Aluminum lithium alloy tube multi-point servo adaptive correction method and system

Abstract

The application provides an aluminum-lithium alloy workpiece multi-point servo adaptive correction method and system, which comprises the following steps: collecting actual and target three-dimensional profile data of the workpiece to obtain an error vector, constructing a far-field influence matrix through a single-point pressure test, and obtaining a singular value matrix, a left singular vector matrix and a right singular vector matrix through singular value decomposition; building a modal domain parallel PI controller, which is both set as a diagonal matrix, and completing parameter configuration relying on the singular value reciprocal relationship, the global error state and the modal energy dissipation rate respectively; projecting the profile error to the modal space to solve the modal control quantity; monitoring the change rate of the Gaussian curvature of the correction surface in real time, shielding the high-order spatial frequency modal component and locking the integral operation when the change rate exceeds the standard, restoring the high-order modal output in a ramp mode and limiting the integral item after the curvature change recovers to safety, and mapping the correction modal control quantity to a servo command through the right singular vector matrix; and removing the high-order modal restriction after the curvature recovers to normal, and completing the workpiece profile correction control.

Description

Technical Field

[0001] This application belongs to the field of aluminum-lithium alloys, and particularly relates to a multi-point servo adaptive correction method and system for thin aluminum-lithium alloy parts. Background Technology

[0002] Aluminum-lithium alloys, characterized by low density, high specific stiffness, high strength, and good fatigue resistance, have been widely used in aerospace and high-end equipment manufacturing, playing a crucial role, especially in thin-walled structural components such as aircraft skins and shell panels. However, these aluminum-lithium alloy thin parts are susceptible to flexural deformation during forming, heat treatment, and assembly due to the combined effects of residual stress release, material anisotropy, and external loads, causing their three-dimensional morphology to deviate from design requirements. To meet the high geometric accuracy manufacturing requirements of thin-walled structural components, morphological correction is typically performed in the later stages of manufacturing. Multi-point servo correction technology, through multiple spatially distributed servo actuators, applies coordinated displacement to the workpiece surface, driving the thin-walled curved surface to gradually approach the target shape. This is a crucial technique for achieving high-precision morphological control of large-sized curved thin-walled components. This process requires reliable contact between each actuator and the workpiece, and the output of corresponding normal displacements based on morphological deviations; therefore, a stable and efficient collaborative control system is essential.

[0003] Due to the continuous medium characteristics of thin-walled curved surfaces, there is a significant spatial coupling effect between correction points. A servo action at a certain location not only alters the local displacement but also triggers a chain reaction in the surrounding area and even the overall morphology. Ordinary independent point-to-point control strategies struggle to effectively handle this global interaction. Furthermore, the stiffness response of aluminum-lithium alloy thin parts varies considerably under different spatial deformation modes. The control system, in approximating the target morphology, struggles to simultaneously consider both global response speed and local accuracy convergence. Conventional fixed control parameters also cannot adapt to real-time changes in error states during the correction process. More importantly, during multi-point coordinated forced deformation, local morphological distortions easily occur on the curved surface. Without monitoring and constraint of higher-order spatial deformation trends, sudden increases in local curvature may occur, causing latent damage to the material surface and continuously accumulating invalid errors in integral calculations, further leading to correction command oscillations or even system divergence. Therefore, a correction method for aluminum-lithium alloy thin parts that can decouple multi-point interference, dynamically adjust control parameters, and suppress sudden changes in local morphology is urgently needed. Summary of the Invention

[0004] According to one aspect of the present invention, a multi-point servo adaptive correction method for thin aluminum-lithium alloy parts is proposed for decoupling multi-point interference, adjusting control parameters, and controlling local morphological abrupt changes, comprising the following steps: Acquire the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculate the normal topographic error of the correction point and form an error vector, apply normal step displacement to the servo actuator of a single correction point in sequence, measure the normal displacement following value of all correction points, splice column vectors to form a far-field influence matrix, and perform singular value decomposition to obtain the singular value matrix, left singular vector matrix and right singular vector matrix. A parallel PI controller is set up in the modal space. The proportional gain is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of the overall topographic error. The integral gain is a diagonal matrix, and the diagonal elements are bounded according to the energy dissipation rate of the corresponding mode in the integral period. The error vector is projected onto the modal space through the left singular vector matrix to generate the modal error vector. The modal control output is generated by calculating the modal error vector using the proportional gain and integral gain. The Gaussian curvature change rate of the surface reconstructed from the correction point is monitored in real time. When the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen. The processed modal control output is mapped to the actuator space through the right singular vector matrix to generate servo commands. After the Gaussian curvature change rate falls back to within the threshold, the component output is restored according to the preset recovery rule. The integral accumulation value held during the freezing period is subjected to amplitude limiting or reset processing before the integral accumulation control is restored.

[0005] According to another aspect of the present invention, a multi-point servo adaptive correction system for thin aluminum-lithium alloy parts is proposed, comprising the following modules: The calculation module is used to acquire the current and target three-dimensional topography data of the aluminum-lithium alloy thin part, calculate the normal topography error of the correction point and form an error vector, apply normal step displacement to the servo actuator of a single correction point in sequence, measure the normal displacement following value of all correction points, splice column vectors to form a far-field influence matrix, and perform singular value decomposition to obtain the singular value matrix, left singular vector matrix and right singular vector matrix. The generation module is used to set the parallel PI controller in the modal space. The proportional gain is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of the overall topographic error. The integral gain is a diagonal matrix, and the diagonal elements are bounded according to the energy dissipation rate of the corresponding mode in the integral period. The error vector is projected onto the modal space through the left singular vector matrix to generate the modal error vector. The modal control output is generated by calculating the modal error vector using the proportional gain and integral gain. The output module is used to monitor the Gaussian curvature change rate of the surface reconstructed from the correction points in real time. When the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen. The processed modal control output is mapped to the actuator space through the right singular vector matrix to generate servo commands. After the Gaussian curvature change rate falls back to within the threshold, the component output is restored according to the preset recovery rule. The integral accumulation value held during the freezing period is subjected to amplitude limiting or reset processing before the integral accumulation control is restored.

[0006] This invention addresses the spatial fusion and deformation abruptness problems in the multi-point servo correction process of thin aluminum-lithium alloy parts. It constructs and decomposes the far-field influence matrix to represent the interference effect between multiple actuators. Decoupling is achieved by projecting spatial topography errors onto modal space. The proportional gain is flexibly adjusted based on the strength of the compliance response reflected by singular values ​​and the global error state. The integral gain is also scheduled according to the energy dissipation rate within the same mode, improving the convergence speed and stability of multi-point collaborative control and reducing correction oscillations caused by multi-axis interference. Simultaneously, the rate of change of signed Gaussian curvature is used as a forming safety indicator. When local deformation is severe, the output of higher-order modes determined by spatial oscillation degree is promptly cut off and the integral is frozen. This reduces the occurrence of problems such as local buckling, wrinkling, and excessive deformation, and lowers the risk of secondary oscillations caused by abrupt changes in control quantities during higher-order mode recovery. This ensures both high-precision correction and the safety and forming quality of the thin part structure. Attached Figure Description

[0007] Figure 1 A flowchart of the first embodiment; Figure 2 This is a diagram showing the current topographic error vector distribution. Figure 3 This is a distribution diagram of modal energy evolution and tracking. Detailed Implementation

[0008] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0009] In the first embodiment, the present invention proposes a multi-point servo adaptive correction method for thin aluminum-lithium alloy parts, such as... Figure 1 It includes the following steps: S1. Acquire the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculate the normal topographic error of the correction point and form an error vector, apply normal step displacement to the single correction point servo actuator in sequence, measure the normal displacement following value of all correction points, splice the column vectors to form the far-field influence matrix, and perform singular value decomposition to obtain the singular value matrix, left singular vector matrix and right singular vector matrix.

[0010] The current 3D point cloud data of the aluminum-lithium alloy thin part is acquired, and the iterative nearest-point algorithm is used to register and align the current 3D point cloud data with the target 3D topography data generated by the computer-aided design model. The coordinates of N preset correction points are extracted, and an N×1 error vector is generated by calculating the coordinate difference of each correction point in the normal direction. Pulse width modulation signals are sequentially sent to the 1st to Nth servo actuators to drive the ball screws to apply a preset small-amplitude normal calibration displacement within the elastic linear response range of the aluminum-lithium alloy thin part, for example, 0.05 mm to 1.00 mm. During this process, the actual normal displacement tracking values ​​of all N correction points are synchronously collected through a laser displacement sensor network to obtain an N×1 column vector. This column vector is then divided by the actual applied amplitude of the preset small-amplitude normal calibration displacement to form a dimensionless response coefficient column vector. The above single-point excitation process is repeated N times, and the obtained N column vectors are concatenated column by column to construct a far-field influence matrix of dimension N×N. The far-field influence matrix is ​​used to represent the compliance response relationship between the unit input normal displacement and the follow-up displacement of all correction points. The matrix itself is not required to be symmetric. The far-field influence matrix is ​​factored using a singular value decomposition function to extract the singular value matrix composed of non-negative singular values, the left singular vector matrix representing the shape response mode, and the right singular vector matrix representing the servo command mode.

[0011] In an optional embodiment, the step of acquiring the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculating the correction point normal topographic error, and forming an error vector includes: During the calibration process, a 3D laser scanner is used to scan the surface of the aluminum-lithium alloy thin part in real time to obtain measured point cloud data. The measured point cloud data is then registered with the set target 3D CAD model through spatial coordinate transformation. The spatial coordinates of each calibration point marked on the target 3D CAD model are extracted as the target 3D topography data. Neighborhood search or interpolation is performed along the theoretical normal direction corresponding to the spatial coordinates of each correction point to obtain the measured point cloud coordinates corresponding to the theoretical normal direction as the current three-dimensional topography data. The normal height value of the current three-dimensional topography data is subtracted from the normal height value of the target three-dimensional topography data to obtain the specific difference value of the current topography error. The specific difference value is arranged in the order of the points to construct an error vector.

[0012] A 3D laser scanner with a spatial resolution of 0.02 mm and a scanning frequency of 50 Hz was used to continuously scan the surface of a thin aluminum-lithium alloy part in a free or constrained state from multiple angles above a multi-point servo forming device, acquiring complete measured point cloud data. The measured point cloud data, after bilateral filtering and noise reduction, was then globally translated and rotated with the imported STEP format target 3D CAD model using an iterative nearest-neighbor algorithm. This achieved spatial registration of the two sets of data in the same machine coordinate system, with the root mean square error of registration controlled within 0.05 mm. The preset discrete correction point array in the target CAD model, such as the 3D coordinates of the top positions of 64 grid-distributed servo actuators, was analyzed and set as the target 3D topographic data. Virtual intersection rays were emitted along the theoretical normal direction of each target correction point on the model surface. The Kd-tree nearest neighbor search algorithm was used to interpolate and extract the intersection point coordinates in the registered point cloud, and these coordinates were used as the current 3D topographic data. By subtracting the height of the target coordinate along the normal direction from the current coordinate at each calibration point location, a scalar difference in the current topographic error is obtained. Its effective measurement accuracy is determined by both the scanning resolution and the root mean square error of the registration. This difference is then filled sequentially from top to bottom according to the bus communication address order of the underlying servo motors, constructing a 64×1 column vector error vector. The normal topographic error distribution corresponding to each calibration node is shown below. Figure 2 As shown.

[0013] In an optional embodiment, the step of sequentially applying normal step displacement to a single correction point servo actuator, measuring the normal displacement following values ​​of all correction points, concatenating column vectors to form a far-field influence matrix, and performing singular value decomposition to obtain a singular value matrix, a left singular vector matrix, and a right singular vector matrix includes: A preset small normal calibration displacement within the elastic linear response range of the aluminum-lithium alloy thin part is applied to the single calibration point servo actuator in sequence, and the normal displacement following value of all calibration points is measured and recorded simultaneously using a displacement sensor. The total response displacement value corresponding to the applied displacement at each calibration point is divided by the amplitude of the preset small normal calibration displacement to construct a one-dimensional column vector. A real square matrix matching the total number of correction points is constructed by concatenating all column vectors, and this matrix is ​​set as the far-field influence matrix. The singular value decomposition algorithm is applied to decompose the far-field influence matrix into the product of the left singular vector matrix, the singular value matrix, and the transpose of the right singular vector matrix. The diagonal matrix formed by arranging the non-negative singular values ​​in descending order on the diagonal is extracted as the singular value matrix. At the same time, the left and right singular vector matrices obtained by orthogonal decomposition are extracted. The left singular vector matrix is ​​used to represent the shape response mode, and the right singular vector matrix is ​​used to represent the servo command mode.

[0014] To measure the global spatial fusion effect of the multi-point array actuator on the aluminum-lithium alloy thin part, during the initialization phase, each independent servo motor is driven sequentially, causing the corresponding single correction point servo actuator to output a preset small normal calibration displacement within the elastic linear response range, for example, 0.05 mm to 1.00 mm. During this time, other non-active points maintain their original support state. After a steady-state delay of 100 milliseconds following the occurrence of this single excitation, high-resolution wire-type displacement sensors arranged at the bottom of each node synchronously collect the passive normal displacement following response values ​​of all correction points on the thin part. For each excitation point, the response values ​​of all nodes triggered by that point are arranged vertically as a single-dimensional column vector. After completing the excitation test of all nodes, all the obtained column vectors are sequentially spliced ​​horizontally according to the excitation order to construct a real square matrix of the same order as the total number of correction points, for example, a 64×64 array, which is the far-field influence matrix of the system deformation interaction. Since this matrix originates from the measured displacement response and is affected by contact friction, structural boundaries, and geometric nonlinearity, it can be a general asymmetric square matrix; therefore, projection and inverse transformation of a single eigenvector matrix are not used. For this size of real-valued matrix, the singular value decomposition (SVD) algorithm from the linear algebra library is used to perform matrix decomposition, yielding a left singular vector matrix U, a singular value matrix Σ, and a right singular vector matrix V. The non-negative singular values ​​are arranged in descending order along the main diagonal. These singular values ​​represent the strength of the morphological response induced by a unit servo input in the corresponding mode. A larger singular value indicates that the mode is more easily excited, but this is not directly equivalent to the structural stiffness coefficient.

[0015] S2, sets the parallel PI controller for the modal space, and the proportional gain. It is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of all topographic errors, with integral gain. The matrix is ​​a diagonal matrix. The diagonal elements are bounded according to the energy dissipation rate of the corresponding mode during the integration period. The error vector is projected onto the mode space through the left singular vector matrix to generate the mode error vector. The proportional gain is then used. With integral gain The modal error vector is calculated to generate the modal control output.

[0016] Initialize the modal-space parallel proportional-integral controller and calculate the L2 norm of the topography error vector as the global norm. Proportional gain. The diagonal element is set as the base proportional gain multiplied by the reciprocal of the sum of the corresponding singular value and the preset regularization constant, and then multiplied by an exponential adjustment factor composed of the dimensionless ratio of the global norm. This allows the more compliant mode with a stronger response to obtain a smaller base proportional gain, and increases the overall correction speed when the global error is large, while reducing the command amplitude to suppress chattering when the error is small. Integral gain The scheduling is based on calculating the dissipation rate based on the energy flow difference within the same mode; the faster the rate, the larger the value of the corresponding diagonal element. Spatial decoupling is achieved by left-multiplying the spatial error vector by the transpose of the left singular vector matrix to obtain the modal error vector. In the controller, the modal error vector is then multiplied by the diagonal matrix... and The calculation is performed, and the proportional term result is added to the discrete integral term result multiplied by the control cycle duration. Then, the modal control output is generated after directional correction in the negative feedback direction that makes the modal error vector approach zero.

[0017] In an optional embodiment, the proportional gain It is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of all topographic errors, including: The arithmetic square root is calculated by summing the squares of all scalar elements in the error vector to obtain the global norm value of the current control cycle. Each singular value recorded on the diagonal of the singular value matrix is ​​added to a preset regularization constant and the reciprocal is taken. The reciprocal value is then multiplied by a set fixed stiffness reduction constant to obtain the basic proportional term. Take a set fixed basis constant, divide the global norm value by the set reference length to obtain the dimensionless ratio, use the dimensionless ratio as the exponent of the fixed basis constant, and calculate the adjustment factor. The base proportional term is multiplied by the adjustment factor to generate an adjustment number. This adjustment number is then truncated according to a preset upper and lower limit of proportional gain. The truncated adjustment number is placed on the diagonal of a newly established matrix in the order of its corresponding modes to generate the proportional gain for the current control cycle. .

[0018] To address the variable stiffness issue caused by large deformations during multi-point correction, the proportional gain of the controller is tuned. L2 norm calculation is performed on the real-time topography error vector, which involves summing the squared errors of all nodes and taking the square root to obtain a global norm value representing the overall deviation across the entire field. The diagonal elements of the previously calculated singular value matrix are extracted, added to a preset regularization constant, and the reciprocal is taken. This reciprocal is then multiplied term by term by a fixed stiffness reduction constant calibrated in experiments (e.g., set to 0.10) to calculate the basic proportional gain value for each mode. This setting avoids applying excessively large proportional gains to easily excited modes with high compliance responses, thereby reducing the risk of overshoot and oscillation. To ensure rapid convergence of the system when initial errors are large and to suppress chattering when final errors are small, the natural constant *e* is selected as the basis constant. The global norm value calculated in the current cycle is divided by a set engineering reference length, for example, 0.50 mm, to match the springback scale of the aluminum-lithium alloy. The resulting dimensionless ratio is used as the exponential term of the basis constant *e*, and an exponentially increasing adjustment factor is calculated. The basis proportional term for each mode is multiplied by this real-time updated adjustment factor to obtain the adjustment value. This adjustment value is then saturated and truncated according to preset upper and lower limits. The adjustment value is then reconstructed into a diagonal matrix according to the original modal order, generating a dedicated and decoupled proportional gain diagonal matrix for this iteration cycle. This enables variable speed servo compensation.

[0019] In an optional embodiment, the integral gain This is a diagonal matrix, and the diagonal elements are boundedly scheduled according to the energy dissipation rate of the corresponding mode during the integration period, including: Within a set five-millisecond single control cycle, the modal servo reaction force component of each mode is multiplied by the modal servo command displacement increment component before and after control to obtain the external work input value of the corresponding mode. Project the workpiece side support reaction force vector at each correction point and the actual normal following displacement increment vector at the corresponding correction point onto the same modal space, and multiply the reaction force component of the corresponding mode with the actual normal following displacement increment component to calculate the elastic strain energy value of the corresponding mode within the control cycle. The candidate dissipated energy is obtained by subtracting the value of the elastic strain energy added to the corresponding mode from the value of the external work input of the corresponding mode. When the candidate dissipated energy is greater than zero, the candidate dissipated energy is taken as the positive dissipated energy. When the candidate dissipated energy is less than or equal to zero, it is taken as zero or processed according to the preset filtering rules. The positive dissipated energy is divided by the duration of five milliseconds to obtain the real-time energy dissipation scalar rate. The dimensionless dissipation ratio is obtained by dividing the aforementioned real-time energy dissipation scalar rate by the set reference power. A basic integral amplification factor with a time reciprocal dimension is set. The basic integral amplification factor is multiplied by the aforementioned dimensionless dissipation ratio, and amplitude limiting is performed according to the set lower and upper thresholds with time reciprocal dimensions to obtain updated parameters. These updated parameters are then placed in the corresponding diagonal positions of the diagonal matrix to construct the integral gain that generates the aforementioned period. .

[0020] The integral term is scheduled by monitoring the energy flow direction based on modal dissipation characteristics. Within a set 5-millisecond single hard real-time cycle, the servo equivalent reaction force component along the corresponding modal axis is extracted. This component is multiplied by the scalar of the modal servo command displacement increment for the current cycle to calculate the external work input value of the servo mechanism in the corresponding degree of freedom. Simultaneously, the servo triaxial force sensor data of each node and the actual normal following displacement increment of the corresponding node are projected into the modal space through the left singular vector matrix or their corresponding modal transformation relationship to obtain the reaction force component and displacement increment component in the same mode. The two components in the corresponding mode are then multiplied to solve for the increase in elastic strain energy in the current cycle. The external work in the same mode is subtracted from the increase in elastic strain energy in the same mode to obtain the candidate dissipation energy. Only when the candidate dissipation energy is positive is it taken as the irreversible residual dissipation generated by plastic flow or friction in that mode. When the candidate dissipation energy is non-positive, it is taken as zero or processed according to the preset filtering rules. By dividing the positive dissipation energy by a time span of 0.005 seconds, the real-time energy dissipation scalar rate with physical meaning in the corresponding mode can be derived. Dividing this scalar rate by a calibration-set reference power scale, such as 1.0 watt, converts the result into a dimensionless dissipation ratio. A preset time reciprocal constant, such as 30 cycles / second, is selected as the basic integration amplification factor and multiplied by this dimensionless ratio. Then, limiting processing is performed according to preset lower and upper limits of the integration gain to obtain the integration gain parameters for the current step. These updated parameters are then diagonally assembled to generate the diagonal matrix of the integration gain for that period. ,like Figure 3 As shown.

[0021] In an optional embodiment, the step of projecting the error vector onto the modal space via a left singular vector matrix to generate a modal error vector utilizes a scaling gain. With integral gain The modal error vector is calculated to generate the modal control output, including: Find the transpose operation matrix array of the left singular vector matrix, and multiply the error vector by the left side of the transpose operation matrix array to generate the modal error vector in the modal space. Then, calculate the proportional gain of the current iteration step. Multiplying the modal error vector of the current iteration step by left yields the proportional action feedback matrix. Extract the historical mode error vector obtained from each control cycle between the start time and the current iteration step, and perform an accumulation operation by multiplying the corresponding single control cycle duration among the elements of the same order to obtain an integral cumulative error column matrix with the dimensions of length and time product; Integral gain Multiply the cumulative error column matrix by left to obtain the integral action feedback matrix. Perform the corresponding element summation operation to add the proportional action feedback matrix to the integral action feedback matrix. Then, invert the negative feedback direction that makes the modal error vector approach zero or apply a direction sign correction to generate the modal control output corresponding to all system degrees of freedom.

[0022] To decouple multi-point topographic deviations within the mathematical domain, the left singular vector matrix is ​​called and transposed to obtain an orthogonal transformation matrix for response space projection. This transposed matrix is ​​then multiplied by the original spatial error vector, and the coordinate system is transferred from the geometric node positions to the independent principal space response modes through spatial mapping, generating a modal error vector representing the modal order deviation. The proportional gain diagonal matrix tuned in this iteration step is then used. Multiply the modal error vector by the left to calculate the transient proportional action feedback matrix, which is sensitive to real-time errors. During the long-term deformation accumulation phase, a dedicated buffer queue continuously records all discrete modal error column vectors from time zero to the current iteration step. Using the discrete-domain Euler forward numerical integration method, the scalar elements at the same position in each column vector are multiplied by the corresponding control cycle duration and then accumulated to form an integral cumulative error column matrix with the dimensions of the product of length and time. Then, the integral gain diagonal matrix of the current cycle is used... Multiply the cumulative column matrix on the left to extract the integral action feedback matrix after removing the steady-state static margin. Add and merge the proportional feedback vector and integral feedback vector of the same order mode term by term to generate the complete modal control output, which serves as the control input for the next stage to drive the independent deformation modes to approach zero deviation.

[0023] S3 monitors the Gaussian curvature change rate of the surface reconstructed from the correction point in real time. When the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen. The processed modal control output is mapped to the actuator space through the right singular vector matrix to generate servo commands. After the Gaussian curvature change rate falls back to within the threshold, the component output is restored according to the preset recovery rule. The integral accumulation value held during the freezing period is subjected to amplitude limiting or reset processing before the integral accumulation control is restored.

[0024] The OpenNURBS modeling library is invoked to perform surface fitting or interpolation reconstruction based on real-time 3D point cloud data and the current 3D coordinates of all calibration points, generating a smooth topographic surface for curvature calculation. The signed Gaussian curvature of each discrete grid point on the surface is calculated using a differential geometry algorithm. The difference between the signed Gaussian curvature of the current control cycle and the previous control cycle is calculated using the finite difference method and divided by the sampling time to obtain the Gaussian curvature change rate. A conditional statement is used to compare the absolute value of the Gaussian curvature change rate of each region with a preset curvature change safety threshold in real time. Once an exceedance is detected, high-frequency mode suppression is triggered. Based on the pre-established calibration point adjacency topology, the second-order difference energy or the mean square value of the adjacent difference between each modal vector and adjacent calibration points is calculated as the spatial oscillation degree. Combined with the candidate mode range located in the last 50% of all modes after descending sorting of singular values, the array index of the higher-order spatial frequency modes is determined. The value corresponding to the above higher-order mode index in the modal control output vector is rewritten to 0. A Boolean flag is set to stop accumulating the current error to prevent integral saturation. The matrix-vector multiplication function is invoked again, and the modal control output is multiplied by the right singular vector matrix. This is then mapped from the modal space to the actuator space to generate displacement commands for each servo actuator. The servo interpolation cycle is 1 millisecond, the PI control update cycle is 5 milliseconds, and the update cycle for the 3D topography data and the Gaussian curvature change rate is 20 milliseconds. Between two adjacent topography measurements, the controller uses the most recent topography measurement result or the state prediction result to participate in the PI control calculation. In subsequent loops, the Gaussian curvature change rate is continuously evaluated. When the value is smoothed by a first-order low-pass filter and remains within the curvature change safety threshold for three consecutive cycles, the Boolean flag is cleared. The control components of the higher-order spatial frequency modes are gradually restored according to the preset ramp coefficient. The integral accumulation value held during the freeze period is limited or reset before the corresponding integrator accumulation operation is restored. The curvature change safety threshold is determined by the plate thickness of the aluminum-lithium alloy thin part, the allowable surface strain, the principal curvature change limit, and offline bending calibration tests.

[0025] In an optional embodiment, the real-time monitoring of the Gaussian curvature change rate of the surface reconstructed from the correction points, wherein when the absolute value of the Gaussian curvature change rate in any region exceeds a threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen, includes: The topography surface is reconstructed using real-time 3D topography data from each correction point. The maximum and minimum principal curvatures of the central region of each tiny triangular mesh on the topography surface are collected along two mutually orthogonal principal directions at 20-millisecond intervals. The signed Gaussian curvature value is obtained by multiplying the two principal curvatures. The slope of the change of the signed Gaussian curvature value between two consecutive time points is solved by subtraction difference operation to obtain the Gaussian curvature change rate. The absolute value of the Gaussian curvature change rate is detected and confirmed to have exceeded the set safety judgment limit value. The candidate mode number in the last 50% of the total number of modes after being sorted in descending order of singular values ​​at the current time is calculated. The higher-order spatial frequency mode is confirmed by combining the spatial oscillation degree of each candidate mode on the adjacent topology of the correction point.

[0026] To address the tendency of thin-walled aluminum-lithium alloy parts to experience localized wrinkling, an online intervention based on differential geometry was implemented. An industrial control computer captures the 3D height data of servo correction points in real time and uses a triangular meshing algorithm to instantaneously reconstruct the fitted spatial morphology of the entire alloy skin. Sampling is triggered with a cycle of four times the basic control beat (20 milliseconds) to calculate the maximum and minimum principal curvatures along two mutually orthogonal principal directions in the neighborhood of each micro-grid center. These two values ​​are then multiplied to output a signed Gaussian curvature value K. A first-order backward difference subtraction is performed using the values ​​from two consecutive samples, divided by a time difference of 0.02 seconds, to extract the Gaussian curvature change rate, representing the curvature deterioration trend. The absolute value of this Gaussian curvature change rate is then compared with a safety threshold. When the absolute value of the Gaussian curvature change rate in any monitored grid region exceeds the safety threshold of 0.003 mm / s², a protection strategy is activated. A pre-established mapping table of modal orders and spatial oscillations is read. This spatial oscillation is determined based on the differential amplitude, second-order differential energy, or number of sign changes of the corresponding modal vector between adjacent correction points, and is used to characterize the short-wavelength local fluctuations of the mode. In the 64-node model, after offline calibration, the 33rd to 64th orders, arranged in descending order of singular values, are confirmed to belong to the candidate range of high spatial oscillations. Therefore, modes that meet the spatial oscillation threshold are characterized as high-order spatial frequency modes. A truncation operation is then performed on the data bus, overwriting the data in the row corresponding to the high-order mode index in the modal control output matrix with the number 0, thus cutting off the high-frequency micro-motion excitation. The discrete integral operators for these high-order modes are frozen in the accumulator register group, stopping the algebraic superposition of the operator and saving it as the recorded value of the previous safe period, avoiding local material instability or yielding caused by stress accumulation.

[0027] In an optional embodiment, the step of mapping the processed modal control output to the actuator space via a right singular vector matrix to generate servo commands, restoring the component output according to a preset recovery rule after the Gaussian curvature change rate falls back to within a threshold, and performing amplitude limiting or reset processing on the integral accumulation value held during the freeze period before restoring the integral accumulation control includes: The modal control output after left multiplication of the right singular vector matrix and zeroing operation is converted to obtain a set of digital combinations of the expected coordinate displacement changes of the nodes used to control each servo support mechanism. Each individual parameter in the set is extracted, dispatched through the communication bus, and converted into the specific step size of the field servo motor feed actuator. This triggers the execution of a constant-rate feed command sequence. The Gaussian curvature change rate is checked according to the interruption cycle. When the Gaussian curvature change rate, after being smoothed by a first-order low-pass filter, falls back to a limit state of less than or equal to 0.003 mm / s for three consecutive detection cycles, the corresponding stop action holding flag is cleared. The component output of the higher-order spatial frequency mode is gradually restored according to the preset ramp coefficient. The integral accumulation value held during the freeze period is limited or reset before the integral accumulation control is restored.

[0028] To remap the high-frequency filtered and state-safe modal control quantities into actual actions, a coordinate space mapping operation is performed. Using the extracted right singular vector matrix as the basis for the actuator space transformation, and multiplying it by the column matrix that has undergone local truncation and zeroing, the inner product result is transformed into a set of numerical combinations of desired coordinate displacement changes for controlling all array nodes within the geometric space. Each individual scalar instruction in this combination is traversed and parsed, and converted into a specific number of microstep pulses matching the ball screw lead resolution. This instructs each actuator motor on-site to coordinately perform a constant-rate interpolation displacement feed with a 1-millisecond cycle. During this process, the controller backend maintains high-priority interrupt monitoring at the millisecond level through a hardware timer, continuously and cyclically checking the Gaussian curvature change rate of the global surface. Only when the Gaussian curvature change rate, after being smoothed by a first-order low-pass filter, is less than or equal to the safe threshold of 0.003 mm / s² for three consecutive detection cycles is the stop action holding flag written to memory due to previous intervention cleared and reset. The above actions restore the full-band computing link of the system, remove the signal shielding of the high-order characteristic channel and gradually restore the output of the control component according to the preset ramp coefficient. The integrator performs amplitude limiting or reset processing on the integral value held during the freeze period and then reconnects the new difference at the current moment and adds it to the closed-loop control logic to ensure that the correction shaping operation achieves a continuous and flexible process.

[0029] The above description represents the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A multi-point servo adaptive correction method for thin aluminum-lithium alloy parts, characterized in that, include: Acquire the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculate the normal topographic error of the correction point and form an error vector, apply normal step displacement to the servo actuator of a single correction point in sequence, measure the normal displacement following value of all correction points, splice column vectors to form a far-field influence matrix, and perform singular value decomposition to obtain the singular value matrix, left singular vector matrix and right singular vector matrix. A parallel PI controller is set up in the modal space. The proportional gain is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of the overall topographic error. The integral gain is a diagonal matrix, and the diagonal elements are bounded according to the energy dissipation rate of the corresponding mode in the integral period. The error vector is projected onto the modal space through the left singular vector matrix to generate the modal error vector. The modal control output is generated by calculating the modal error vector using the proportional gain and integral gain. The Gaussian curvature change rate of the surface reconstructed from the correction point is monitored in real time. When the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen. The processed modal control output is mapped to the actuator space through the right singular vector matrix to generate servo commands. After the Gaussian curvature change rate falls back to within the threshold, the component output is restored according to the preset recovery rule. The integral accumulation value held during the freezing period is subjected to amplitude limiting or reset processing before the integral accumulation control is restored.

2. The method according to claim 1, characterized in that, The process of acquiring the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculating the normal topographic error of the correction point, and forming an error vector includes: During the calibration process, a 3D laser scanner is used to scan the surface of the aluminum-lithium alloy thin part in real time to obtain measured point cloud data. The measured point cloud data is then registered with the set target 3D CAD model through spatial coordinate transformation. The spatial coordinates of each calibration point marked on the target 3D CAD model are extracted as the target 3D topography data. Neighborhood search or interpolation is performed along the theoretical normal direction corresponding to the spatial coordinates of each correction point to obtain the measured point cloud coordinates corresponding to the theoretical normal direction as the current three-dimensional topography data. The normal height value of the current three-dimensional topography data is subtracted from the normal height value of the target three-dimensional topography data to obtain the specific difference value of the current topography error. The specific difference value is arranged in the order of the points to construct an error vector.

3. The method according to claim 1, characterized in that, The process involves sequentially applying normal step displacements to the single-point servo actuator, measuring the normal displacement following values ​​of all calibration points, concatenating column vectors to form a far-field influence matrix, and performing singular value decomposition to obtain a singular value matrix, a left singular vector matrix, and a right singular vector matrix, including: A preset small normal calibration displacement within the elastic linear response range of the aluminum-lithium alloy thin part is applied to the single calibration point servo actuator in sequence, and the normal displacement following value of all calibration points is measured and recorded simultaneously using a displacement sensor. The total response displacement value corresponding to the applied displacement at each calibration point is divided by the amplitude of the preset small normal calibration displacement to construct a one-dimensional column vector. A real square matrix matching the total number of correction points is constructed by concatenating all column vectors, and this matrix is ​​set as the far-field influence matrix. The singular value decomposition algorithm is applied to decompose the far-field influence matrix into the product of the left singular vector matrix, the singular value matrix, and the transpose of the right singular vector matrix. The diagonal matrix formed by arranging the non-negative singular values ​​in descending order on the diagonal is extracted as the singular value matrix. At the same time, the left and right singular vector matrices obtained by orthogonal decomposition are extracted. The left singular vector matrix is ​​used to represent the shape response mode, and the right singular vector matrix is ​​used to represent the servo command mode.

4. The method according to claim 1, characterized in that, The scaling gain is a diagonal matrix, and its diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and based on the global norm of all topographic errors, including: The arithmetic square root is calculated by summing the squares of all scalar elements in the error vector to obtain the global norm value of the current control cycle. Each singular value recorded on the diagonal of the singular value matrix is ​​added to a preset regularization constant and the reciprocal is taken. The reciprocal value is then multiplied by a set fixed stiffness reduction constant to obtain the basic proportional term. Take a set fixed basis constant, divide the global norm value by the set reference length to obtain the dimensionless ratio, use the dimensionless ratio as the exponent of the fixed basis constant, and calculate the adjustment factor. The basic proportional term number is multiplied by the adjustment factor to generate the adjustment number, and the adjustment number is saturated and truncated according to the preset upper limit and lower limit of the proportional gain. The truncated adjustment number is placed in the diagonal position of the newly established matrix according to the corresponding modal order to generate the proportional gain of the current control cycle.

5. The method according to claim 1, characterized in that, The integral gain is a diagonal matrix, and the diagonal elements are boundedly scheduled according to the energy dissipation rate of the corresponding mode during the integration period, including: Within a set five-millisecond single control cycle, the modal servo reaction force component of each mode is multiplied by the modal servo command displacement increment component before and after control to obtain the external work input value of the corresponding mode. Project the workpiece side support reaction force vector at each correction point and the actual normal following displacement increment vector at the corresponding correction point onto the same modal space, and multiply the reaction force component of the corresponding mode with the actual normal following displacement increment component to calculate the elastic strain energy value of the corresponding mode within the control cycle. The candidate dissipated energy is obtained by subtracting the value of the elastic strain energy added to the corresponding mode from the value of the external work input of the corresponding mode. When the candidate dissipated energy is greater than zero, the candidate dissipated energy is taken as the positive dissipated energy. When the candidate dissipated energy is less than or equal to zero, it is taken as zero or processed according to the preset filtering rules. The positive dissipated energy is divided by the duration of five milliseconds to obtain the real-time energy dissipation scalar rate. The dimensionless dissipation ratio is obtained by dividing the aforementioned real-time energy dissipation scalar rate by the set reference power. A basic integral amplification factor with a time reciprocal dimension is set. The basic integral amplification factor is multiplied by the aforementioned dimensionless dissipation ratio, and amplitude limiting is performed according to the set lower and upper thresholds with time reciprocal dimensions to obtain updated parameters. These updated parameters are then placed in the corresponding diagonal positions of the diagonal matrix to construct the integral gain that generates the aforementioned period. .

6. The method according to claim 1, characterized in that, The step of projecting the error vector onto the modal space via a left singular vector matrix to generate a modal error vector, and then using proportional gain and integral gain to calculate the modal control output quantity from the modal error vector, includes: Find the transpose operation matrix array of the left singular vector matrix, multiply the error vector by the transpose operation matrix array to generate the modal error vector in the modal space, and multiply the proportional gain of the current iteration step by the modal error vector of the current iteration step to obtain the proportional action feedback matrix. Extract the historical mode error vector obtained from each control cycle between the start time and the current iteration step, and perform an accumulation operation by multiplying the corresponding single control cycle duration among the elements of the same order to obtain an integral cumulative error column matrix with the dimensions of length and time product; Multiply the integral gain by the integral cumulative error column matrix to obtain the integral action feedback matrix. Perform the corresponding element summation operation to add the proportional action feedback matrix to the integral action feedback matrix. Then, invert the negative feedback direction that makes the modal error vector approach zero or apply a direction sign correction to generate the modal control output corresponding to all system degrees of freedom.

7. The method according to claim 1, characterized in that, The real-time monitoring of the Gaussian curvature change rate of the surface reconstructed from the correction points, when the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, sets the higher-order spatial frequency modal components in the modal control output to zero and freezes their integral accumulation, including: The topography surface is reconstructed using real-time 3D topography data from each correction point. The maximum and minimum principal curvatures of the central region of each tiny triangular mesh on the topography surface are collected along two mutually orthogonal principal directions at 20-millisecond intervals. The two principal curvatures are multiplied to obtain the signed Gaussian curvature value. The slope of the change of the signed Gaussian curvature value between two consecutive moments is calculated by subtraction difference operation to obtain the Gaussian curvature change rate. The absolute value of the Gaussian curvature change rate is detected and confirmed to have exceeded the set safety judgment limit value. The candidate mode number in the last 50% of the total number of modes after being sorted in descending order of singular values ​​at the current moment is calculated. The higher-order spatial frequency mode is confirmed by combining the spatial oscillation degree of each candidate mode on the adjacent topology of the correction point. A zeroing operation is performed on the coordinate components corresponding to the modal control output quantity determined by the above-mentioned higher spatial frequency mode sequence number, so that the algebraic superposition of the integral accumulation operation corresponding to the above-mentioned higher spatial frequency mode is stopped, and the accumulated value is kept in the saved record state of the previous period.

8. The method according to claim 1, characterized in that, The process of mapping the processed modal control output to the actuator space via a right singular vector matrix to generate servo commands, restoring the component output according to a preset recovery rule after the Gaussian curvature rate of change falls back to within a threshold, and performing amplitude limiting or reset processing on the integral accumulation value held during the freeze period before restoring integral accumulation control includes: The modal control output after left multiplication of the right singular vector matrix and zeroing operation is converted to obtain a set of digital combinations of the expected coordinate displacement changes of the nodes used to control each servo support mechanism. Each individual parameter in the set is extracted, dispatched through the communication bus, and converted into the specific step size of the field servo motor feed actuator. This triggers the execution of a constant-rate feed command sequence. The Gaussian curvature change rate is checked according to the interruption cycle. When the Gaussian curvature change rate, after being smoothed by a first-order low-pass filter, falls back to a limit state of less than or equal to 0.003 mm / s for three consecutive detection cycles, the corresponding stop action holding flag is cleared. The component output of the higher-order spatial frequency mode is gradually restored according to the preset ramp coefficient. The integral accumulation value held during the freeze period is limited or reset before the integral accumulation control is restored.

9. A multi-point servo adaptive correction system for thin aluminum-lithium alloy parts, characterized in that, include: The calculation module is used to acquire the current and target three-dimensional topography data of the aluminum-lithium alloy thin part, calculate the normal topography error of the correction point and form an error vector, apply normal step displacement to the servo actuator of a single correction point in sequence, measure the normal displacement following value of all correction points, splice column vectors to form a far-field influence matrix, and perform singular value decomposition to obtain the singular value matrix, left singular vector matrix and right singular vector matrix. The generation module is used to set the parallel PI controller in the modal space. The proportional gain is a diagonal matrix, and the diagonal elements are adjusted according to the reciprocal relationship of the corresponding singular values ​​in the singular value matrix and the global norm of the overall topographic error. The integral gain is a diagonal matrix, and the diagonal elements are bounded according to the energy dissipation rate of the corresponding mode in the integral period. The error vector is projected onto the modal space through the left singular vector matrix to generate the modal error vector. The modal control output is generated by calculating the modal error vector using the proportional gain and integral gain. The output module is used to monitor the Gaussian curvature change rate of the surface reconstructed from the correction points in real time. When the absolute value of the Gaussian curvature change rate in any region exceeds the threshold, the higher-order spatial frequency modal components in the modal control output are set to zero and their integral accumulation is frozen. The processed modal control output is mapped to the actuator space through the right singular vector matrix to generate servo commands. After the Gaussian curvature change rate falls back to within the threshold, the component output is restored according to the preset recovery rule. The integral accumulation value held during the freezing period is subjected to amplitude limiting or reset processing before the integral accumulation control is restored.

10. The system according to claim 9, characterized in that, The process of acquiring the current and target three-dimensional topographic data of the aluminum-lithium alloy thin part, calculating the normal topographic error of the correction point, and forming an error vector includes: During the calibration process, a 3D laser scanner is used to scan the surface of the aluminum-lithium alloy thin part in real time to obtain measured point cloud data. The measured point cloud data is then registered with the set target 3D CAD model through spatial coordinate transformation. The spatial coordinates of each calibration point marked on the target 3D CAD model are extracted as the target 3D topography data. Neighborhood search or interpolation is performed along the theoretical normal direction corresponding to the spatial coordinates of each correction point to obtain the measured point cloud coordinates corresponding to the theoretical normal direction as the current three-dimensional topography data. The normal height value of the current three-dimensional topography data is subtracted from the normal height value of the target three-dimensional topography data to obtain the specific difference value of the current topography error. The specific difference value is arranged in the order of the points to construct an error vector.

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