of vibration information, the system's ability to judge vibration state is improved. Feature vector fusion is used for this purpose.

[0095] ;

[0096] in, The final vibration characteristic data includes vibration amplitude and main frequency information. This data is used to evaluate the vibration state of the linear module and provide a basis for optimizing the control system.

[0097] In one specific embodiment, the process of performing step 102 may specifically include the following steps:

[0098] The displacement measurement data were used to identify the parameters of the motion equation and perform dynamic modeling to obtain the displacement-force mapping relationship. At the same time, the vibration characteristic data were subjected to frequency domain analysis and damping characteristic extraction to obtain the damping coefficient. The displacement-force mapping relationship and the damping coefficient were combined to construct a nonlinear dynamic model M(p)d. 2 p / dt 2 +C(p,dp / dt)(dp / dt)+G(p)+F(dp / dt)+W(t)=u, where M(p) is the inertia matrix, p is the displacement vector, C(p,dp / dt) is the Coriolis force matrix, G(p) is the gravity term, F(dp / dt) is the friction term, W(t) is the external disturbance term, u is the control input, and t is time;

[0099] By defining the state variables of the nonlinear dynamic model, we obtain the state vector expression X(t)=[p(t),dp / dt] T , where X(t) is the state vector, p(t) is the displacement component state variable, and dp / dt is the velocity component state variable;

[0100] By performing nonlinear term compensation on the state vector expression, a feedback linearized control law is obtained, which is expressed as: u=M(p)[vM -1 (p)(C(p,dp / dt)(dp / dt)+G(p)+F(dp / dt)+W(t))], where v is the new control input;

[0101] Substituting the feedback linearized control law into the nonlinear dynamics model, we obtain the linearized system expression dX / dt=AX(t)+Bv(t);

[0102] The system matrix is ​​constructed from the linearized system expression to obtain the standard linear state equation X'(t)=AX(t)+Bv(t)+E(t), where X'(t) is the derivative vector of the state variables, A is the n×n dimensional system matrix, B is the input matrix, E(t) is the disturbance vector, and n is the system order.

[0103] Specifically, using the measured displacement data and externally applied forces Dynamic modeling is performed. During the motion of the linear module, its dynamic characteristics are represented as a controlled rigid body system, including inertial forces, Coriolis forces, gravity, friction, and external disturbances. To obtain the dynamic model of the system, a parameter identification method is used, and based on the system's input-output relationship, a mapping relationship between displacement and force is fitted. In the dynamic system, the acceleration of the object... By the applied control force And determined by the physical characteristics of the system itself, it can be expressed as:

[0104] ;

[0105] in, The inertia matrix represents the mass inertia characteristic of the system and is a displacement matrix. The function; The Coriolis force matrix describes the inertial coupling effect caused by motion. This is the gravity term, representing the gravitational influence on the module at different positions; The term representing friction is a function of velocity and can be expressed as static friction, kinetic friction, or viscous friction. External disturbances include external vibrations, airflow resistance, etc. The control input to the system is the force applied by the drive motor. To refine the dynamic model, frequency domain analysis is performed on the vibration characteristic data, and the system's damping characteristics are extracted to obtain the damping coefficient. Vibration characteristic data Transform to the frequency domain using Fourier transform:

[0106] ;

[0107] in It is the frequency spectrum of displacement. The frequency is used. By analyzing the main vibration frequencies and amplitudes of the system, the damping ratio of the system is calculated. :

[0108] ;

[0109] in It is the damping coefficient. For equivalent quality, Let be the system stiffness. This damping coefficient is used to compensate for the system's vibration effects and improve motion accuracy. After establishing the nonlinear dynamic model, the system's state variables are defined for control design. The state vector is defined as:

[0110] ;

[0111] in, The state vector contains displacement components. and velocity components The original second-order dynamic equations are transformed into first-order state equations. Since the dynamic model contains nonlinear terms, nonlinear compensation is performed. A feedback linearization method is used to design a control law that makes the system behavior linear in the transformed coordinate system. The feedback linearized control law is expressed as:

[0112] ;

[0113] in, It is a new control input used to replace the nonlinear force term in a nonlinear system; The inverse of the inertia matrix allows the control law to act directly on the system's acceleration term. This feedback linearization control law transforms the original nonlinear system into a standard linear system, expressed as:

[0114] ;

[0115] in, It is the system matrix, which determines the inherent dynamic characteristics of the system; This is the input matrix, describing the effect of the control input on the system state. To obtain the standard linear state equations, the system matrix is ​​constructed. The final standard linear state equations are expressed as:

[0116] ;

[0117] in, The vector of derivatives of the state variables; for A three-dimensional system matrix describes the intrinsic properties of the system; The input matrix describes the effect of the control input on the system. This is the perturbation vector, which includes the influence of the external environment.

[0118] In one specific embodiment, the process of performing step 103 may specifically include the following steps:

[0119] By defining the displacement tracking error in the standard linear state equation, we obtain the tracking error equation e(t) = X(t) - Xd(t), where e(t) is the tracking error vector, X(t) is the state vector, and Xd(t) is the desired state vector.

[0120] Based on the tracking error equation, a sliding surface is constructed, and the sliding surface expression s(t)=ce(t)+de(t) / dt is obtained, where s(t) is the sliding surface vector, c is the sliding surface coefficient matrix of a positive definite diagonal matrix, and de(t) / dt is the tracking error derivative vector.

[0121] By designing a continuous reaching law for the expression of the sliding surface, the reaching law equation is obtained as ds / dt=-η|s|-k∫|s|dt, where ds / dt is the derivative vector of the sliding surface, η is the reaching velocity coefficient matrix of the positive definite diagonal matrix, k is the integral coefficient matrix of the positive definite diagonal matrix, and ∫|s|dt is the surface integral vector of the sliding surface.

[0122] Substituting the approach law equation into the standard linear state equation for solution, we obtain the sliding mode control law v(t) = vs(t) + vn(t), where v(t) is the control input vector, vs(t) is the equivalent control term vector used to compensate for known dynamics, and vn(t) is the switching control term vector used to suppress unknown disturbances.

[0123] Based on the sliding mode control law, an adaptive gain update law is designed, and the dynamic equation of the gain parameter is obtained as dk / dt=γ|s|, where dk / dt is the derivative of the gain matrix, γ is the learning rate coefficient matrix of the positive definite diagonal matrix, and |s| is the absolute value vector of the sliding surface.

[0124] The initial sliding mode controller parameters are obtained by combining the sliding mode control law and the dynamic equation of the gain parameter.

[0125] Specifically, we first define the system's tracking error to quantify the deviation between the system's current state and the desired state. In control theory, the tracking error is expressed as:

[0126] ;

[0127] in, The tracking error vector represents the current state of the system. With the expected state The differences between them Let be the current state vector of the system, and Let be the desired state vector corresponding to the target trajectory. The error vector guides the controller's adjustments to ensure the system moves along the desired trajectory and compensates for errors in the presence of disturbances. After defining the error equation, a sliding surface is constructed so that the system remains stable and effectively suppresses errors when running on the sliding surface. The sliding surface is defined by the following expression:

[0128] ;

[0129] in, Let be the sliding mode surface vector, representing the state variables of the system in sliding mode control. The sliding surface coefficient matrix is ​​a positive definite diagonal matrix used to adjust the sliding mode dynamic characteristics of the system. The derivative vector of the tracking error describes the rate of change of the error. By choosing a suitable... and A matrix is ​​used to adjust the sliding mode control performance of the system to ensure that the error converges quickly and the system slides stably on the sliding surface. To enable the system state to converge quickly to the sliding surface, a reaching law is designed so that the error decreases rapidly according to the expected trajectory, thereby achieving robust trajectory tracking control. The reaching law adopts an exponential reaching strategy, and its mathematical expression is:

[0130] ;

[0131] in, Let be the sliding surface derivative vector, representing the rate of change of the sliding state of the system. The approach velocity coefficient matrix, which is a positive definite diagonal matrix, determines the velocity at which the system approaches the sliding surface. The integral coefficient matrix is ​​a positive definite diagonal matrix, and the influence of error accumulation in the control system is considered. The sliding mode surface integral vector reflects the cumulative effect of system errors. The reaching law ensures that the system state can quickly enter the sliding surface and maintain stable motion there, thereby improving the system's robustness and dynamic response. After constructing the reaching law, it is substituted into the standard linear state equations and solved to obtain the sliding mode control law. The standard linear state equations are in the form of:

[0132] ;

[0133] To design a sliding mode controller, a sliding mode control law is constructed so that the system can be controlled according to the sliding surface. Therefore, the sliding mode control law is expressed as:

[0134] ;

[0135] in, To control the input vector, This is the equivalent control term vector, used to compensate for the known dynamic characteristics of the system, enabling the system to move along the expected trajectory. The switching of the control term vector serves to suppress unknown disturbances in the system and improve its robustness. Equivalent control term. Determined by the system's dynamic model, and the switching control term A sign function or saturation function is used for adjustment to reduce control chattering and ensure system stability. An adaptive gain update law is designed so that the controller can automatically adjust the control gain according to the error. The dynamic adjustment of the gain parameter is expressed as:

[0136] ;

[0137] in, The derivative of the gain matrix represents the rate of change of the system gain parameter. The learning rate coefficient matrix, being a positive definite diagonal matrix, determines the speed of gain adjustment. The absolute value vector of the sliding mode surface is used to guide the gain update process. The purpose of adaptive gain update is to increase the control gain when the error is large to improve the convergence speed of the system, and to decrease the gain when the error is small to reduce control chattering. The initial sliding mode controller parameters are obtained by combining the sliding mode control law with the dynamic equation of the gain parameters.

[0138] In one specific embodiment, the process of performing step 104 may specifically include the following steps:

[0139] Seventh-order polynomial trajectory planning was performed on the positioning task of the linear module to obtain the desired trajectory data of position, velocity and acceleration.

[0140] The desired trajectory data is processed using third-order continuity based on the initial sliding mode controller parameters to obtain smooth trajectory interpolation data.

[0141] The position and velocity of the linear module are collected in real time to obtain real-time motion feedback data;

[0142] The real-time position deviation data is obtained by comparing and calculating the smooth trajectory interpolation data with the real-time motion feedback data.

[0143] Specifically, a mathematical model for trajectory planning is established. The goal of seventh-order polynomial trajectory planning is to ensure the smoothness, continuity, and feasibility of the trajectory, enabling the linear module to move with high precision along the set path during motion. The basic form of a seventh-order polynomial trajectory is expressed as follows:

[0144] ;

[0145] in, In time The expected position at any given time These are the trajectory parameters that need to be determined. To ensure that the trajectory meets the boundary conditions, initial position, final position, initial velocity, final velocity, initial acceleration, final acceleration, and higher-order derivatives, such as jerk, are set to ensure that the trajectory has high smoothness at each time point. The boundary conditions for trajectory planning are set as follows:

[0146] ;

[0147] in, These represent the initial position and the final position, respectively. These represent the initial velocity and the final velocity, respectively. These represent the initial acceleration and the final acceleration, respectively. Let this be the total time for trajectory planning. The coefficients of the seventh-degree polynomial are determined by solving the above system of equations. arrive This yields the complete trajectory planning function. The expected values ​​of velocity and acceleration are calculated by differentiation:

[0148] ;

[0149] This step yields complete desired trajectory data, including location information. Speed ​​information and acceleration information This provides an ideal motion path for the motion control of the linear module. Third-order continuity processing is applied to the desired trajectory data to ensure the smoothness of the track edges. Third-order continuity means that the trajectory remains continuous at the position, velocity, and acceleration levels, satisfying the following conditions:

[0150] ;

[0151] in, To introduce jerk, we use the acceleration to describe the rate of change of the system's acceleration. To ensure the smoothness of the trajectory, a third-order spline interpolation method is used to further optimize the seventh-order polynomial trajectory. The core idea of ​​the spline interpolation method is to construct a third-order polynomial between known data points, ensuring that the interpolation curve satisfies the continuity requirement in all intervals, i.e.:

[0152] ;

[0153] in, Indicates the first Interpolation function for segment trajectory, These are the coefficients that need to be solved, and these coefficients are constrained by boundary conditions to ensure a smooth trajectory transition. The resulting smooth trajectory interpolation data can improve the control accuracy of the system and reduce shocks and vibrations caused by abrupt trajectory changes. Simultaneously, to ensure the system can accurately execute the planned trajectory, the motion state of the linear module is acquired in real time, and its position and velocity are collected. High-precision sensors, such as grating rulers, laser rangefinders, or inertial measurement units, are used to measure the module's position data in real time. Velocity data is obtained through direct measurement or numerical differentiation calculation, that is:

[0154] ;

[0155] in, The sampling time interval is defined as follows. This process acquires real-time motion feedback data from the linear module, providing the control system with information about its actual operating status. After obtaining the smooth trajectory interpolation data and real-time motion feedback data, the data are compared to calculate the real-time position deviation. The method for calculating the position deviation is as follows:

[0156] ;

[0157] in, The position error represents the difference between the actual measured position and the target trajectory. Similarly, the velocity error is calculated as follows:

[0158] ;

[0159] in, It reflects the deviation between the actual speed and the target speed. The calculated results of position deviation and speed deviation are used to adjust the control strategy in real time to ensure that the linear module can run strictly according to the planned trajectory and to make appropriate compensation when subjected to external disturbances.

[0160] In one specific embodiment, the process of performing step 105 may specifically include the following steps:

[0161] The positioning accuracy and response time are calculated from the real-time position deviation data to obtain performance evaluation index data. Based on the performance evaluation index data, the index threshold is determined to obtain parameter optimization direction data.

[0162] A weight allocation matrix is ​​constructed for the parameter optimization direction data. The sliding surface coefficient, approach velocity coefficient, and integral coefficient in the parameter optimization direction data are weighted hierarchically to obtain the optimization weight matrix.

[0163] The initial gradient vector is obtained by performing matrix multiplication on the optimized weight matrix and the parameter optimization direction data;

[0164] The initial gradient vector is dynamically calculated by grouping it according to displacement error, velocity error and acceleration error, and the maximum allowable step size of each group is calculated to obtain adaptive step size data.

[0165] Based on the adaptive step size data, the initial gradient vector is piecewise linearly mapped, and different mapping functions are used for different error intervals to obtain the mapped gradient vector.

[0166] The mapped gradient vector is orthogonally decomposed to extract the coupling components between each control parameter, and a decoupling compensation matrix is ​​constructed to obtain the decoupling gradient vector.

[0167] The decoupled gradient vector is dynamically decayed. The decay coefficient is dynamically adjusted based on the number of historical iterations to obtain parameter adjustment data. The parameter adjustment data is then iteratively calculated with the initial sliding mode controller parameters to obtain the target sliding mode controller parameters.

[0168] Specifically, positioning accuracy is calculated and response time is statistically analyzed based on real-time position deviation data. Positioning accuracy is a crucial indicator of whether a linear module can accurately reach the target position, while response time determines the speed at which the system reaches steady state. Positioning accuracy is measured by calculating the root mean square value of the position error, and its expression is as follows:

[0169] ;

[0170] in, Represents the root mean square error. For the first The actual location at each point in time. For the desired position, Number of sampling points. A smaller root mean square error indicates higher positioning accuracy. Response time. It is the time required for the system to enter a steady state from the initial state. It is calculated by analyzing the system's error signal to converge to a certain threshold. Calculation of time within:

[0171] ;

[0172] in, The time when the system begins to move. This is the error threshold. It is calculated... and The system's performance evaluation metrics data are obtained. This data is compared with preset thresholds to determine whether current system parameters require optimization and to identify the direction of optimization. Weights are assigned to the parameter optimization direction data to allocate optimization resources appropriately. Weight assignment is based on the degree of influence of different control parameters on system performance, allocating appropriate optimization weights. An optimization weight matrix is ​​then established. As a diagonal matrix, each element represents the optimization weight for the corresponding parameter:

[0173] ;

[0174] in, The optimization weights representing the sliding surface coefficients, The optimization weights represent the approach velocity coefficient. These represent the optimization weights for the integral coefficients. The weights are set based on empirical values ​​or adaptively adjusted online to ensure the optimization process effectively improves system performance. The optimization weight matrix... Data related to parameter optimization direction Perform matrix multiplication to obtain the initial gradient vector:

[0175] ;

[0176] in, This represents the initial gradient vector, describing the optimization trend of each control parameter. Dynamic step size calculations are performed on the initial gradient vector to ensure that the optimization process can be reasonably adjusted under different error conditions. The basic principle of step size calculation is to set different optimization step sizes according to different types of errors (such as position error, velocity error, and acceleration error). The step size matrix is ​​then defined. for:

[0177] ;

[0178] in, This represents the step size corresponding to the position error. This represents the step size corresponding to the speed error. This represents the step size corresponding to the acceleration error. The step size is calculated using the maximum tolerance error method:

[0179] ;

[0180] in, These represent the maximum permissible errors for position, velocity, and acceleration, respectively. After the step size calculation is complete, the initial gradient vector is... With step matrix Perform calculations to obtain adaptive step size data:

[0181] ;

[0182] in, This represents the gradient vector after adaptive step size adjustment. To optimize the parameter update process, [the following is done / implemented]. Piecewise linear mapping is performed to ensure that parameter adjustments for different error ranges are reasonably set. And define the mapping function:

[0183] ;

[0184] in, For the error mapping function, a piecewise linear mapping is used, such as:

[0185] ;

[0186] in, This is the proportionality coefficient. This is the error threshold. Mapping the gradient vector. To more effectively guide parameter updates, after gradient mapping, orthogonal decomposition is performed to reduce mutual interference between parameters, extracting the coupling components between control parameters and constructing a decoupling compensation matrix. :

[0187] ;

[0188] in, This is the decoupling compensation matrix, obtained through methods such as principal component analysis or singular value decomposition, ensuring that the updates of different parameters do not affect each other. It also relates to the decoupling gradient vector. Dynamic decay is applied to ensure that the optimization process gradually converges in the later stages of iteration. A dynamic decay factor is set. :

[0189] ;

[0190] in, For decay rate, This represents the number of iterations. The final parameter adjustment data is as follows:

[0191] ;

[0192] And compare it with the initial sliding mode controller parameters. Update:

[0193] ;

[0194] Finally, the target sliding mode controller parameters are obtained.

[0195] The high-precision positioning control method for linear modules in the embodiments of the present invention has been described above. The high-precision positioning control system for linear modules in the embodiments of the present invention will be described below. Please refer to [link / reference]. Figure 2 One embodiment of the high-precision positioning control system for linear modules in this invention includes:

[0196] The feature point tracking module 201 is used to extract and track feature points from the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data.

[0197] Nonlinear compensation module 202 is used to perform nonlinear compensation on the linear module based on displacement measurement data and vibration characteristic data, and to construct a standard linear state equation;

[0198] Calculation module 203 is used to design the sliding surface and calculate the gain parameters based on the standard linear state equation to obtain the initial sliding controller parameters;

[0199] Feedback module 204 is used to perform trajectory interpolation and motion feedback on the linear module based on the initial sliding mode controller parameters to obtain real-time position deviation data;

[0200] The optimization module 205 is used to iteratively optimize the initial sliding mode controller parameters based on real-time position deviation data to obtain the target sliding mode controller parameters.

[0201] Through the collaborative efforts of the aforementioned components, a combination of visual measurement and dual-matching tracking was employed to achieve high-precision measurement of the motion state of the linear module. By using feature point array design and sub-pixel feature extraction algorithms, the limitations of traditional sensors were overcome, simultaneously acquiring displacement and vibration information and improving measurement accuracy. Based on nonlinear dynamic modeling and feedback linearization methods, the nonlinear characteristics of the system were effectively compensated. By establishing a complete dynamic model, considering the influence of various factors such as inertial force, Coriolis force, and friction, the system maintains good linearity even during large-scale motion. An adaptive gain sliding mode controller was designed to enhance the system's anti-interference capability. The use of a continuous reaching law instead of the traditional sign function effectively suppressed chattering caused by control switching, while the adaptive gain mechanism enabled the controller to automatically adapt to load changes. A parameter optimization method based on multidimensional performance indicators was proposed, achieving automatic optimization of controller parameters. Innovative designs such as hierarchical weight calculation, dynamic step size adjustment, and decoupling compensation solved the coupling problem in the parameter optimization process, ensuring continuous improvement in system performance. The use of seventh-order polynomial trajectory planning and third-order continuity processing ensured the smoothness of the motion trajectory. By designing a reasonable trajectory, the impact during acceleration and deceleration is reduced, effectively reducing system vibration and improving positioning accuracy.

[0202] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0203] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0204] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-precision positioning control method for a linear module, characterized in that, The method includes: Feature point extraction and feature point tracking are performed on the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data; Based on the displacement measurement data and the vibration characteristic data, nonlinear compensation is performed on the linear module to construct a standard linear state equation; Based on the standard linear state equation, the sliding surface is designed and the gain parameters are calculated to obtain the initial sliding controller parameters. Based on the initial sliding mode controller parameters, trajectory interpolation and motion feedback are performed on the linear module to obtain real-time position deviation data; The initial sliding mode controller parameters are iteratively optimized based on the real-time position deviation data to obtain the target sliding mode controller parameters.

2. The high-precision positioning control method for linear modules according to claim 1, characterized in that, The process of extracting and tracking feature points from the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data includes: Gaussian filtering is applied to a 5×5 feature point array pre-set on the surface of the moving parts in the linear module to reduce noise, resulting in filtered image data. The filtered image data is subjected to Hough transform circular contour detection to obtain feature point contour data, and the feature point contour data is fitted with a two-dimensional Gaussian curve to obtain feature point center coordinate data. The coordinates of the feature point center are input into the global coordinate system transformation matrix to perform coordinate transformation and obtain the displacement coordinate data; Perform time series differentiation on the displacement coordinate data to obtain velocity and acceleration data; The displacement coordinate data, the velocity and acceleration data are fused with the motor torque, load mass and ambient temperature of the linear module to obtain a motion state dataset. Feature point tracking is performed on the motion state dataset to obtain displacement measurement data and vibration characteristic data of the linear module.

3. The high-precision positioning control method for linear modules according to claim 2, characterized in that, The step of tracking feature points in the motion state dataset to obtain displacement measurement data and vibration feature data of the linear module includes: The motion state dataset is input into the spatial matching layer, the affine transformation matrix of the feature point array in adjacent image frames is calculated, and the optimal matching pair is selected to obtain the spatial matching displacement data. The spatial matching displacement data is input into the time matching layer to construct a state vector, thereby obtaining a filter state model. The state vector contains position and velocity components. Based on the spatial matching displacement data and the filter state model, trajectory prediction and smoothing are performed to obtain displacement measurement data; The vibration amplitude is calculated from the displacement measurement data to obtain vibration amplitude data, and the frequency features are extracted from the displacement measurement data to obtain vibration frequency data. The vibration amplitude data and the vibration frequency data are fused to obtain vibration feature data.

4. The high-precision positioning control method for linear modules according to claim 1, characterized in that, The step of performing nonlinear compensation on the linear module based on the displacement measurement data and the vibration characteristic data, and constructing a standard linear state equation, includes: The displacement measurement data is subjected to motion equation parameter identification and dynamic modeling to obtain the displacement-force mapping relationship. Simultaneously, the vibration characteristic data is subjected to frequency domain analysis and damping characteristic extraction to obtain the damping coefficient. The displacement-force mapping relationship and the damping coefficient are then combined to construct a nonlinear dynamic model M(p)d. 2 p / dt 2 +C(p,dp / dt)(dp / dt)+G(p)+F(dp / dt)+W(t)=u, where M(p) is the inertia matrix, p is the displacement vector, C(p,dp / dt) is the Coriolis force matrix, G(p) is the gravity term, F(dp / dt) is the friction term, W(t) is the external disturbance term, u is the control input, and t is time; The nonlinear dynamic model is then defined with state variables, yielding the state vector expression X(t) = [p(t), dp / dt]. T , where X(t) is the state vector, p(t) is the displacement component state variable, and dp / dt is the velocity component state variable; The state vector expression is subjected to nonlinear term compensation to obtain a feedback linearized control law, which is expressed as: u=M(p)[vM -1 (p)(C(p,dp / dt)(dp / dt)+G(p)+F(dp / dt)+W(t))], where v is the new control input; Substituting the feedback linearization control law into the nonlinear dynamic model, we obtain the linearized system expression dX / dt=AX(t)+Bv(t); The linearized system expression is used to construct the system matrix, resulting in the standard linear state equation X'(t)=AX(t)+Bv(t)+E(t), where X'(t) is the derivative vector of the state variables, A is the n×n dimensional system matrix, B is the input matrix, E(t) is the disturbance vector, and n is the system order.

5. The high-precision positioning control method for linear modules according to claim 1, characterized in that, The process of designing the sliding surface and calculating the gain parameters based on the standard linear state equation to obtain the initial sliding controller parameters includes: The displacement tracking error is defined on the standard linear state equation to obtain the tracking error equation e(t)=X(t)-Xd(t), where e(t) is the tracking error vector, X(t) is the state vector, and Xd(t) is the desired state vector. Based on the tracking error equation, a sliding surface is constructed, and the sliding surface expression s(t)=ce(t)+de(t) / dt is obtained, where s(t) is the sliding surface vector, c is the sliding surface coefficient matrix of a positive definite diagonal matrix, and de(t) / dt is the tracking error derivative vector. A continuous reaching law is designed for the sliding surface expression, resulting in the reaching law equation ds / dt=-η|s|-k∫|s|dt, where ds / dt is the sliding surface derivative vector, η is the reaching velocity coefficient matrix of the positive definite diagonal matrix, k is the integral coefficient matrix of the positive definite diagonal matrix, and ∫|s|dt is the sliding surface integral vector. Substituting the approach law equation into the standard linear state equation for solution, we obtain the sliding mode control law v(t) = vs(t) + vn(t), where v(t) is the control input vector, vs(t) is the equivalent control term vector used to compensate for known dynamics, and vn(t) is the switching control term vector used to suppress unknown disturbances. Based on the sliding mode control law, an adaptive gain update law is designed, and the dynamic equation of the gain parameter dk / dt=γ|s| is obtained, where dk / dt is the derivative of the gain matrix, γ is the learning rate coefficient matrix of the positive definite diagonal matrix, and |s| is the absolute value vector of the sliding surface. The initial sliding mode controller parameters are obtained by combining the sliding mode control law and the dynamic equation of the gain parameter.

6. The high-precision positioning control method for linear modules according to claim 1, characterized in that, The step of performing trajectory interpolation and motion feedback on the linear module based on the initial sliding mode controller parameters to obtain real-time position deviation data includes: The positioning task of the linear module is performed using a seventh-order polynomial trajectory planning method to obtain the desired trajectory data of position, velocity, and acceleration. The desired trajectory data is subjected to third-order continuity processing based on the initial sliding mode controller parameters to obtain smooth trajectory interpolation data; The position and velocity of the linear module are collected in real time to obtain real-time motion feedback data. The smooth trajectory interpolation data is compared and calculated with the real-time motion feedback data to obtain the real-time position deviation data.

7. The high-precision positioning control method for linear modules according to claim 1, characterized in that, The step of iteratively optimizing the initial sliding mode controller parameters based on the real-time position deviation data to obtain the target sliding mode controller parameters includes: The positioning accuracy and response time are calculated and statistically analyzed on the real-time position deviation data to obtain performance evaluation index data. Based on the performance evaluation index data, the index threshold is determined to obtain parameter optimization direction data. A weight allocation matrix is ​​constructed for the parameter optimization direction data, and the sliding surface coefficient, approach velocity coefficient, and integral coefficient in the parameter optimization direction data are weighted in a hierarchical manner to obtain the optimization weight matrix. The initial gradient vector is obtained by performing matrix multiplication between the optimized weight matrix and the parameter optimization direction data; The initial gradient vector is dynamically calculated by grouping it according to displacement error, velocity error and acceleration error, and the maximum allowable step size of each group is calculated to obtain adaptive step size data. Based on the adaptive step size data, the initial gradient vector is piecewise linearly mapped, and different mapping functions are used for different error intervals to obtain the mapped gradient vector. The mapped gradient vector is orthogonally decomposed to extract the coupling components between each control parameter, and a decoupling compensation matrix is ​​constructed to obtain the decoupling gradient vector. The decoupled gradient vector is dynamically decayed, and the decay coefficient is dynamically adjusted based on the number of historical iterations to obtain parameter adjustment data. The parameter adjustment data is then iteratively calculated with the initial sliding mode controller parameters to obtain the target sliding mode controller parameters.

8. A high-precision positioning control system for a linear module, characterized in that, The system is used to perform the high-precision positioning control method for a linear module as described in any one of claims 1-7, the system comprising: The feature point tracking module is used to extract and track feature points from the motion image sequence of the linear module to obtain displacement measurement data and vibration feature data. The nonlinear compensation module is used to perform nonlinear compensation on the linear module based on the displacement measurement data and the vibration characteristic data, and to construct a standard linear state equation. The calculation module is used to design the sliding surface and calculate the gain parameters based on the standard linear state equation to obtain the initial sliding controller parameters; The feedback module is used to perform trajectory interpolation and motion feedback on the linear module based on the initial sliding mode controller parameters to obtain real-time position deviation data; The optimization module is used to iteratively optimize the initial sliding mode controller parameters based on the real-time position deviation data to obtain the target sliding mode controller parameters.

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