Method and device for controlling multi-directional operating servo sliding table module

Abstract

The invention relates to the technical field of module control, and discloses a multi-directional operating servo sliding table module control method and device, and the method comprises the steps: carrying out the motion state collection of an X axis, a Y axis and a Z axis of a servo sliding table module, and obtaining multi-dimensional inter-axis coupling data containing a lead screw lead error, a guide rail friction characteristic and motor torque fluctuation; constructing a tensor compensation model for describing XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data; carrying out CP decomposition dimension reduction based on the tensor compensation model to obtain dimension reduction coupling relation data; executing multi-axis synchronous linear prediction according to the dimension reduction coupling relation data to obtain multi-axis coordination trajectory planning data; according to the method, nonlinear control law calculation is performed based on multi-axis coordination trajectory planning data to obtain an optimal control instruction sequence, so that redundant information and noise components in original coupling data are effectively removed, the robustness of a control system to environmental interference and parameter change is improved, and stable control performance under different working conditions is ensured.

Description

Technical Field

[0001] The present invention relates to the field of module control technology, and in particular to a method and device for controlling a servo slide module that operates in multiple directions. Background Art

[0002] Traditional multi-axis servo control systems generally adopt an independent-axis PID control strategy, treating the three axes (X, Y, and Z) as independent control objects. This approach can meet basic control requirements in low-speed, short-stroke applications. However, in actual multi-directional, high-speed motion, complex mechanical coupling exists between the axes of the slide module. This includes position coupling caused by lead screw errors, dynamic coupling caused by the friction characteristics of the guideway pair, and vibration coupling caused by servo motor torque fluctuations. These coupling factors cause the motion states of the axes to influence each other, and traditional independent-axis control methods cannot effectively address this dynamic coupling between axes.

[0003] Although existing cross-coupling compensation technologies can improve the performance of multi-axis coordinated control to a certain extent, most of them use matrix-based linear compensation methods. Such methods face the problem of a sharp increase in computational complexity when dealing with large-stroke, high-precision three-dimensional motion. When the working space of the slide module increases, the coupling parameters that need to be processed increase cubically, resulting in an excessive computational load on the real-time control system, making it difficult to meet the millisecond-level response requirements during high-speed motion. In addition, traditional linear compensation methods cannot accurately describe the nonlinear variation characteristics of the coupling strength of the slide module at different positions and speeds. In particular, when dealing with complex factors such as the nonlinearity of the screw drive and the friction coupling dynamics of the guide rail, the compensation accuracy will deteriorate significantly with the increase of motion speed and stroke. Summary of the Invention

[0004] The present invention provides a multi-directional servo slide module control method and device, thereby effectively removing redundant information and noise components in the original coupling data, improving the robustness of the control system to environmental interference and parameter changes, and ensuring stable control performance under different working conditions.

[0005] A first aspect of the present invention provides a method for controlling a servo slide module for multi-directional operation, the method comprising:

[0006] The motion state of the X, Y, and Z axes of the servo slide module is collected to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuations;

[0007] Constructing a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data;

[0008] Performing CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality-reduced coupling relationship data;

[0009] Perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data;

[0010] A nonlinear control law is calculated based on the multi-axis coordinated trajectory planning data to obtain an optimal control instruction sequence.

[0011] In combination with the first aspect, in a first implementation of the first aspect of the present invention, the motion state of the XYZ three axes of the servo slide module is collected to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuation, including:

[0012] The motion state of the XYZ axes of the servo slide module is collected through position sensors and torque sensors to obtain the position deviation sequence, speed deviation sequence and torque feedback sequence of each axis;

[0013] Performing error detection calculation on the lead of each axis screw based on the position deviation sequence to obtain the lead error of each axis screw;

[0014] Extracting features of the guide rail friction characteristics and motor torque fluctuations based on the speed deviation sequence and the torque feedback sequence to obtain friction force variation curves and torque fluctuation amplitude data for each axis;

[0015] The inter-axis coupling coefficient is calculated based on the screw lead error, the friction force variation curve and the torque fluctuation amplitude data to obtain multi-dimensional inter-axis coupling data including XY axis coupling coefficient, XZ axis coupling coefficient and YZ axis coupling coefficient.

[0016] In combination with the first aspect, in a second implementation of the first aspect of the present invention, constructing a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data includes:

[0017] Performing spatial position discretization processing on the multi-dimensional inter-axis coupling data to obtain a set of discretized position points of the X, Y, and Z axes;

[0018] Constructing a three-dimensional coupling relationship tensor based on the discretized position point set;

[0019] Performing a three-axis coupling strength numerical calculation on each tensor element in the three-dimensional coupling relationship tensor according to the discretized position point set to obtain a tensor element numerical matrix describing the coupling strength distribution at each spatial position;

[0020] A tensor product operation is performed based on the tensor element numerical matrix and the weight vectors of each axis to obtain a tensor compensation model including a cross-coupling compensation operator.

[0021] In combination with the first aspect, in a third implementation of the first aspect of the present invention, the tensor product operation is performed based on the tensor element numerical matrix and each axis weight vector to obtain a tensor compensation model including a cross-coupling compensation operator, including:

[0022] Based on the XYZ three-axis motion characteristic parameters of the servo slide module, the weight vector of each axis is numerically initialized and calculated to obtain the X-axis weight vector, Y-axis weight vector and Z-axis weight vector;

[0023] Performing element-by-element weighted sum calculation on the tensor element numerical matrix and the X-axis weight vector according to a first-dimensional tensor contraction product operation rule to obtain a first intermediate tensor operation result;

[0024] Based on the first intermediate tensor operation result, a dimension-by-dimension weighted summation calculation is performed on the Y-axis weight vector according to the second-dimensional tensor contraction product operation rule and the Z-axis weight vector according to the third-dimensional tensor contraction product operation rule to obtain a target tensor operation result;

[0025] A tensor compensation model including a cross-coupling compensation operator is constructed according to the target tensor operation result.

[0026] In combination with the first aspect, in a fourth implementation of the first aspect of the present invention, performing CP decomposition and dimensionality reduction based on the tensor compensation model to obtain reduced-dimensional coupling relationship data includes:

[0027] Performing a third-order tensor decomposition on the tensor compensation model to obtain CP decomposition initialization data including a decomposition rank parameter R and an initial factor vector group;

[0028] Iteratively calculating and converging the tensor decomposition error based on the CP decomposition initialization data to obtain an optimal decomposition rank value and a corresponding decomposition convergence parameter;

[0029] performing a tensor decomposition operation on the tensor compensation model according to the optimal decomposition rank value and the decomposition convergence parameter to obtain a tensor decomposition result;

[0030] Based on the factor vectors of each axis in the tensor decomposition result, dominant coupling modes are extracted and dimension reduction calculations are performed to obtain dimension-reduced coupling relationship data.

[0031] In combination with the first aspect, in a fifth implementation of the first aspect of the present invention, performing dominant coupling mode extraction and dimensionality reduction calculation based on each axis factor vector in the tensor decomposition result to obtain reduced-dimensionality coupling relationship data includes:

[0032] Performing factor vector separation on the tensor decomposition result to obtain three-axis factor vector data including an X-axis factor vector group, a Y-axis factor vector group, and a Z-axis factor vector group;

[0033] Performing a ranking calculation of the importance of dominant modes based on the modulus of each factor vector in the three-axis factor vector data to obtain a ranking result of dominant coupled modes;

[0034] According to the dominant coupling mode sorting result, the top R dominant modes with the largest coupling strengths are selected for dimensional screening to obtain screened factor vector data including R dominant X-axis factor vectors, R dominant Y-axis factor vectors, and R dominant Z-axis factor vectors;

[0035] Based on the filtered factor vector data and the corresponding decomposition coefficients, a dimensionality reduction coupling relationship reconstruction is performed to obtain dimensionality reduction coupling relationship data.

[0036] In combination with the first aspect, in a sixth implementation of the first aspect of the present invention, performing multi-axis synchronous linear prediction according to the dimensionality reduction coupling relationship data to obtain multi-axis coordinated trajectory planning data includes:

[0037] Inputting the dimension-reduced coupling relationship data as a coupling term for inter-axis influence prediction into a multi-axis synchronous linear prediction model to construct a state vector, thereby obtaining an extended state vector;

[0038] Calculating the inter-axis influence amount based on the extended state vector to obtain an inter-axis influence prediction result;

[0039] Performing feedforward compensation correction on the multi-axis synchronous linear prediction model according to the inter-axis influence prediction result to obtain a corrected prediction model;

[0040] Based on the revised prediction model, the desired trajectory optimization solution and physical constraint condition processing are performed to obtain multi-axis coordinated trajectory planning data.

[0041] In combination with the first aspect, in a seventh implementation of the first aspect of the present invention, the reduced-dimensional coupling relationship data is input into a multi-axis synchronous linear prediction model as a coupling term for inter-axis influence prediction to construct a state vector to obtain an extended state vector, including:

[0042] Based on the current motion state of the XYZ axes of the servo slide module, the basic state vector is assembled to obtain a six-dimensional basic state vector containing the position component and velocity component of each axis;

[0043] Calculating the coupling influence of the reduced-dimensional coupling relationship data according to the decomposition coefficient and factor vector of the dominant coupling mode to obtain a coupling term numerical sequence;

[0044] According to the coupling term numerical sequence, a state equation is constructed and a system matrix is ​​filled in for the multi-axis synchronous linear prediction model to obtain a linear state equation group;

[0045] Based on the linear state equation group, the six-dimensional basic state vector and the coupling term numerical sequence are vector-concatenated and dimensionally expanded to obtain an extended state vector.

[0046] In combination with the first aspect, in an eighth implementation of the first aspect of the present invention, the nonlinear control law calculation based on the multi-axis coordinated trajectory planning data to obtain the optimal control instruction sequence includes:

[0047] The multi-axis coordinated trajectory planning data is subjected to tensor lifting linear reformulation processing by the Koopman operator to obtain a nonlinear observation vector including a base state, a quadratic term, and a trigonometric function term;

[0048] Constructing a linear state equation and a Koopman matrix in the lifting space based on the nonlinear observation vector to obtain a lifted state model;

[0049] Optimizing and solving the feedback control gain matrix and the feedforward control gain matrix according to the improved state model to obtain optimal control gain parameters;

[0050] Based on the optimal control gain parameters, an augmented control law is calculated for the control variables of each axis to generate an optimal control instruction sequence.

[0051] A second aspect of the present invention provides a multi-directional servo slide module control device, the multi-directional servo slide module control device comprising:

[0052] The acquisition module is used to collect the motion status of the X, Y, and Z axes of the servo slide module to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuation;

[0053] A construction module, configured to construct a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data;

[0054] A dimensionality reduction module, configured to perform CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality reduction coupling relationship data;

[0055] A prediction module, configured to perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data;

[0056] The calculation module is used to calculate the nonlinear control law based on the multi-axis coordinated trajectory planning data to obtain the optimal control instruction sequence.

[0057] Compared with the prior art, the present invention has the following beneficial effects: by constructing a multi-dimensional inter-axis coupling data model that includes screw lead error, guide rail friction characteristics and motor torque fluctuations, it overcomes the problem in the prior art that independent control of each axis cannot handle inter-axis dynamic coupling, and realizes comprehensive capture and accurate modeling of the complex coupling relationship of the slide module. The cross-coupling compensation operator is reconstructed in tensor format, and the CP decomposition technology is used to achieve efficient dimensionality reduction processing of high-dimensional coupling relationships, providing an effective solution for the rapid processing of large-scale real-time trajectory data. The coupling intensity distribution model established based on the third-order tensor structure can accurately describe the three-axis coupling characteristics at each spatial position. Compared with the traditional linear compensation method, it effectively captures the nonlinear coupling change law of the slide module during multi-directional motion. By using the reduced-dimensional coupling relationship data as the coupling term for inter-axis influence prediction, a multi-axis synchronous linear prediction model including coupling influence is constructed, which overcomes the coupling interference problem caused by independent prediction of each axis in the prior art and realizes feedforward compensation for inter-axis interaction. The Koopman operator theory is used to perform tensor lifting linear reformulation, transforming complex nonlinear control problems into optimization solutions in linear space. While maintaining an accurate description of the nonlinear characteristics of the original system, it avoids the computational complexity of traditional nonlinear control methods. The control system design adopts a hierarchical tensor structure. Through the coordinated cooperation of the task planning layer, tensor compensation layer, and servo execution layer, it significantly reduces the real-time computing burden of the system compared to the centralized control architecture and improves the control response speed under multi-directional high-speed motion conditions. Through the extraction of dominant coupling modes and dimensionality reduction calculations, redundant information and noise components in the original coupling data are effectively removed, improving the robustness of the control system to environmental interference and parameter changes, and ensuring stable control performance under different working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0059] The structures, proportions, sizes, etc. depicted in the drawings of this specification are only used to match the contents disclosed in the specification so as to facilitate understanding and reading by persons familiar with this technology. They are not intended to limit the conditions under which the present invention can be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportional relationships, or adjustments in size should still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and objectives that can be achieved by the present invention.

[0060] Figure 11 is a flow chart of a method for controlling a multi-directional servo slide module provided by an embodiment of the present invention;

[0061] Figure 2 It is a schematic block diagram of the structure of a multi-directional servo slide module control device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0063] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, combined, or partially merged, so the actual execution order may vary depending on the actual situation.

[0064] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the present invention. As used in the specification and appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0065] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations. Figure 1 In one embodiment of the present invention, a method for controlling a servo slide module for multi-directional operation includes:

[0066] Step 100: Acquire the motion state of the X, Y, and Z axes of the servo slide module to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuation;

[0067] It is understandable that the execution subject of the present invention can be a multi-directional servo slide module control device, or a terminal or a server, which is not limited here. The embodiment of the present invention is described by taking the server as the execution subject as an example.

[0068] Specifically, position sensors and torque sensors are deployed on each motion axis of the servo slide module. The position sensors record the displacement changes of each axis in real time, while the torque sensors capture the actual torque trends at the servo motor output. During data acquisition, the sampling frequency is set at a high level, such as 100kHz, to ensure that even under highly dynamic motion conditions, even small fluctuations in displacement and torque can be recorded at every moment, avoiding data loss or reduced accuracy due to insufficient sampling. Displacement data is processed by comparing the target displacement command trajectory of each axis with the actual measured displacement to generate a time-varying position deviation sequence. This deviation sequence is then used to detect and calculate the lead error of the lead screw. Based on the theoretical relationship between ideal lead screw rotation and displacement and the actual measured position changes, the lead screw deviations at different position intervals are inferred using methods such as least squares fitting. A lead error curve is then constructed for each axis, reflecting nonlinear motion distortion caused by lead screw machining or assembly errors. Simultaneously, based on the collected velocity deviation sequence and torque feedback sequence, feature extraction is performed on the guide rail friction characteristics and motor torque fluctuations. Velocity deviation data can reveal subtle velocity perturbations caused by friction variations during the slide's motion. Combined with torque feedback, an inverse dynamics model is used to derive friction variations for each axis under different motion states. By fitting and segmented modeling the friction within each speed range, friction curves for each axis are derived, characterizing the dynamic characteristics of guideway friction as a function of speed and load. Furthermore, through frequency domain analysis and time domain fluctuation amplitude calculation, motor torque fluctuation amplitude data is extracted from the torque feedback sequence to quantify the motor's fluctuation characteristics under varying loads and speeds. A model for calculating the inter-axis coupling coefficient is established based on lead screw error, friction curves, and torque fluctuation amplitude data. Considering that the slide module's mechanical structure results in a certain degree of dynamic coupling between the axes, such as X-axis motion causing subtle Y-axis vibrations, the correlation and transfer characteristics between the errors and perturbations between the axes are analyzed. Multivariate regression analysis and cross-correlation calculations are then used to calculate the XY, XZ, and YZ coupling coefficients, respectively. The coupling coefficient not only reflects the direct relationship between displacement and torque but also comprehensively considers the complex interactions between friction fluctuations, screw errors, and motor torque disturbances. In this way, the multidimensional inter-axis coupling data constructed can describe the dynamic coupling characteristics between the axes of the servo slide module under multi-directional motion.

[0069] Step 200: constructing a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data;

[0070] Specifically, the spatial position discretization processing is performed on the multi-dimensional inter-axis coupling data. According to the motion range of the slide module in the actual workspace, the three axes XYZ are uniformly discretized along their respective motion directions according to the preset step size to form a set of discrete position points, which correspond to the number of discrete positions of the X-axis, Y-axis and Z-axis respectively. Based on the set of discrete position points, a three-dimensional coupling relationship tensor is constructed with these points as basic units. The structure of this tensor is such that each element corresponds to the coupling strength between the three axes XYZ of the slide module at the spatial position. The coupling strength reflects the multi-axis mutual influence relationship at the specified position point, including torque transmission, vibration coupling and friction linkage effect. Based on the data such as the screw lead error, guide rail friction characteristics and motor torque fluctuation actually measured at each discrete point, a multi-variable function fitting or interpolation algorithm is applied to perform numerical calculations on each element in the tensor. During this process, nonparametric estimation methods such as kernel regression and locally weighted regression are introduced to enhance the model's ability to capture nonlinear trends in the data. This allows the tensor to not only describe linear coupling characteristics but also fully reflect the nonlinear complexity of the slider module's coupling characteristics under highly dynamic conditions. After the tensor elements are numerically calculated and a tensor element matrix is ​​formed, weight vectors for each axis are introduced to optimize the tensor model's applicability and compensation capabilities. These three weight vectors correspond to weight coefficients for discrete positions on the X, Y, and Z axes, respectively. The weights are determined based on the impact of each axis on system performance in the specific application scenario, effectively balancing the dynamic response requirements and compensation accuracy along different axes. A multidimensional tensor product operation is performed based on the tensor element matrix and these three sets of weight vectors. This involves performing a dimension-by-dimension product of the tensor and the weight vector along the corresponding dimension, achieving weighted correction of the tensor along different axes and enhancing the compensation model's ability to detect the coupling effects of key axes. This tensor product operation ultimately results in a tensor compensation model that includes a cross-coupling compensation operator.

[0071] The weight vectors for each axis are numerically initialized based on the servo slide module's X, Y, and Z axis kinematic parameters. Different weighting factors are assigned to each axis based on its inertia, load, friction, and dynamic response requirements. For example, if the X-axis bears a heavier load and requires higher response speed in actual applications, its weight vector should be assigned a higher value within the corresponding range. For the Z-axis, which experiences significant friction fluctuations or greater motion impact, the distribution of the Z-axis weight vector is adjusted to provide greater sensitivity and compensation for coupling effects at key locations. This physics-based weight initialization ensures that the contribution of each axis to the overall coupling relationship during subsequent tensor calculations reflects actual operating conditions, thereby enhancing the targetedness and effectiveness of the compensation. The tensor element matrix and the X-axis weight vector are weighted and summed element-by-element according to the first-dimensional tensor contraction product operation rules. At each discrete position along the X-axis, the corresponding tensor element is multiplied by the element of the X-axis weight vector, and the sum is accumulated along that dimension to achieve weighted contraction of the first dimension, forming the first intermediate tensor operation result. Based on the result of the first intermediate tensor operation, weighted summation is performed with the Y-axis weight vector according to the second-dimensional tensor contraction product operation rule, and then weighted summation is performed with the Z-axis weight vector according to the third-dimensional tensor contraction product operation rule. The intermediate tensor is element-wise multiplied by the weight vector along the Y-axis and Z-axis directions and accumulated in the corresponding dimensions, and the three-dimensional tensor is gradually reduced to the final target tensor operation result through weighted contraction. A tensor compensation model containing a cross-coupling compensation operator is constructed based on the target tensor operation result. This compensation model integrates the contribution of the three axes XYZ to the coupling strength at different spatial positions. Through the reasonable modulation of the weight vector, it dynamically reflects the changes in mechanical properties under different working conditions, and can effectively adapt to the complex coupling behavior of the slide module during high-speed, high-precision multi-axis linkage motion.

[0072] Step 300: Perform CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality-reduced coupling relationship data;

[0073] It should be noted that the tensor compensation model undergoes a third-order tensor decomposition. The CP decomposition initialization data is generated by setting a reasonable decomposition rank parameter R and the corresponding initial factor vector set. The initial factor vector set corresponds to the basic components of the X-, Y-, and Z-axes, respectively. Initialization is performed through random initialization or optimal initialization using methods such as singular value decomposition, aiming to provide a starting point for faster convergence and higher decomposition quality for subsequent iterative calculations. The initial setting of the decomposition rank parameter R balances decomposition compactness and information retention. A too small R will lose key information, while a too large R will lead to model redundancy and increased computational complexity. Based on this CP decomposition initialization data, the tensor decomposition error is iteratively calculated and convergence determined. In each iteration, the tensor is approximated and reconstructed based on the current factor vector set, and an error metric is calculated between the original tensor compensation model and the approximate reconstructed tensor, such as using the Frobenius norm for normalized error evaluation. By repeatedly optimizing and updating the factor vector set, the decomposition error is gradually reduced, and a reasonable convergence threshold, such as a drop below 1%, is set as the stopping condition for the decomposition process. Simultaneously, the decomposition rank parameter R is dynamically adjusted during the iterative process. By comparing the error convergence performance under different R values, the optimal decomposition rank value is determined that maintains the error below a preset threshold while minimizing model complexity. A tensor decomposition operation is performed on the tensor compensation model based on the optimal decomposition rank value and the decomposition convergence parameter. By representing the tensor as a weighted linear combination of multiple rank tensors, the set of axial factor vectors underlying each dominant mode is extracted. This process reduces the data size of the original third-order tensor, transforming the storage of the triaxial coupling strength at each discrete point into a compact representation that only requires the storage of a small number of factor vectors and their combined coefficients. Based on the axial factor vectors in the tensor decomposition results, the dominant coupling modes are extracted and dimensionality reduction is performed, further reducing model complexity. By analyzing the weight and contribution of each axial factor vector in the decomposition, the dominant coupling modes (i.e., the components that play a decisive role in the X, Y, and Z triaxial kinematic coupling relationship) are screened. Secondary modes with contributions below the preset threshold are discarded, while modes with high contributions are retained to construct the reduced-dimensionality coupling relationship data.

[0074] The tensor decomposition results are factored and separated. During the CP decomposition process, the original third-order tensor is decomposed into a weighted combination of a set of rank tensors. Each rank tensor is generated by the outer product of the corresponding X-axis factor vector, Y-axis factor vector, and Z-axis factor vector. The separation operation is to classify these factor vectors according to the axis to form a three-axis factor vector data set containing an X-axis factor vector group, a Y-axis factor vector group, and a Z-axis factor vector group. The dominant mode importance ranking is calculated based on the modulus of each factor vector in the three-axis factor vector data. The modulus reflects the energy intensity of the factor vector, that is, the influence of the mode in the overall coupling relationship. By calculating the modulus of each factor vector and combining it with the tensor decomposition coefficient corresponding to each mode, the contribution of each mode to the overall coupling tensor is comprehensively evaluated to obtain the ranking result of the dominant coupling modes. Based on the above dominant coupling mode ranking results, the top R dominant modes with the largest coupling strength are selected for dimension screening. For the top R modes, the corresponding X-axis factor vectors, Y-axis factor vectors, and Z-axis factor vectors are extracted, forming a filtered factor vector data set consisting of R dominant X-axis factor vectors, R dominant Y-axis factor vectors, and R dominant Z-axis factor vectors. Based on the filtered factor vector data and the corresponding decomposition coefficients, a dimensionality-reduced coupling relationship reconstruction is performed to ultimately obtain the reduced-dimensional coupling relationship data. Using the retained R groups of dominant factor vectors and their decomposition coefficients, the dominant modes are weightedly combined using the tensor reconstruction formula to reconstruct a new low-dimensional coupling relationship approximation tensor.

[0075] Step 400: Perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data;

[0076] Specifically, the reduced-dimensionality coupling relationship data is input into the multi-axis synchronous linear prediction model as a coupling term for inter-axis influence prediction. The reduced-dimensionality coupling relationship data provides a simplified description of the interactions between the X, Y, and Z axes at different spatial positions and dynamic states. Therefore, when constructing the multi-axis synchronous linear prediction model, the traditional single-axis state vector is expanded into an extended state vector that incorporates inter-axis coupling effects. This extended state vector includes displacement and velocity information for each axis. By embedding the reduced-dimensionality coupling relationship data, it dynamically reflects the subtle mechanical coupling effects between axes, enabling the prediction model to more realistically depict the complex dynamic behavior of the actual system under high-speed linkage. After the extended state vector is constructed, the inter-axis influence quantities are calculated based on this vector. By analyzing the interaction components between the axes in the extended state vector and combining it with the modal information provided by the reduced-dimensionality coupling relationship data, the potential influence of each axis's motion state on the other axes at the current moment is calculated. These influence quantities specifically reflect quantitative predictions of phenomena such as torque interference, friction coupling, and dynamic resonance between the axes. The calculation of inter-axis influences not only considers first-order information such as displacement and velocity, but also incorporates higher-order dynamic characteristics such as acceleration and vibration frequency, thereby capturing the coupled disturbances generated by the servo slide module during complex motion. Based on the inter-axis influence prediction results, feedforward compensation is applied to the multi-axis synchronous linear prediction model. Traditional linear prediction models assume independent motion of each axis, making it difficult to effectively address the actual inter-axis coupling problem. Therefore, a feedforward correction mechanism based on coupling prediction results is introduced. By actively compensating for the expected disturbance effects in the control input, the prediction model's adaptability to complex motion environments is improved. The specific correction method involves updating the system matrix and the control matrix, incorporating the dynamic variation of the coupling terms to more accurately capture future motion trends. Through feedforward compensation, the prediction model can improve the robustness and accuracy of trajectory tracking based on reasonable predictions of future coupled disturbances. The desired trajectory is optimized based on the corrected prediction model, while also incorporating physical constraints. Optimizing the desired trajectory requires minimizing the deviation between the actual trajectory and the reference trajectory. Physical constraints of the slide module, including maximum acceleration limits, maximum speed limits, travel boundary conditions, and the mechanical structure constraints of the slide system, are incorporated into the optimization process to ensure that the generated trajectory meets control performance requirements and can be safely and reliably executed in the actual hardware system. Trajectory optimization employs a constrained optimal control method, integrating trajectory error and control input energy consumption into the optimization objective by setting a cost function. Soft or hard constraints are also introduced to address physical limitations, ultimately resulting in the solution for multi-axis coordinated trajectory planning data.

[0077] A basic state vector is assembled based on the current motion state of the servo slide module's three axes, X, Y, and Z. High-precision sensors collect real-time position and velocity information for each axis, extracting the displacement components and corresponding velocity components for the X, Y, and Z axes. These components are then arranged sequentially to form a basic state vector containing six elements, with the first three elements corresponding to the position state of each axis, and the last three elements corresponding to the velocity state. Using the reduced-dimensional coupling relationship data, the coupling influence is calculated based on the decomposition coefficients of the dominant coupling modes and their corresponding factor vectors. The calculation process involves weighting and summing the factor vectors of each dominant mode in the reduced-dimensional tensor decomposition results according to the decomposition coefficients. Combined with the current position and velocity information, the change in inter-axis coupling strength at each position state is mapped, forming a numerical sequence of coupling terms. This reflects the interactions between the X, Y, and Z axes due to mechanical structure, friction characteristics, and dynamic coupling in the current motion state. The quantitative results are directly linked to the time-evolving motion disturbance trends, providing dynamic inter-axis linkage disturbance inputs for the prediction model. Based on this numerical sequence of coupling terms, the state equations and system matrix filling are constructed for the multi-axis synchronous linear prediction model. Based on the traditional state equation, dynamic compensation terms related to the numerical values ​​of the coupling terms are added. This ensures that the system matrix not only reflects the intrinsic dynamic characteristics of the independent motion of each axis, but also reflects the state transition effects caused by the coupling. By properly embedding these coupling terms into the state transition matrix, the constructed linear state equation system can more accurately describe the dynamic behavior of the multi-axis linkage of the slide module under actual working conditions, effectively avoiding the accumulation of prediction errors and the expansion of synchronization deviations caused by ignoring the coupling effect. Based on the linear state equation system, the six-dimensional basic state vector and the numerical sequence of the coupling terms are vector-concatenated and dimensionally expanded to form an extended state vector.

[0078] Step 500: Calculate a nonlinear control law based on the multi-axis coordinated trajectory planning data to obtain an optimal control instruction sequence.

[0079] Specifically, the multi-axis coordinated trajectory planning data is subjected to tensor-lifting linear reformulation using Koopman operator theory. The Koopman operator provides a mathematical method for mapping nonlinear system behavior into a high-dimensional linear space. Therefore, a nonlinear observation vector is constructed based on the original trajectory planning data. This observation vector contains basic state information, such as the position and velocity components of each axis. Quadratic terms of each state variable are also introduced, such as the squared position, the squared velocity, and the cross-product term between position and velocity. Furthermore, nonlinear characteristic terms based on trigonometric functions, such as sine and cosine functions, are introduced to enhance the system's ability to model periodic and oscillatory behaviors. The nonlinear observation vector expanded in this way can enrich the feature space of state description, making the subsequent control design in the lifted space more expressive and adaptable to nonlinear behavior. After the nonlinear observation vector is constructed, the linear state equation and the corresponding Koopman matrix in the lifted space are constructed based on this vector. Based on the time-evolving data of multi-axis trajectories, a linear state transition relationship is fitted in the expanded observation space, transforming the originally nonlinear system evolution process into a linear mapping process in a high-dimensional space. The elements of the Koopman matrix correspond to the linear coupling coefficients between the nonlinear observation variables. Through this process, the system still retains its complex nonlinear characteristics on the surface, but is mathematically transformed into a linear system. Based on the improved state model, the feedback control gain matrix and the feedforward control gain matrix are optimized. To ensure that the control system can achieve fast and accurate trajectory tracking while maintaining good stability, the optimal control gains are solved in the improved space using optimal control theory, such as the linear quadratic regulator method. The feedback control gain matrix is ​​used for error correction and dynamic adjustment based on the current nonlinear observation state, while the feedforward control gain matrix is ​​used for proactive adjustment based on the evolution trend of the reference trajectory. The two work together to suppress trajectory deviations caused by external disturbances or model uncertainty while effectively improving the system's response speed and control accuracy. By optimizing the gain matrices, a set of control gain parameters with the best global performance in the improved space is obtained. Based on the optimal control gain parameters and the expanded nonlinear observation vector, an augmented control law for each axis's control variable is calculated. For each moment of system observation, the optimal control input commands for the X, Y, and Z axes are generated in real time by applying a control law composed of feedback and feedforward gains.

[0080] In a specific embodiment, the process of executing step 100 may specifically include the following steps:

[0081] The motion state of the XYZ axes of the servo slide module is collected through position sensors and torque sensors to obtain the position deviation sequence, speed deviation sequence and torque feedback sequence of each axis;

[0082] Performing error detection calculation on the lead of each axis screw based on the position deviation sequence to obtain the lead error of each axis screw;

[0083] Extracting features of the guide rail friction characteristics and motor torque fluctuations based on the speed deviation sequence and the torque feedback sequence to obtain friction force variation curves and torque fluctuation amplitude data for each axis;

[0084] The inter-axis coupling coefficient is calculated based on the screw lead error, the friction force variation curve and the torque fluctuation amplitude data to obtain multi-dimensional inter-axis coupling data including XY axis coupling coefficient, XZ axis coupling coefficient and YZ axis coupling coefficient.

[0085] Specifically, high-precision position sensors and torque sensors are installed on each axis of the slide module. The position sensors continuously monitor the actual displacement of each axis, while the torque sensors capture real-time torque feedback data from the servo motor during dynamic motion. Throughout the motion process, the position sensors sample data at a high frequency, generating a continuous sequence of displacement measurements. These actual measurements are compared with the theoretical command trajectory to produce a time-varying sequence of displacement deviations for each axis. Simultaneously, by performing a first-order difference operation on the displacement deviation sequence and combining it with the time sampling interval, a velocity deviation sequence for each axis is calculated, revealing velocity disturbances caused by friction, inertia, structural looseness, and other factors during dynamic motion. The torque sensors synchronously output motor torque feedback signals at each time step, generating a torque feedback sequence. Based on the position deviation sequence, the lead error of each axis is detected and calculated. Lead error primarily arises from subtle geometric deviations during screw machining and assembly. These deviations accumulate over long travels, resulting in periodic or random deviations between actual and theoretical displacements. By fitting and comparing the position deviation sequence with the theoretical displacement trajectory, Fourier analysis and least-squares fitting are used to extract the fundamental frequency components and offset patterns of the lead error. Furthermore, high-order fitting or wavelet decomposition techniques are used to separate the systematic and random error components, generating a screw lead error curve for each axis. Simultaneously, based on the velocity deviation sequence and torque feedback sequence, feature extraction is performed on the guideway friction characteristics and motor torque fluctuations. Guideway friction characteristics manifest as resistance variations that exhibit a nonlinear relationship with speed. Therefore, by jointly analyzing the velocity deviation and torque feedback, regression modeling or piecewise fitting techniques are used to construct friction force curves that reflect the friction resistance characteristics of the slide at different speeds and loads, specifically the viscous characteristics in the static friction range and the speed-dependent characteristics in the dynamic friction range. Furthermore, the torque feedback sequence is analyzed in the frequency domain and subjected to time-domain fluctuation statistics to extract the motor output torque fluctuation amplitude. This amplitude reflects the torque instability caused by factors such as current fluctuations, load disturbances, and mechanical resonance during actual servo motor operation. By modeling the temporal evolution of the fluctuation amplitude, key characteristics of the servo system's dynamic stability are effectively captured. The inter-axis coupling coefficient is calculated based on the screw lead error, friction force variation curve, and torque fluctuation amplitude data. Considering the multi-axis linkage of the slide module structure, there is a mechanical coupling phenomenon between the axes during motion. For example, when the X-axis accelerates, the flexible deformation of the transmission mechanism causes a small displacement response in the Y and Z axes. To quantify this dynamic interaction between the axes, a cross-correlation matrix is ​​constructed based on the time-series correlation of the error curves of each axis, or a multivariate regression analysis is performed to calculate the dynamic response coupling coefficients between the XY, XZ, and YZ axes.Specific operations include using screw lead error data to analyze the synchronization of displacement deviations across different axes, using friction curves to analyze the correlation of velocity disturbances across different axes, and using torque fluctuation amplitude data to analyze the synergy of torque variation trends across different axes. By comprehensively analyzing these data sources, a multidimensional coupling coefficient matrix is ​​established that reflects the dynamic correlation between each axis. The XY-axis coupling coefficient describes the influence of X-axis motion changes on the dynamic response of the Y-axis. The XZ-axis and YZ-axis coupling coefficients are similar. By quantifying these coupling coefficients, a multidimensional inter-axis coupling dataset is constructed.

[0086] In a specific embodiment, the process of executing step 200 may specifically include the following steps:

[0087] Performing spatial position discretization processing on the multi-dimensional inter-axis coupling data to obtain a set of discretized position points of the X, Y, and Z axes;

[0088] Constructing a three-dimensional coupling relationship tensor based on the discretized position point set;

[0089] Performing a three-axis coupling strength numerical calculation on each tensor element in the three-dimensional coupling relationship tensor according to the discretized position point set to obtain a tensor element numerical matrix describing the coupling strength distribution at each spatial position;

[0090] A tensor product operation is performed based on the tensor element numerical matrix and the weight vectors of each axis to obtain a tensor compensation model including a cross-coupling compensation operator.

[0091] Specifically, the multi-dimensional inter-axis coupling data is spatially discretized. The servo slide module has a continuous range of motion in the actual operating space, and the travel ranges of the three axes (X, Y, and Z) vary in physical dimensions. Therefore, a reasonable discretization step size is defined for each axis. The selection of the discretization step size requires a comprehensive consideration of modeling accuracy and computational complexity, ensuring that key details of coupling strength variations are captured while avoiding data expansion caused by an excessively small step size. This approach allows for efficient data processing while maintaining accuracy. According to the set step size, the travel ranges of the X, Y, and Z axes are evenly divided into multiple discrete position points, forming an X-axis position point set, a Y-axis position point set, and a Z-axis position point set, respectively. Each element in each set represents a discrete spatial position along the corresponding axis, thereby constructing a regular and uniform three-dimensional grid system in three-dimensional space. Based on the discretized position point set for the three axes (X, Y, and Z), a three-dimensional coupling relationship tensor is constructed. Each element of the three-dimensional tensor corresponds to a specific position point combination in the discretized spatial grid, and the three dimensions of the tensor correspond to the discrete position coordinates along the X, Y, and Z axes, respectively. Therefore, the elements of a three-dimensional tensor are defined as indices of the coupling strength between the three axes at corresponding spatial locations. These indices quantify the dynamic interactions between the X, Y, and Z axes at specific position combinations, caused by factors such as mechanical structure, friction pair characteristics, lead error, and motor torque fluctuation. During the tensor construction process, the coupling strength corresponding to each discrete location is assigned based on coupling data previously acquired through sensor data acquisition and multi-source feature extraction, resulting in a continuous and measurable coupling strength distribution in the three-dimensional tensor. To improve the physical interpretability of the tensor model, a smooth interpolation method is introduced during the construction process to ensure a certain degree of spatial continuity in the strength distribution between discrete locations and avoid mutations or noise interference caused by discretization. Based on this set of discretized locations, the three-axis coupling strength of each tensor element in the three-dimensional coupling relationship tensor is numerically calculated. The numerical calculation of the coupling strength requires integrating multiple factors such as lead error of the screw, variation in guideway friction, and the amplitude of motor torque fluctuation. Methods such as multivariate regression analysis, local weighted regression, or kernel function estimation are used to establish a nonlinear mapping between coupling strength and spatial position. In actual calculations, based on the sample point data, a fitting function is used to predict the intensity value of each spatial grid point, or the data is completed in space through interpolation methods to form a tensor element numerical matrix covering the entire discretized space. This matrix describes the coupling strength distribution characteristics between the three axes X, Y, and Z of the servo slide module at different spatial positions. Based on the tensor element numerical matrix and the weight vector of each axis, a tensor product operation is performed, and the importance of each axis in the coupling modeling process is adjusted according to the actual application requirements. For example, if the X-axis carries a larger load in a certain application scenario, or the Z-axis has a higher acceleration requirement, then the axis is given a higher weight value in the weight vector to strengthen the influence of the axis on the overall contribution of the coupling model.During the specific calculation process, the product operations of the tensor and the corresponding weight vector are performed in sequence along the X, Y, and Z dimensions to achieve axis-by-axis weighted correction. By weighted summing the tensor elements in each dimension, the spatial coupling intensity distribution is optimized and adjusted, and the sensitivity of key axes to changes in dynamic characteristics is effectively highlighted, improving the physical matching and control targeting of the tensor model. Through the above tensor product operation, a tensor compensation model containing a cross-coupling compensation operator is finally obtained.

[0092] In a specific embodiment, the step of performing a tensor product operation based on the tensor element numerical matrix and the axis weight vector to obtain a tensor compensation model including a cross-coupling compensation operator may specifically include the following steps:

[0093] Based on the XYZ three-axis motion characteristic parameters of the servo slide module, the weight vector of each axis is numerically initialized and calculated to obtain the X-axis weight vector, Y-axis weight vector and Z-axis weight vector;

[0094] Performing element-by-element weighted sum calculation on the tensor element numerical matrix and the X-axis weight vector according to a first-dimensional tensor contraction product operation rule to obtain a first intermediate tensor operation result;

[0095] Based on the first intermediate tensor operation result, a dimension-by-dimension weighted summation calculation is performed on the Y-axis weight vector according to the second-dimensional tensor contraction product operation rule and the Z-axis weight vector according to the third-dimensional tensor contraction product operation rule to obtain a target tensor operation result;

[0096] A tensor compensation model including a cross-coupling compensation operator is constructed according to the target tensor operation result.

[0097] Specifically, the motion characteristic parameters of each axis of the servo slide module are analyzed. In actual operation, different axes of the servo slide module bear different motion functions and load conditions. For example, the X-axis corresponds to large-scale positioning motion, the Y-axis is responsible for precise displacement of medium loads, and the Z-axis is more related to dynamic working conditions such as vertical fine-tuning and load changes. Therefore, the motion inertia, maximum acceleration, speed range, friction characteristics and load variation coefficient of the three axes are different. Based on the dynamic and kinematic parameters, a corresponding weight distribution strategy is constructed for each axis. The size of the weight value reflects the importance of the axis in the overall motion control and the dynamic response requirements. In the specific numerical initialization process, based on indicators such as the moment of inertia, maximum operating speed, acceleration upper limit and friction characteristic change rate of each axis, normalization processing is used to eliminate the dimensions of different physical quantities and obtain the influencing factors under a unified dimension. Through methods such as weighted averaging or principal component analysis, multidimensional characteristic parameters are further integrated to form a comprehensive weight value corresponding to each discrete position. This generates X-axis, Y-axis, and Z-axis weight vectors, respectively. The length of each weight vector corresponds to the number of discrete positions on each axis, and the weight values ​​vary at different positions to reflect the response priority of each axis due to dynamic characteristics or load changes at different spatial locations. The tensor element matrix and the X-axis weight vector are then weighted and summed element by element according to the first-dimensional tensor contraction product operation. The first-dimensional tensor contraction product operation multiplies each element in the tensor along the dimension corresponding to the X-axis by the weight value at the corresponding position in the X-axis weight vector, followed by a weighted summation operation along this dimension. This compresses the information in the X-axis direction of the original three-dimensional tensor to form a new two-dimensional tensor. This two-dimensional tensor is the result of the first intermediate tensor operation and contains the YZ plane coupling strength distribution characteristics, taking into account the weighted influence of the dynamic characteristics of each X-axis position. Based on the result of the first intermediate tensor operation, the second- and third-dimensional tensor contraction products are performed. The first intermediate tensor and the Y-axis weight vector are weighted and summed according to the second-dimensional tensor contraction product operation rule. That is, along the dimension corresponding to the Y-axis, each element of the intermediate tensor is multiplied by the corresponding weight value in the Y-axis weight vector, and the sum is accumulated in this dimension to obtain a one-dimensional tensor with the Z-axis discrete position point as the dimension. The above one-dimensional tensor and the Z-axis weight vector are then weighted and summed according to the third-dimensional tensor contraction product operation rule. That is, along the Z-axis direction, the value of each position point is multiplied by the corresponding Z-axis weight value, and the sum is accumulated to finally obtain a scalar target tensor operation result. Based on the target tensor operation result, a tensor compensation model containing a cross-coupling compensation operator is constructed. This compensation model incorporates the weighted information of the motion characteristics of each axis into the tensor structure, so that the model can dynamically reflect the changing trend of the coupling strength between multiple axes at different spatial positions, and by controlling the setting of weights, the model can flexibly adjust the emphasis of the model's sensitivity to the motion characteristics of different axes.

[0098] In a specific embodiment, the process of executing step 300 may specifically include the following steps:

[0099] Performing a third-order tensor decomposition on the tensor compensation model to obtain CP decomposition initialization data including a decomposition rank parameter R and an initial factor vector group;

[0100] Iteratively calculating and converging the tensor decomposition error based on the CP decomposition initialization data to obtain an optimal decomposition rank value and a corresponding decomposition convergence parameter;

[0101] performing a tensor decomposition operation on the tensor compensation model according to the optimal decomposition rank value and the decomposition convergence parameter to obtain a tensor decomposition result;

[0102] Based on the factor vectors of each axis in the tensor decomposition result, dominant coupling modes are extracted and dimension reduction calculations are performed to obtain dimension-reduced coupling relationship data.

[0103] Specifically, the tensor compensation model undergoes a third-order tensor decomposition, factoring the originally complex three-dimensional coupling intensity distribution via CP decomposition. Initially, a reasonable decomposition rank parameter R is set, and a corresponding set of initial factor vectors is generated. These factor vectors correspond to the components of the tensor in the X, Y, and Z axes. The decomposition rank R represents the number of rank tensors required to represent the original three-dimensional tensor as a weighted sum of several rank tensors. The initial R value is determined based on experience or by estimating the internal data complexity of the tensor. Furthermore, the determination of the initial factor vector set directly impacts the convergence rate and final accuracy of the decomposition algorithm. Therefore, random initialization combined with orthogonalization or initial approximate factor vectors extracted based on high-order singular value decomposition are employed to improve the rationality of the initial point. The tensor decomposition error is iteratively calculated and convergence determined based on the CP decomposition initialization data. During each iteration, the factor vectors for each axis are continuously updated based on the criterion of minimizing the tensor reconstruction error, so that the difference between the tensor reconstructed by the current factor vector set and the original tensor compensation model is gradually reduced. The specific error calculation uses the Frobenius norm to measure the difference between the original tensor and the reconstructed tensor. The smaller the error value, the better the current decomposition approximation effect. During the iterative process, reasonable convergence conditions are set, including the error reduction being less than a preset threshold or reaching the maximum number of iterations. To further determine the optimal decomposition rank value, a cross-validation method is used to evaluate the reconstruction error corresponding to different R values. By plotting the error change curve, the error inflection point is found, that is, the location where the error reduction significantly slows down, as the basis for selecting the optimal decomposition rank R. At the same time, the decomposition convergence parameters corresponding to the optimal decomposition effect are recorded, including the final error value, the number of iterations, and the stability index of the factor vectors on each axis. Tensor decomposition operations are performed on the tensor compensation model based on the optimal decomposition rank value and decomposition convergence parameters. Based on the determined R value and convergence conditions, the ALS (alternating least squares) algorithm or other optimization algorithm is used to iteratively update the factor vector group until the optimal decomposition effect is achieved. By decomposition, the original third-order tensor is disassembled into a weighted sum of R groups of rank tensors. Each group of rank tensors consists of the outer product of an X-axis factor vector, a Y-axis factor vector and a Z-axis factor vector, and is equipped with a decomposition coefficient. Based on the tensor decomposition results obtained by decomposition, the dominant coupling modes of each axis factor vector are extracted and the dimension reduction is calculated. The modulus or contribution of each group of factor vectors is calculated. The modulus reflects the energy intensity or influence of the factor on the corresponding axis. The contribution is further quantified by the product of the factor vector and the decomposition coefficient. All modes are sorted from large to small according to their contribution, and the dominant coupling modes of the top R groups are selected as the core feature subset for subsequent modeling and control design. For modes with low contribution, they are discarded on the premise that the overall reconstruction error does not increase significantly, further compressing the model size and improving computational efficiency.By extracting dominant modes and reducing dimensions, the primary dynamic coupling characteristics of the servo slide module during multi-axis linkage can be retained to the greatest extent possible, effectively reducing the interference of redundant information on subsequent synchronization prediction and control performance. After completing dominant mode screening, the dimensionality-reduced coupling relationship data is reconstructed based on the retained factor vectors and corresponding decomposition coefficients. According to the CP decomposition and reconstruction formula, the R groups of dominant factor vectors are combined by outer product and weighted summation to generate a low-rank approximate tensor. This tensor serves as the new dimensionality-reduced coupling relationship data, depicting the interactive influence relationship between the three axes of X, Y, and Z under the main motion modes.

[0104] In a specific embodiment, the execution step performs dominant coupling mode extraction and dimensionality reduction calculation based on each axis factor vector in the tensor decomposition result to obtain the reduced-dimensional coupling relationship data, which may specifically include the following steps:

[0105] Performing factor vector separation on the tensor decomposition result to obtain three-axis factor vector data including an X-axis factor vector group, a Y-axis factor vector group, and a Z-axis factor vector group;

[0106] Performing a ranking calculation of the importance of dominant modes based on the modulus of each factor vector in the three-axis factor vector data to obtain a ranking result of dominant coupled modes;

[0107] According to the dominant coupling mode sorting result, the top R dominant modes with the largest coupling strengths are selected for dimensional screening to obtain screened factor vector data including R dominant X-axis factor vectors, R dominant Y-axis factor vectors, and R dominant Z-axis factor vectors;

[0108] Based on the filtered factor vector data and the corresponding decomposition coefficients, a dimensionality reduction coupling relationship reconstruction is performed to obtain dimensionality reduction coupling relationship data.

[0109] Specifically, the factor vectors are separated based on the tensor decomposition results. The tensor decomposition results contain several groups of factor vectors and corresponding decomposition coefficients. Each group of factor vectors consists of an X-axis factor vector, a Y-axis factor vector, and a Z-axis factor vector, which correspond to the characteristic components of the three-dimensional tensor in three different dimensions of X, Y, and Z, respectively. During the separation process, all factor vectors are classified according to the axis, and all factor vectors belonging to the X-axis direction are extracted to form an X-axis factor vector group, all factor vectors belonging to the Y-axis direction are extracted to form a Y-axis factor vector group, and all factor vectors belonging to the Z-axis direction are extracted to form a Z-axis factor vector group, thereby obtaining a three-axis factor vector data set containing complete factor vector data in the three directions of X, Y, and Z. Based on the three-axis factor vector data, the dominant mode importance ranking calculation is performed. The specific sorting process takes the modulus of each factor vector as the core indicator. The size of the modulus reflects the energy intensity or characteristic influence of the corresponding factor vector in its axis. By calculating the modulus lengths of each factor vector along the X, Y, and Z axes and combining them with their corresponding decomposition coefficients, a comprehensive importance index is constructed. This index comprehensively considers the modal contribution along the three axes and its weight in the overall tensor reconstruction. The comprehensive evaluation method employed is to combine the sum of the squares of the modulus lengths along each axis with the product of the decomposition coefficients to quantify the overall importance of each mode. By sorting the comprehensive importance indexes of all modes from highest to lowest, a ranking of the dominant coupled modes is obtained. Based on the ranking of the dominant coupled modes, the top R dominant modes with the highest coupling strengths are selected for dimensionality screening based on their contribution. During the specific screening process, the top R modes are selected from the sorted results, and the corresponding X-axis factor vectors, Y-axis factor vectors, and Z-axis factor vectors are extracted to form a filtered factor vector dataset. This dataset contains R dominant X-axis factor vectors, R dominant Y-axis factor vectors, and R dominant Z-axis factor vectors, representing the most representative characteristic components in dimensionality reduction modeling. By retaining this part of the dominant factor vectors, the original coupling characteristic information of the tensor is preserved to the greatest extent possible, and the noise and redundant information brought by the secondary modes are effectively eliminated. This significantly reduces the data dimension while maintaining the model's good approximation of the original data structure and accurate representation of the complex coupling dynamic characteristics. The dimensionality reduction coupling relationship is reconstructed based on the filtered factor vector data and the corresponding decomposition coefficients. Each group of dominant factor vectors is weighted and combined according to the decomposition coefficients. The outer product operation is performed on the X, Y, and Z factor vectors of each dominant mode, and the weighted summation of each outer product result according to the decomposition coefficient is then performed to generate the coupling relationship tensor after dimensionality reduction.

[0110] In a specific embodiment, the process of executing step 400 may specifically include the following steps:

[0111] Inputting the dimension-reduced coupling relationship data as a coupling term for inter-axis influence prediction into a multi-axis synchronous linear prediction model to construct a state vector, thereby obtaining an extended state vector;

[0112] Calculating the inter-axis influence amount based on the extended state vector to obtain an inter-axis influence prediction result;

[0113] Performing feedforward compensation correction on the multi-axis synchronous linear prediction model according to the inter-axis influence prediction result to obtain a corrected prediction model;

[0114] Based on the revised prediction model, the desired trajectory optimization solution and physical constraint condition processing are performed to obtain multi-axis coordinated trajectory planning data.

[0115] Specifically, an extended state vector of the multi-axis synchronous linear prediction model is constructed based on the reduced-dimensional coupling relationship data. Through preliminary tensor decomposition and modal screening, the reduced-dimensional coupling relationship data has extracted low-dimensional feature information that can accurately describe the main dynamic coupling characteristics of the servo slide module's X, Y, and Z axes during multi-axis linkage. Therefore, when constructing the state vector, basic position information and velocity information are comprehensively considered with the characteristic quantities of each mode in the reduced-dimensional coupling relationship data. The basic state vector includes the current position and current velocity of each axis, as well as necessary high-order dynamic variables such as acceleration or vibration amplitude, to comprehensively describe the basic motion state of each axis. At the same time, the reduced-dimensional coupling relationship data is introduced as an additional feature vector dimension into the extended state space, so that the extended state vector not only reflects the independent dynamic changes of a single axis, but also explicitly includes the interactive influence characteristics between the axes due to the coupling effect. The inter-axis influence quantity is calculated based on the extended state vector. By analyzing the coupling components in the extended state vector and combining them with the current motion state, the indirect motion interference caused by the dynamic changes of other axes at the current moment, namely the inter-axis influence, is calculated for each axis using linear regression, cross-correlation analysis, or state transition deduction methods based on the observation matrix. This calculation process combines the independent dynamic information of each axis with the coupling characteristic quantities to dynamically evaluate the mechanical transmission effects and dynamic response correlations between different axes. This allows for a relatively accurate prediction of the motion error propagation trends caused by coupling relationships within a short time window. This inter-axis influence calculation based on the extended state vector allows for a rapid estimation of the potential dynamic interference between axes without relying on extensive historical data. Based on the inter-axis influence prediction results, feedforward compensation is applied to the existing multi-axis synchronization linear prediction model. Traditional multi-axis synchronization prediction models assume that each axis' motion is independent, ignoring the complex mechanical coupling and dynamic interference between multiple axes during actual operation. This can easily lead to synchronization error accumulation under high-speed and variable operating conditions. Therefore, during the correction process, the predicted inter-axle influence is introduced as a feedforward compensation term into the state transition equation of the prediction model. By adjusting the system matrix and the control input matrix, the revised prediction model can not only predict the future state of each axis based on its current state, but also estimate and actively compensate for possible future linkage disturbances based on the predicted inter-axle interference. Specifically, the coupling term feedback matrix is ​​introduced into the state equation to adjust the dynamic response characteristics of the system, so that the control system can dynamically correct for possible future inter-axle interference during the prediction phase, thereby improving the accuracy and stability of trajectory tracking. Based on the revised prediction model, the desired trajectory optimization solution and physical constraint condition processing are carried out.The goal of desired trajectory optimization is to generate an optimal path that minimizes trajectory tracking error and control energy consumption. A weighted least-squares cost function or a linear quadratic optimization objective function is used. During the optimization process, not only is the minimum deviation between the trajectory and the target path considered, but also the smoothness requirements of acceleration, velocity, and displacement are comprehensively considered to ensure that the generated trajectory meets the servo system's execution capabilities in terms of continuity and controllability. Furthermore, a series of physical constraints are introduced during the optimization process, including maximum velocity constraints, maximum acceleration constraints, travel limit constraints, and smoothness constraints to prevent large sudden changes from causing system instability. By constructing an inequality constraint matrix, these physical constraints are directly embedded in the optimization solution framework. Alternatively, a soft constraint plus penalty function is used to dynamically penalize violations of physical limits in the optimization objective, ensuring the feasibility and safety of the optimization results in actual execution. Based on the modified multi-axis synchronous linear prediction model and the physical constraints, the optimization problem is solved to ultimately obtain multi-axis coordinated trajectory planning data. This planning data includes the expected position trajectory of each axis throughout the entire motion cycle, and is further refined to the velocity and acceleration changes at each time step. This ensures that the slide module maintains high synchronization and a smooth trajectory during multi-axis linkage motion, avoiding mechanical vibration and trajectory deviation caused by lag or excessively rapid changes in single-axis control. Furthermore, by introducing dimensionality-reduced coupling relationship data and a feedforward compensation correction mechanism, trajectory planning can effectively offset synchronization errors caused by the system's coupling characteristics, improving the trajectory tracking performance and synchronous control accuracy of the servo slide module under high-dynamic conditions.

[0116] In a specific embodiment, the step of inputting the dimension-reduced coupling relationship data as a coupling term for inter-axis influence prediction into a multi-axis synchronous linear prediction model to construct a state vector, and the process of obtaining an extended state vector may specifically include the following steps:

[0117] Based on the current motion state of the XYZ axes of the servo slide module, the basic state vector is assembled to obtain a six-dimensional basic state vector containing the position component and velocity component of each axis;

[0118] Calculating the coupling influence of the reduced-dimensional coupling relationship data according to the decomposition coefficient and factor vector of the dominant coupling mode to obtain a coupling term numerical sequence;

[0119] According to the coupling term numerical sequence, a state equation is constructed and a system matrix is ​​filled in for the multi-axis synchronous linear prediction model to obtain a linear state equation group;

[0120] Based on the linear state equation group, the six-dimensional basic state vector and the coupling term numerical sequence are vector-concatenated and dimensionally expanded to obtain an extended state vector.

[0121] Specifically, a basic state vector is assembled based on the current motion state of the servo slide module's X, Y, and Z axes. High-precision position sensors acquire the current position data for the X, Y, and Z axes. The velocity components of the X, Y, and Z axes are obtained by time-differentiating the position signals or directly sampling the velocity signals output by the encoders. To ensure the consistency and usability of subsequent state modeling, the collected displacement and velocity signals are filtered to eliminate noise interference and high-frequency jitter, ensuring the smoothness and continuity of the state data. During the data sorting process, the displacement and velocity components of the X, Y, and Z axes are arranged in sequence to form a six-dimensional basic state vector, where the first three elements represent the displacements of the X, Y, and Z axes, and the last three elements represent the corresponding velocity information. Using coupling relationship data, the coupling influence is calculated based on the decomposition coefficients of the dominant coupling mode and the factor vectors for each axis. For each dominant mode, the X-axis factor vector, Y-axis factor vector, and Z-axis factor vector are mapped to the current displacement state based on the magnitude of the decomposition coefficient. Interpolation or basis function mapping is used to determine the response value of each factor vector in the current motion state. These response values ​​are then weighted and accumulated with the corresponding decomposition coefficients to obtain the coupling influence of each mode in the current motion state. By traversing all dominant modes and summing the coupling influences of each mode, a numerical sequence of coupling terms is obtained. This numerical sequence reflects the combined effects of the dynamic coupling influences between the X, Y, and Z axes at the current moment, caused by mechanical structural characteristics, friction nonlinearity, torque perturbations, and other factors. Based on the numerical sequence of coupling terms, the state equations of the multi-axis synchronous linear prediction model are constructed and the system matrix is ​​populated. Traditional linear state prediction models only consider the dynamic changes of each axis and ignore the mutual influences between multiple axes. This can easily lead to synchronization error accumulation and trajectory deviation expansion during high-speed and high-acceleration motion. Therefore, when constructing the state equations, the system matrix is ​​expanded and modified based on the original system state transfer matrix and combined with the numerical sequence of coupling terms. The coupling influence coefficients are introduced into the state transfer matrix to dynamically correlate the dynamic changes of each axis with the coupling perturbations of other axes. This ensures that the system matrix not only reflects the independent motion characteristics of a single axis but also explicitly reflects the interactions between multiple axes. At the same time, appropriately adding feedforward compensation paths related to the coupling terms to the control input matrix allows future control inputs to proactively sense and offset any dynamic coupling disturbances, thereby improving the overall system's dynamic stability and trajectory tracking accuracy. By filling and expanding the system matrix, the resulting linear state equations accurately describe the complex dynamic behavior of the servo slide module during multi-axis linkage, enhancing the predictive model's expressive power and control effectiveness. Based on the linear state equations, the previously assembled six-dimensional basic state vector and the numerical sequence of the coupling terms are vector-concatenated and dimensionally expanded to generate an extended state vector.The six-dimensional basic state vector and the coupling term numerical sequence are spliced ​​in the column direction to form a new high-dimensional vector. The first six elements of the vector are still the displacement and velocity information of each axis, while the newly added elements are the dynamic influence of the coupling between the axes at the current moment.

[0122] In a specific embodiment, the process of executing step 500 may specifically include the following steps:

[0123] The multi-axis coordinated trajectory planning data is subjected to tensor lifting linear reformulation processing by the Koopman operator to obtain a nonlinear observation vector including a base state, a quadratic term, and a trigonometric function term;

[0124] Constructing a linear state equation and a Koopman matrix in the lifting space based on the nonlinear observation vector to obtain a lifted state model;

[0125] Optimizing and solving the feedback control gain matrix and the feedforward control gain matrix according to the improved state model to obtain optimal control gain parameters;

[0126] Based on the optimal control gain parameters, an augmented control law is calculated for the control variables of each axis to generate an optimal control instruction sequence.

[0127] Specifically, a nonlinear observation vector is constructed based on the multi-axis coordinated trajectory planning data of the servo slide module. The trajectory planning data contains displacement, velocity, and acceleration information for each axis. This basic state information can reflect the initial dynamic characteristics of the system, but it is difficult to directly reveal complex nonlinear behavior. Therefore, using the Koopman operator, the nonlinear state data originally located in a low-dimensional space is mapped to a high-dimensional observation space, making the system appear approximately linear in this high-dimensional space. In the specific operation, the original displacement and velocity state variables are used as basic observation quantities. Subsequently, higher-order nonlinear observation quantities are constructed based on these basic quantities, including quadratic terms of each state variable, such as position squared, velocity squared, and the cross term between position and velocity. By introducing these quadratic nonlinear terms, the fundamental nonlinear coupling relationships existing in the system can be captured. Furthermore, periodic nonlinear terms based on sine and cosine functions are introduced. These trigonometric terms effectively capture the nonlinear oscillation characteristics of the servo slide module during actual operation caused by factors such as mechanical flexibility and periodic disturbances. By integrating the basic state, quadratic terms, and trigonometric terms, a nonlinear observation vector containing multidimensional and complex characteristics is formed. Based on the nonlinear observation vector, a linear state equation is constructed in the lifting space, and the Koopman matrix is ​​determined. By analyzing the changing trends of the nonlinear observation vector in a continuous time series, numerical methods such as least squares fitting, regression analysis, or dynamic mode decomposition are used to fit the linear transition relationship of the observation vector as time progresses. This is done by describing the mapping relationship between the current observation state and the next observation state through matrix operations. Each element of the Koopman matrix reflects the strength of the linear coupling between different nonlinear observation features. This matrix essentially transforms the originally complex nonlinear system dynamics into a linear state transition system that is approximately linear in the lifting space, thereby simplifying the mathematical complexity of subsequent controller design. The constructed linear state equation maintains an accurate description of the original nonlinear dynamics and enables efficient control law solution based on linear system control theory. Based on the lifted state model, the feedback control gain matrix and the feedforward control gain matrix are optimized to obtain the optimal control gain parameters. The feedback control gain matrix dynamically adjusts the control input based on the current system state to achieve timely suppression of trajectory deviations and disturbances, while the feedforward control gain matrix applies preemptive compensation control based on the expected trend of the target trajectory, improving the system's response speed and tracking accuracy. The specific solution process utilizes a linear quadratic regulator design method, with the goal of optimizing system performance indicators. A cost function with state deviation and control energy terms is constructed. While ensuring system stability, the optimal feedback gain matrix is ​​determined by solving the Riccati equation. Simultaneously, the feedforward gain matrix is ​​solved using pseudo-inverse operations or optimization objective decoupling analysis, enabling the system to evolve along the desired trajectory in the absence of external disturbances, further improving trajectory tracking accuracy and stability.By optimizing the feedback and feedforward gain matrices, the system maintains good control performance under different dynamic conditions. Even in the presence of model uncertainty, external disturbances, or structural flexibility, the slide module can still achieve high-precision, high-response motion control. The augmented control law is calculated for the control quantity of each axis based on the optimal control gain parameters. The augmented control law combines the advantages of feedback control and feedforward compensation. Specifically, in each control cycle, the feedback gain matrix is ​​applied to perform error correction control based on the currently observed nonlinear observation vector, and the pre-compensation control quantity is applied through the feedforward gain matrix based on the desired trajectory state. Through the joint control mechanism, the position and speed of each axis of the servo slide module are controlled, and the error accumulation caused by the dynamic coupling between axes is actively eliminated, thereby generating the optimal control instruction sequence.

[0128] The above describes the control method of the servo slide module for multi-directional operation in the embodiment of the present invention. The following describes the control device of the servo slide module for multi-directional operation in the embodiment of the present invention. Figure 2 In one embodiment of the present invention, a multi-directional servo slide module control device includes:

[0129] The acquisition module 11 is used to collect the motion state of the X, Y, and Z axes of the servo slide module to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuation;

[0130] A construction module 12 is used to construct a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data;

[0131] A dimensionality reduction module 13 is configured to perform CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality-reduced coupling relationship data;

[0132] A prediction module 14 is configured to perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data;

[0133] The calculation module 15 is used to calculate the nonlinear control law based on the multi-axis coordinated trajectory planning data to obtain the optimal control instruction sequence.

[0134] Through the collaborative efforts of the various components mentioned above, a multi-dimensional inter-axis coupling data model that includes screw lead error, guide rail friction characteristics, and motor torque fluctuations is constructed. This overcomes the problem in existing technologies where independent control of each axis cannot handle inter-axis dynamic coupling, and achieves comprehensive capture and accurate modeling of the complex coupling relationship of the slide module. The cross-coupling compensation operator is reconstructed in tensor format, and efficient dimensionality reduction of high-dimensional coupling relationships is achieved through CP decomposition technology, providing an effective solution for the rapid processing of large-scale real-time trajectory data. The coupling intensity distribution model established based on the third-order tensor structure can accurately describe the three-axis coupling characteristics at each spatial position. Compared with traditional linear compensation methods, it effectively captures the nonlinear coupling change law of the slide module during multi-directional motion. By using the reduced-dimensional coupling relationship data as the coupling term for inter-axis influence prediction, a multi-axis synchronous linear prediction model that includes coupling influence is constructed, overcoming the coupling interference problem caused by independent prediction of each axis in existing technologies and achieving feedforward compensation for inter-axis interactions. The Koopman operator theory is used to perform tensor lifting linear reformulation, transforming complex nonlinear control problems into optimization solutions in linear space. While maintaining an accurate description of the nonlinear characteristics of the original system, it avoids the computational complexity of traditional nonlinear control methods. The control system design adopts a hierarchical tensor structure. Through the coordinated cooperation of the task planning layer, tensor compensation layer, and servo execution layer, it significantly reduces the real-time computing burden of the system compared to the centralized control architecture and improves the control response speed under multi-directional high-speed motion conditions. Through the extraction of dominant coupling modes and dimensionality reduction calculations, redundant information and noise components in the original coupling data are effectively removed, improving the robustness of the control system to environmental interference and parameter changes, and ensuring stable control performance under different working conditions.

[0135] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0136] If the integrated unit is implemented in the form of 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, 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. The computer software product is stored in a storage medium and includes several instructions for enabling an electronic device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, and other media that can store program code.

[0137] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling a multi-directional servo slide module, characterized in that: include: The motion state of the X, Y, and Z axes of the servo slide module is collected to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuations; Constructing a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data; Performing CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality-reduced coupling relationship data; Perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data; A nonlinear control law is calculated based on the multi-axis coordinated trajectory planning data to obtain an optimal control instruction sequence.

2. The multi-directional servo slide module control method according to claim 1, characterized in that: The motion state of the XYZ three axes of the servo slide module is collected to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics and motor torque fluctuation, including: The motion state of the XYZ axes of the servo slide module is collected through position sensors and torque sensors to obtain the position deviation sequence, speed deviation sequence and torque feedback sequence of each axis; Performing error detection calculation on the lead of each axis screw based on the position deviation sequence to obtain the lead error of each axis screw; Extracting features of the guide rail friction characteristics and motor torque fluctuations based on the speed deviation sequence and the torque feedback sequence to obtain friction force variation curves and torque fluctuation amplitude data for each axis; The inter-axis coupling coefficient is calculated based on the screw lead error, the friction force variation curve and the torque fluctuation amplitude data to obtain multi-dimensional inter-axis coupling data including XY axis coupling coefficient, XZ axis coupling coefficient and YZ axis coupling coefficient.

3. The multi-directional servo slide module control method according to claim 1, characterized in that: The tensor compensation model describing the XYZ three-axis coupling intensity distribution is constructed based on the multi-dimensional inter-axis coupling data, comprising: Performing spatial position discretization processing on the multi-dimensional inter-axis coupling data to obtain a set of discretized position points of the X, Y, and Z axes; Constructing a three-dimensional coupling relationship tensor based on the discretized position point set; Performing a three-axis coupling strength numerical calculation on each tensor element in the three-dimensional coupling relationship tensor according to the discretized position point set to obtain a tensor element numerical matrix describing the coupling strength distribution at each spatial position; A tensor product operation is performed based on the tensor element numerical matrix and the weight vectors of each axis to obtain a tensor compensation model including a cross-coupling compensation operator.

4. The multi-directional servo slide module control method according to claim 3, characterized in that: The tensor product operation is performed based on the tensor element numerical matrix and the weight vectors of each axis to obtain a tensor compensation model including a cross-coupling compensation operator, including: Based on the XYZ three-axis motion characteristic parameters of the servo slide module, the weight vector of each axis is numerically initialized and calculated to obtain the X-axis weight vector, Y-axis weight vector and Z-axis weight vector; Performing element-by-element weighted sum calculation on the tensor element numerical matrix and the X-axis weight vector according to a first-dimensional tensor contraction product operation rule to obtain a first intermediate tensor operation result; Based on the first intermediate tensor operation result, a dimension-by-dimension weighted summation calculation is performed on the Y-axis weight vector according to the second-dimensional tensor contraction product operation rule and the Z-axis weight vector according to the third-dimensional tensor contraction product operation rule to obtain a target tensor operation result; A tensor compensation model including a cross-coupling compensation operator is constructed according to the target tensor operation result.

5. The multi-directional servo slide module control method according to claim 1, characterized in that: The CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality-reduced coupling relationship data includes: Performing a third-order tensor decomposition on the tensor compensation model to obtain CP decomposition initialization data including a decomposition rank parameter R and an initial factor vector group; Iteratively calculating and converging the tensor decomposition error based on the CP decomposition initialization data to obtain an optimal decomposition rank value and a corresponding decomposition convergence parameter; Performing a tensor decomposition operation on the tensor compensation model according to the optimal decomposition rank value and the decomposition convergence parameter to obtain a tensor decomposition result; Based on the factor vectors of each axis in the tensor decomposition result, dominant coupling modes are extracted and dimension reduction calculations are performed to obtain dimension-reduced coupling relationship data.

6. The multi-directional servo slide module control method according to claim 5, characterized in that: The extracting of dominant coupling modes and dimensionality reduction calculation based on each axis factor vector in the tensor decomposition result to obtain dimension-reduced coupling relationship data includes: Performing factor vector separation on the tensor decomposition result to obtain three-axis factor vector data including an X-axis factor vector group, a Y-axis factor vector group, and a Z-axis factor vector group; Performing a ranking calculation of the importance of dominant modes based on the modulus of each factor vector in the three-axis factor vector data to obtain a ranking result of dominant coupled modes; According to the dominant coupling mode sorting result, the top R dominant modes with the largest coupling strengths are selected for dimensional screening to obtain screened factor vector data including R dominant X-axis factor vectors, R dominant Y-axis factor vectors, and R dominant Z-axis factor vectors; Based on the filtered factor vector data and the corresponding decomposition coefficients, a dimensionality reduction coupling relationship reconstruction is performed to obtain dimensionality reduction coupling relationship data.

7. The multi-directional servo slide module control method according to claim 1, characterized in that: The performing of multi-axis synchronous linear prediction according to the dimension reduction coupling relationship data to obtain multi-axis coordinated trajectory planning data includes: Inputting the dimension-reduced coupling relationship data as a coupling term for inter-axis influence prediction into a multi-axis synchronous linear prediction model to construct a state vector, thereby obtaining an extended state vector; Calculating the inter-axis influence amount based on the extended state vector to obtain an inter-axis influence prediction result; Performing feedforward compensation correction on the multi-axis synchronous linear prediction model according to the inter-axis influence prediction result to obtain a corrected prediction model; Based on the revised prediction model, the desired trajectory optimization solution and physical constraint condition processing are performed to obtain multi-axis coordinated trajectory planning data.

8. The multi-directional servo slide module control method according to claim 7, characterized in that: The reduced-dimensional coupling relationship data is input into a multi-axis synchronous linear prediction model as a coupling term for inter-axis influence prediction to construct a state vector, thereby obtaining an extended state vector, including: Based on the current motion state of the XYZ axes of the servo slide module, the basic state vector is assembled to obtain a six-dimensional basic state vector containing the position component and velocity component of each axis; Calculating the coupling influence of the reduced-dimensional coupling relationship data according to the decomposition coefficient and factor vector of the dominant coupling mode to obtain a coupling term numerical sequence; According to the coupling term numerical sequence, the state equation of the multi-axis synchronous linear prediction model is constructed and the system matrix is ​​filled to obtain a linear state equation group; Based on the linear state equation group, the six-dimensional basic state vector and the coupling term numerical sequence are vector-concatenated and dimensionally expanded to obtain an extended state vector.

9. The multi-directional servo slide module control method according to claim 1, characterized in that: The nonlinear control law calculation based on the multi-axis coordinated trajectory planning data to obtain the optimal control instruction sequence includes: The multi-axis coordinated trajectory planning data is subjected to tensor lifting linear reformulation processing by the Koopman operator to obtain a nonlinear observation vector including a base state, a quadratic term, and a trigonometric function term; Constructing a linear state equation and a Koopman matrix in the lifting space based on the nonlinear observation vector to obtain a lifted state model; Optimizing and solving the feedback control gain matrix and the feedforward control gain matrix according to the improved state model to obtain optimal control gain parameters; Based on the optimal control gain parameters, an augmented control law is calculated for the control variables of each axis to generate an optimal control instruction sequence.

10. A multi-directional servo slide module control device, characterized in that: A method for controlling a servo slide module for multi-directional operation according to any one of claims 1 to 9, wherein the servo slide module control device for multi-directional operation comprises: The acquisition module is used to collect the motion status of the X, Y, and Z axes of the servo slide module to obtain multi-dimensional inter-axis coupling data including screw lead error, guide rail friction characteristics, and motor torque fluctuation; A construction module, configured to construct a tensor compensation model describing the XYZ three-axis coupling strength distribution based on the multi-dimensional inter-axis coupling data; A dimensionality reduction module, configured to perform CP decomposition and dimensionality reduction based on the tensor compensation model to obtain dimensionality reduction coupling relationship data; A prediction module, configured to perform multi-axis synchronous linear prediction based on the dimension-reduced coupling relationship data to obtain multi-axis coordinated trajectory planning data; The calculation module is used to calculate the nonlinear control law based on the multi-axis coordinated trajectory planning data to obtain the optimal control instruction sequence.

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