Multi-axis cooperative control method, system and device based on digital-analog linkage

Abstract

The invention belongs to the technical field of networked multi-axis motion control, and discloses a multi-axis cooperative control method, system and device based on digital-analog linkage, and the method comprises the steps: outputting a tracking error prediction value corresponding to a reference trajectory through an offline single-axis tracking error prediction model, and compensating the tracking error prediction value to the reference trajectory to obtain a new reference trajectory; the feedback controller generates a control signal according to the new single-axis reference trajectory and the actual trajectory, and the disturbance observer estimates external disturbance in real time based on the control signal and the actual trajectory and outputs a disturbance estimation result; according to the reference trajectory and the actual trajectory, estimating a contour error by using a Newton iteration method, inputting the contour error into a generalized cross coupling controller, and calculating to obtain a contour error compensation amount for each single axis; and combining the single-axis control signal, the disturbance estimation result and the contour error compensation amount to serve as control input of the mechanism model, and obtaining an actual track output by the mechanism model. According to the invention, high-precision contour tracking control of networked multi-axis equipment is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked multi-axis motion control, and specifically relates to a multi-axis collaborative control method, system and device based on digital-analog linkage. Background Art

[0002] As the core equipment of high-end manufacturing and intelligent manufacturing, the control technology of multi-axis linkage equipment plays a decisive role in system performance and efficiency. In recent years, the industry has put forward higher requirements for the accuracy and intelligence level of multi-axis linkage control. As one of the core tasks of multi-axis motion control, contour tracking control has traditional control methods including single-axis-based model predictive control, PID control and zero-phase error control, as well as multi-axis-based cross-coupling control, master-slave synchronization control and virtual spindle control. Traditional control methods usually rely on accurate physical models to design controllers, but in actual industrial environments with high speed, high precision and strong real-time performance, in the face of complex working conditions and unmodeled system dynamics, the model is often inconsistent with the actual system, resulting in large tracking errors.

[0003] In recent years, intelligent controllers based on data-driven and machine learning have gradually become a research hotspot due to their excellent universal approximation capabilities. These data-driven controllers can handle complex nonlinear systems that are difficult to deal with by traditional model-based control methods, and perform modeling, prediction, and control; especially in strongly coupled multi-axis motion control, by offline training of historical dynamic data, the dynamic characteristics of the system can be accurately modeled, and by pre-adjusting the reference trajectory, the tracking accuracy of a single axis can be significantly improved. However, the offline training method is completely dependent on historical data, has a poor response to the real-time uncertain dynamic changes of the system, and cannot be adjusted online, which limits its applicability in industrial applications. Summary of the invention

[0004] In view of the shortcomings of traditional control methods in dealing with complex dynamic characteristics and the limitations of data-driven learning methods in real-time online adjustment, the present invention proposes a multi-axis collaborative control method, system and device based on digital-analog linkage, aiming to solve the tracking accuracy problem of multi-axis equipment. This method has significant advantages in improving the contour tracking performance of multi-axis motion control systems.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] In the first aspect, the present invention provides a multi-axis collaborative control method based on digital-analog linkage. In a data-driven manner, the historical operation data of the multi-axis equipment is modeled, and a machine learning method is used to establish a mapping relationship between input and output data, so as to obtain a prediction model for the single-axis tracking error through offline training. The prediction model can accurately predict the tracking error of the new trajectory, and through offline adjustment of the input reference trajectory, effectively suppress the influence of the unmodeled dynamic characteristics on the control system, thereby improving the single-axis tracking accuracy; a disturbance suppression tracking controller based on a mechanism model is designed, combining classical feedback control and disturbance observer. The controller uses the mechanism model information of the control object to design an efficient disturbance observer, which can quickly estimate and compensate for external disturbances and significantly improve the robustness of the system; in view of the complexity of the reference trajectory, the Newton iteration method is used to estimate the contour error in real time, and the shortest distance between the actual position and the reference position is calculated to obtain the contour error value. Subsequently, the generalized cross-coupling controller is used to calculate the contour error compensation amount of each axis, and the control input is compensated to further improve the overall control effect of the contour, thereby forming an online real-time contour error estimation and compensation controller. Through the comprehensive control of the above three parts, the present invention effectively reduces the influence of the system's unmodeled dynamics and external disturbances on the control accuracy, and improves the overall control performance of the multi-axis equipment.

[0007] The present invention provides a multi-axis collaborative control method based on digital-analog linkage, comprising:

[0008] A data-driven offline single-axis tracking error prediction model is constructed, and the tracking error prediction value corresponding to the reference trajectory is outputted using the offline single-axis tracking error prediction model. The tracking error prediction value is then compensated to the reference trajectory to obtain a new reference trajectory for each axis.

[0009] A disturbance suppression tracking controller based on a mechanism model is constructed, wherein the disturbance suppression tracking controller includes a feedback controller and a disturbance observer, wherein the feedback controller generates a control signal according to a new reference trajectory of a single axis and an actual trajectory output by the mechanism model, and the disturbance observer estimates the external disturbance in real time based on the control signal and the actual trajectory, and outputs a disturbance estimation result;

[0010] An online real-time contour error estimation and compensation controller is constructed. The online real-time contour error estimation and compensation controller estimates the contour error by using the Newton iteration method according to the reference trajectory and the actual trajectory of each axis, and inputs the contour error into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis;

[0011] The control signal of the single axis, the disturbance estimation result and the contour error compensation amount are combined as the control input of the mechanism model to obtain the actual trajectory output by the mechanism model. Preferably, the construction of the data-driven offline single axis tracking error prediction model includes:

[0012] The tracking error is defined as ,in for The reference trajectory of the axis, for The actual trajectory of the axis, is the axis index;

[0013] An acquisition data set is divided into a training set and a validation set, wherein the data set is historical operation data of a multi-axis device;

[0014] The training set is input into the machine learning algorithm to establish the mapping relationship between the reference trajectory and the tracking error, and the machine learning model with the best prediction effect on the validation set is selected and saved as the offline single-axis tracking error prediction model.

[0015] Preferably, the feedback controller adopts a PID controller, which is expressed as:

[0016]

[0017] In the formula, for The control signal output by the axis PID controller, for The tracking error of the axis with respect to the new reference trajectory, for The first-order differential of for The scale factor of the axis, for The differential coefficient of the axis, for The integration coefficient of the axis;

[0018]

[0019] In the formula, represents the output of the offline single-axis tracking error prediction model The tracking error prediction of the axis.

[0020] Preferably, the estimating the contour error by using the Newton iteration method comprises:

[0021] Denote the reference trajectory as time The function is as follows:

[0022]

[0023] In the formula, express The reference position at the moment, express The X-axis coordinate of the reference position at the moment, express The Y-axis coordinate of the reference position at the moment;

[0024] Will The actual position at a moment is expressed as:

[0025]

[0026] In the formula, express The actual location at the moment, express The X-axis coordinate of the actual position at the moment, express The Y-axis coordinate of the actual position at the moment;

[0027] The error vector is defined as:

[0028]

[0029] In the formula, Indicates from the actual location arrive Reference position at time vector of;

[0030] The contour error Defined as:

[0031]

[0032] Indicated in Moment profile error Get the minimum value, where express The reference position at the moment, i.e. the contour error point, represents the L2 norm;

[0033] The cost function is constructed as follows:

[0034]

[0035] In the formula, is the cost function, represents the Euclidean norm;

[0036] The Newton iteration method is used to calculate the minimum value of the cost function, and we get The contour error corresponding to the moment and contour error points , as the estimated contour error and contour error point.

[0037] Preferably, the contour error is input into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis, including:

[0038] Output contour error points through Newton iteration method And contour error ,Pick Reference position at time , Actual location at the moment , according to the reference position and actual location Determine the axial tracking error corresponding to the X-axis Axial tracking error corresponding to the Y axis ;

[0039] Connect contour error points and reference position ,straight line Axial tracking error Where the straight lines intersect the point , axial tracking error Linear and axial tracking errors The straight line is compared to the point , then the triangle is constructed ,Pick The actual location point To the straight line The distance between the two ends is obtained, and the calculation expression of the profile error of the straight line profile by the cross-coupling control is obtained as follows:

[0040]

[0041] In the formula, Indicates angle , and the contour error is obtained and distance The relationship between them is:

[0042]

[0043] In the formula, is the contour error and distance The angle between Described as an analytical expression for the axial tracking error, namely:

[0044]

[0045] The contour error compensation output by the generalized cross-coupling controller is obtained , expressed as:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In the formula, is the proportional gain, is the differential gain, is the contour error The first-order differential of is the cross-coupling gain of the X-axis, is the cross-coupling gain on the Y axis, is the contour error compensation of the X-axis, is the contour error compensation amount of the Y axis.

[0052] Preferably, the method of combining the control signal of the single axis, the disturbance estimation result and the contour error compensation amount as the control input of the mechanism model comprises:

[0053]

[0054] In the formula, for The control input of the axis mechanism model, for The control signal output by the axis feedback controller, for The contour error compensation of the axis, for The perturbation estimation results of the axis.

[0055] In a second aspect, the present invention further provides a multi-axis collaborative control system based on digital-analog linkage, including a data-driven prediction module, a disturbance suppression tracking control module, a contour error estimation and compensation module and an output module, wherein:

[0056] The data-driven prediction module is configured to: output a tracking error prediction value corresponding to a reference trajectory using an offline single-axis tracking error prediction model, and compensate the tracking error prediction value to the reference trajectory to obtain a new reference trajectory for each axis;

[0057] The disturbance suppression tracking control module is configured to: generate a control signal according to a new reference trajectory of a single axis and an actual trajectory output by a mechanism model using a feedback controller, estimate an external disturbance in real time based on the control signal and the actual trajectory using a disturbance observer, and output a disturbance estimation result;

[0058] The contour error estimation and compensation module is configured to: estimate the contour error using the Newton iteration method according to the reference trajectory and the actual trajectory of each axis, and input the contour error into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis;

[0059] The output module is configured to: combine the control signal of the single axis, the disturbance estimation result and the contour error compensation amount as the control input of the mechanism model to obtain the actual trajectory of the mechanism model output.

[0060] In a third aspect, the present invention provides a multi-axis collaborative control device based on digital-analog linkage, comprising a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the multi-axis collaborative control method based on digital-analog linkage.

[0061] The multi-axis collaborative control method, system and device based on digital-analog linkage proposed in the present invention have the following beneficial effects:

[0062] 1. The prediction model trained by the data-driven machine learning algorithm, combined with offline adjustment of the reference trajectory, can significantly improve the tracking accuracy of the single axis and reduce the negative impact of the system's unmodeled dynamics on the tracking accuracy. The model is trained with historical data and not only has high prediction accuracy, but also has good generalization ability, and can adapt to the control requirements of a variety of complex trajectories.

[0063] 2. In response to external disturbances that may occur in complex machining environments, the designed disturbance suppression tracking controller, combined with the mechanism model of the controlled object, can quickly estimate and compensate for external disturbances, making up for the limitations of relying solely on offline prediction models and significantly enhancing the robustness of the system in practical applications.

[0064] 3. In response to the coupling problem in multi-axis motion control, the generalized cross-coupling controller based on the Newton iteration method can perform contour control on contours of any shape, accurately calculate the contour error generated during system operation in real time, and decompose the error into each axis for compensation through the generalized cross-coupling controller, thereby further improving the contour control accuracy.

[0065] 4. Through the synergistic effect of the above three control parts, the fusion of mechanism model and data model, and the combination of offline prediction and online real-time control, not only the tracking accuracy of the single axis is significantly improved, but also the contour tracking accuracy of the multi-axis system is effectively improved, and finally the high-precision control of the multi-axis equipment is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a single-axis controller framework diagram of a multi-axis collaborative control method based on digital-analog linkage of the present invention;

[0067] Figure 2 A multi-axis controller framework diagram of a multi-axis cooperative control method based on digital-analog linkage of the present invention;

[0068] Figure 3 is a two-dimensional plane profile error map of the present invention;

[0069] Figure 4 It is a schematic diagram of the generalized cross-coupling of the present invention;

[0070] Figure 5 The disturbance applied on the X-axis and the disturbance estimation result diagram in the experiment of the present invention;

[0071] Figure 6 The disturbance applied on the Y axis and the disturbance estimation result diagram in the experiment of the present invention;

[0072] Figure 7 It is the tracking error diagram of the X axis in the experiment of the present invention;

[0073] Figure 8 It is the tracking error diagram of the Y axis in the experiment of the present invention;

[0074] Fig. 9 This is the contour error diagram in the experiment of the present invention. DETAILED DESCRIPTION

[0075] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0076] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0077] The present invention aims to solve the shortcomings of traditional control methods in dealing with dynamic characteristics, and the limitations of data-driven learning methods in real-time online adjustment, and proposes a multi-axis collaborative control method, system and device based on digital-analog linkage. The method forms a digital-analog linkage control strategy by combining a mechanism model and a data-driven method. The mechanism model provides prior knowledge of the system, which helps to capture the basic dynamic characteristics of the system, and designs a disturbance observer. At the same time, based on the offline training of the data-driven method, the pre-optimization adjustment of the reference trajectory is achieved through the learning of the system's historical data, so as to better adapt to the dynamic changes of the system. This collaborative mechanism not only retains the ability of the data-driven method in pre-adjusting the reference trajectory and improves the single-axis tracking accuracy, but also, the disturbance observer designed based on the mechanism model enhances the system's online adjustment ability to external disturbances, ensuring that the system can quickly respond to changes in a dynamic environment, thereby improving the accuracy, robustness and adaptability of the multi-axis motion control system.

[0078] Example 1: Figure 1 and Figure 2 As shown, a multi-axis collaborative control method based on digital-analog linkage includes the following steps:

[0079] Step 1: Construct a data-driven offline single-axis tracking error prediction model, use the offline single-axis tracking error prediction model to output the tracking error prediction value corresponding to the reference trajectory, and compensate the tracking error prediction value to the reference trajectory to obtain a new reference trajectory for each axis.

[0080] This embodiment adopts a data-driven approach and uses machine learning methods to model by establishing a mapping relationship between input and output. A variety of machine learning methods can be selected, such as GRU (Gated Recurrent Unit) neural network, LSTM (Long Short-Term Memory) neural network or Gaussian process regression. These methods are only optional examples. In actual use, other suitable machine learning algorithms can be flexibly selected according to the system requirements, characteristics and modeling accuracy requirements.

[0081] The modeling process is as follows: First, define the tracking error as ,in for The reference trajectory of the axis, for The actual trajectory of the axis, is the axis index. Next, using the historical data of the multi-axis equipment, including the reference trajectory, expected speed, and tracking error, a preset proportion of the data is used as the training set to train the model, and the remaining data is used as the validation set to test the prediction effect of the model. The training data set is input into the selected machine learning model to establish a mapping relationship between the reference trajectory data and the tracking error data. Finally, the machine learning model with the best prediction effect on the validation set is selected and saved as the offline single-axis tracking error prediction model for subsequent single-axis tracking error prediction of new trajectories.

[0082] The predicted output for the new trajectory is , the new trajectory is adjusted offline, and the new reference trajectory is expressed as: .

[0083] Step 2: Construct a disturbance suppression tracking controller based on the mechanism model, which includes a feedback controller and a disturbance observer. The feedback controller receives the new reference trajectory of the single axis and the actual trajectory output by the mechanism model, and generates a control signal to make the system follow the new reference trajectory; the disturbance observer uses the control signal and the actual trajectory to estimate the external disturbance in the system in real time, and outputs the disturbance estimation result.

[0084] The feedback controller adopts the classic PID (proportional-integral-differential) controller, and the disturbance observer can choose EID (equivalent input disturbance estimator), ESO (extended state observer) and DOB (disturbance observer), etc. The specific choice of disturbance observer needs to be weighed and decided based on the system's needs, characteristics and control accuracy.

[0085] The construction process is as follows: First, using the system's mechanism model, based on the system's state matrix, input matrix and output matrix, analyze the system's dynamic characteristics and design a suitable PID controller, which is expressed as:

[0086]

[0087]

[0088] In the formula, for The control signal output by the axis PID controller, for The tracking error of the axis with respect to the new reference trajectory, for The first-order differential of for The scale factor of the axis, for The differential coefficient of the axis, for The integration coefficient of the axis, represents the output of the offline single-axis tracking error prediction model The tracking error prediction of the axis.

[0089] At the same time, according to the needs of the system, select a suitable disturbance observer (such as EID, ESO or DOB, etc.). The disturbance observer estimates the external disturbance in real time based on the control signal and the actual trajectory and outputs the disturbance estimation result. The estimated result of the axis is ; Finally, by adjusting the PID parameters and the gain of the disturbance observer, combined with information such as the system's state matrix and output matrix, the system is optimized and adjusted to reduce the impact of disturbances on control accuracy.

[0090] Step three: Construct an online real-time contour error estimation and compensation controller. The online real-time contour error estimation and compensation controller estimates the contour error based on the reference trajectory and actual trajectory of each axis using the Newton iteration method, and inputs the contour error into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis.

[0091] The contour error is defined as the shortest distance from the actual position to the reference trajectory. When solving the contour error, it can be converted into an extreme value problem to be processed. The Newton iteration method is used to solve the extreme value of the nonlinear equation. This method can not only improve the calculation accuracy of the contour error, but also effectively avoid the error distortion problem that may occur at large curvature points of the geometric method. The generalized cross-coupled control (GCCC) method is an improvement on the cross-coupled control method. The GCCC method can be applied to any free-form contour for contour control. After obtaining an accurate contour error estimate, the contour error is compensated by the GCCC method, and the contour error is decomposed into each axial control loop, thereby reducing the overall contour error and improving the tracking accuracy of the multi-axis system.

[0092] Among them, Figure 3 As shown, the contour error is estimated using the Newton iteration method, including:

[0093] Denote the reference trajectory as time The function is as follows:

[0094]

[0095] In the formula, express The reference position at the moment, express The X-axis coordinate of the reference position at the moment, express The Y-axis coordinate of the reference position at the moment;

[0096] Will The actual position at a moment is expressed as:

[0097]

[0098] In the formula, express The actual location at the moment, express The X-axis coordinate of the actual position at the moment, express The Y-axis coordinate of the actual position at the moment;

[0099] The error vector is defined as:

[0100]

[0101] In the formula, Indicates from the actual location arrive Reference position at time vector of;

[0102] The contour error Defined as:

[0103]

[0104] Indicated in Moment profile error Get the minimum value, where express The reference position at the moment, i.e. the contour error point, represents the L2 norm;

[0105] The cost function is constructed as follows:

[0106]

[0107] In the formula, is the cost function, represents the Euclidean norm;

[0108] The Newton iteration method is used to calculate the minimum value of the cost function, and we get The contour error corresponding to the moment and contour error points as the estimated contour error and contour error points.

[0109] Among them, the contour error is input into the generalized cross-coupling controller to calculate the contour error compensation amount of each single axis, including:

[0110] like Figure 4 As shown, the output contour error points are estimated by Newton iteration method. And contour error ,Pick Reference position at time , Actual location at the moment , according to the reference position and actual location Determine the axial tracking error corresponding to the X-axis Axial tracking error corresponding to the Y axis ;

[0111] Connect contour error points and reference position ,straight line Axial tracking error Where the straight lines intersect the point , axial tracking error Linear and axial tracking errors The straight lines intersect at the point , then the triangle is constructed ,Pick The actual location point To the straight line The distance between the two ends is obtained, and the calculation expression of the profile error of the straight line profile by the cross-coupling control is obtained as follows:

[0112]

[0113] In the formula, Indicates angle , and the contour error is obtained and distance The relationship between them is:

[0114]

[0115] In the formula, is the contour error and distance The angle between Described as an analytical expression for the axial tracking error, namely:

[0116]

[0117] The contour error compensation output by the generalized cross-coupling controller is obtained , expressed as:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] In the formula, is the proportional gain, is the differential gain, is the contour error The first-order differential of is the cross-coupling gain of the X-axis, is the cross-coupling gain on the Y axis, is the contour error compensation of the X-axis, is the contour error compensation amount of the Y axis.

[0124] Step 4: Combine the single-axis control signal, disturbance estimation result and contour error compensation as the input of the mechanism model to obtain the actual trajectory of the mechanism model output. The control input of the mechanism model is expressed as:

[0125]

[0126] In the formula, for The control input of the axis mechanism model, for The control signal output by the axis feedback controller, for The contour error compensation of the axis, for The perturbation estimation results of the axis.

[0127] Embodiment 2: Based on embodiment 1, Axis and Taking the two-axis equipment of the axis as an example, a specific algorithm is introduced to describe a multi-axis cooperative control method based on digital-analog linkage of the present invention as follows:

[0128] Step 1: In this embodiment, a single-axis tracking error prediction model is established through machine learning methods in a data-driven manner, and the mapping relationship between input and output is used for modeling. Optional machine learning methods include GRU, LSTM neural network or Gaussian process regression, etc. The specific choice depends on the system requirements and characteristics to ensure the adaptability and accuracy of the model. This embodiment uses Gaussian process to construct a prediction model for single-axis tracking error. The specific process is as follows:

[0129] 1) Data collection: Collect the running data of the multi-axis motion control system under different trajectories. The running trajectories are arcs with different radii and speeds. The reference positions of the X-axis and Y-axis are The expected speeds are , the actual location of the acquisition output , calculate the single-axis tracking error of the X-axis and Y-axis, denoted as , , ; Make a data set for Gaussian process training and input features and the target variable Respectively expressed as:

[0130]

[0131]

[0132] The training data set contains a set of circular trajectory data. The reference trajectory corresponding to each set of data is generated by cosine waves and sine waves of different frequencies, with frequency values ​​of 0.1π, 0.2π, 0.3π and 0.4π, and amplitudes of 9mm, 10mm and 11mm respectively. Through these waveforms of different frequencies, the training data set covers a variety of periodic motion modes, aiming to improve the generalization ability and accuracy of the prediction model when processing various trajectories.

[0133] 2) Data standardization: Process the input and output data through Z-score standardization and calculate the mean and standard deviation , get standardized data and .

[0134] 3) Dataset division: The data set is randomly divided into 70% for training and 30% for testing; the training data is , the test data is .

[0135] 4) Gaussian process regression model training:

[0136] The Gaussian regression process defines the similarity between input data points through the kernel function, using the Matern kernel function, which is defined as:

[0137]

[0138] in, is the signal variance, is the length scale, Is the input point and The performance of Gaussian process regression depends on the choice of hyperparameters, especially the hyperparameters of the kernel function ( and By optimizing the hyperparameters, the model can better fit the training data. After the training is completed, the kernel function parameters ( and ).

[0139] The trained Gaussian process regression model is used to predict the tracking error of the new trajectory, and the new trajectory is expressed as:

[0140]

[0141] Get the predicted output value and , the predicted tracking error is compensated to the reference trajectory, and the new reference trajectory is expressed as:

[0142]

[0143]

[0144] Step 2: Construct a disturbance suppression tracking controller based on the mechanism model. In this embodiment, a disturbance suppression tracking controller combining a PD controller and an EID (equivalent input disturbance estimator) is selected. In this embodiment, although EID is selected as the disturbance observer, other types of disturbance observers, such as ESO (extended state observer) or DOB (disturbance observer), can also be selected according to the needs, characteristics and accuracy requirements of the system.

[0145] The PD controller is used to achieve stable tracking of the new reference trajectory, which is expressed as:

[0146]

[0147]

[0148] in, For PD control output, for The proportional and differential coefficients of the axes, for The tracking error of the axis with respect to the new reference trajectory, for The first-order differential of .

[0149] The state space model (i.e. mechanism model) of the networked motion control system is established and described as follows:

[0150]

[0151] In the formula, express The system status of the axis, and are the system position and velocity, for The first-order differential of It is the system control input of the motion control system. is the system output of the motion control system, are system matrices of suitable dimensions, namely the state matrix, the input matrix, and the output matrix, represents the external disturbance, represents the gain matrix corresponding to the external disturbance, The motion control system constructed is observable and controllable;

[0152] Introduce the concept of equivalent input interference and define is the equivalent input disturbance of the motion control system, that is The impact on the system output is equivalent to external disturbance Output to the system The influence of , then rewrite the motion control system as:

[0153]

[0154] The equivalent input disturbance state space model of the motion control system is obtained.

[0155] The designed state observer is:

[0156]

[0157] In the formula, express The observed value of Indicates system output The observed value of represents the state observer gain, For PD control output, is the system matrix.

[0158] The equivalent input disturbance estimator estimates the total disturbance composed of various external disturbances and obtains the total disturbance estimate , the formula is as follows:

[0159]

[0160] in, express The observed value of represents the Moore-Penrose generalized inverse matrix, that is , is the control input, PD control output.

[0161] The final output of the equivalent input disturbance estimator is , which represents the perturbation to the sum The perturbation estimate after filtering, where the filter is represented by , the disturbance estimate after filtering is expressed as:

[0162]

[0163]

[0164]

[0165] In the formula, and represent inverse Laplace transform and Laplace transform respectively, and Respectively and The Laplace transform of .

[0166] Step 3: Construct a generalized cross-coupled controller based on Newton iteration method. In this embodiment, Newton iteration method is used to calculate the contour error. In two-dimensional contour tracking control, the reference trajectory is usually known and can be expressed as time Function:

[0167]

[0168] In the formula, Expressed as time, Indicated in The position on the reference trajectory at all times. The actual position at a moment is expressed as:

[0169]

[0170] Define the error vector as:

[0171]

[0172] Indicates from the actual location arrive Time reference trajectory point The contour error is defined as the shortest distance from the actual position to the reference trajectory, so the contour error It can be defined as:

[0173]

[0174] Indicated in Moment profile error Get the minimum value, where Expressed as L2 norm, is the contour error point, such as Figure 3 shown.

[0175] To find the contour error and the corresponding time , define a cost function as:

[0176]

[0177] in, represents the Euclidean norm. and It is related to the minimum value of the cost function. In order to obtain an accurate estimate of the contour error, the Newton iteration method is used to calculate the minimum value of the cost function. Assume that the cost function There are non-zero second-order derivatives for The derivative of Through Taylor expansion, we can get:

[0178]

[0179] In the formula, and The cost functions are In order to obtain the first and second derivatives of The minimum value of ,but , and the recursive formula of Newton's iteration method is derived as follows:

[0180]

[0181] In the formula, is the number of iterations, and the iteration amount is gradually updated through multiple iterations , so that it gradually converges to satisfy , thus obtaining the cost function The minimum value of the contour error and contour error points .

[0182] In order to verify the convergence of Newton's algorithm and ensure its effectiveness in actual calculations, the following assumptions are introduced:

[0183]

[0184] We can get:

[0185]

[0186] In the formula, for The third-order derivative of exist Taylor expansion is performed at the position, retaining the second-order terms and introducing higher-order remainder terms , we can get:

[0187]

[0188] In the formula, is a high-order infinitesimal. According to the assumptions , then The formula is , and from the assumed formula we know , then bring in The formula is:

[0189]

[0190] In the formula, can be ignored because is a high-order infinitesimal term, when When , its value is 0; is a bounded constant; From the formula, we can see that the current iteration error is The error with the previous round is proportional to the square of , that is:

[0191]

[0192] This shows that the iterative process of Newton's method satisfies the characteristics of second-order convergence, that is, the speed at which the error decreases with each iteration decreases in a quadratic manner.

[0193] Contour error points found by Newton iteration method And contour error . , They are The reference position and actual position at the moment, , They are axis, Axis tracking error corresponding to the axis; connection , construct a triangle , The actual location point To the straight line The error calculation expression of the straight line profile according to the cross-coupling control is:

[0194]

[0195] In the formula, express , indicating the passing point and Point The straight line and The angle between the axes. Figure 4 It can be clearly seen that the contour error and The relationship between them is:

[0196]

[0197] Substituting in, we get:

[0198]

[0199] From this, the cross-coupling gain can be derived as:

[0200]

[0201]

[0202] In the formula, In the known and Then it can be calculated that Available from And contour error By deriving the cross-coupling gain formula, the contour error can be described as an analytical expression of the tracking error, namely:

[0203]

[0204] By establishing an analytical expression, the contour error is decomposed into a functional relationship of the tracking errors of each axis. The coupling gain is dynamically adjusted according to the real-time tracking state, thereby optimizing the control quantity of each axis in the control law, accurately compensating the contour error, and improving the tracking accuracy under complex trajectories.

[0205] The PD-type generalized cross-coupling controller is used to compensate for the error. The corresponding control input can be adjusted according to the error information of each axis to reduce the coupling effect between the axes, thereby effectively reducing the contour error. The compensation amount output by the generalized cross-coupling controller is , expressed as:

[0206]

[0207]

[0208] in, are proportional gain and differential gain respectively, is the cross-coupling gain, They are Axis, Axis contour error compensation amount.

[0209] Step 4: In summary, the control input of the multi-axis collaborative control method based on digital-analog linkage can be obtained as follows:

[0210]

[0211] In order to verify the effectiveness and superiority of the proposed method, the following experiments were conducted based on the method of the present invention:

[0212] Set the dual-axis motion control system to track the following desired trajectory:

[0213]

[0214] The transfer functions of the X-axis and Y-axis are:

[0215]

[0216]

[0217] Further converted into the state space equation form, we have , , , , The single-axis tracking error predicted by the Gaussian process is adjusted offline to the reference trajectory, expressed as . The PD controller parameters of the axis are , The PD controller parameters of the axis are , reference of PD type generalized cross-coupled controller ; Configure the system sampling period to 10ms, observer polesx=[-200 -200], polesy=[-200 -200], equivalent input interference estimation parameters , , filter function The disturbance was injected from 7s to 17s, and the system was tested using three strategies: PD, PD+EID, and PD+EID+GP+GCCC. The disturbance estimation diagram is shown in Figure 5 and Figure 6 As shown, the vertical axis is the disturbance (dis), the unit is revolutions per minute (rpm), and the horizontal axis is time (t), the unit is seconds (s); the single-axis tracking error is as follows Figure 7 and Figure 8 As shown, the ordinate is the tracking error of a single axis relative to the reference trajectory. , the error symbols are and The unit is millimeter (mm), the horizontal axis is time (t), the unit is second (s); the contour error is Fig. 9 As shown in the figure, the ordinate is the profile error of a single axis, and the error symbol is The unit is millimeter (mm), and the horizontal axis is time (t), and the unit is second (s). Figure 5 and Figure 6 It can be seen that the EID disturbance estimator accurately estimates the disturbance and eliminates the influence of the disturbance on the tracking accuracy. Figure 7 and Figure 8 It can be seen that after the reference trajectory is predicted and compensated offline by the Gaussian process, the single-axis tracking accuracy is significantly improved, and the EID can effectively suppress the influence of disturbances. Fig. 9 It can be seen that the control strategy based on PD+EID+GP+GCCC proposed in the present invention can effectively improve the contour tracking accuracy of the multi-axis motion control system and realize high-precision multi-axis collaborative control compared with the other two control strategies.

[0218] Embodiment 3: This embodiment proposes a multi-axis collaborative control system based on digital-analog linkage, including a data-driven prediction module, a disturbance suppression tracking control module, a contour error estimation and compensation module and an output module.

[0219] The data-driven prediction module is configured to: output the tracking error prediction value corresponding to the reference trajectory, and compensate the tracking error prediction value to the reference trajectory to obtain a new reference trajectory for each axis; this module uses historical data to train a prediction model through a machine learning algorithm (such as GRU, LSTM or Gaussian process, etc.), and based on the prediction model, adjust the reference trajectory offline to improve the single-axis tracking accuracy and reduce the impact of the system's unmodeled dynamics on the tracking accuracy.

[0220] The disturbance suppression tracking control module is configured as follows: using a feedback controller to generate a control signal based on the new reference trajectory of a single axis and the actual trajectory output by the mechanism model, and using a disturbance observer to estimate the external disturbance in real time based on the control signal and the actual trajectory, and output the disturbance estimation result; this module designs and implements a disturbance suppression tracking controller, which estimates and compensates for external disturbances in real time by combining a disturbance observer (such as EID, ESO or DOB), making up for the shortcomings of the offline prediction model and significantly improving the robustness of the system.

[0221] The contour error estimation and compensation module is configured as follows: according to the reference trajectory and actual trajectory of each axis, the contour error is estimated using the Newton iteration method, and the compensation amount of each axis is output according to the contour error through the generalized cross-coupling controller; the module calculates the contour error in real time based on the Newton iteration method, inputs the contour error into the generalized cross-coupling controller, and calculates the contour error compensation amount for each single axis, thereby improving the contour control accuracy of the multi-axis system.

[0222] The output module is configured to: combine the control signal output by the single-axis feedback controller, the disturbance estimation result and the contour error compensation amount as the input of the mechanism model to obtain the actual trajectory output by the mechanism model.

[0223] For the specific limitations of the multi-axis collaborative control system based on digital-analog linkage, please refer to the limitations of the multi-axis collaborative control method based on digital-analog linkage in Example 1 or Example 2, which will not be repeated here.

[0224] Example 4: This example provides a multi-axis collaborative control device based on digital-analog linkage, including a processor and a memory storing a plurality of computer instructions, wherein the computer instructions, when executed by the processor, implement the steps of the multi-axis collaborative control method based on digital-analog linkage.

[0225] For the specific limitations of the multi-axis collaborative control system based on digital-analog linkage, please refer to the limitations of the multi-axis collaborative control method based on digital-analog linkage in Example 1 or Example 2, which will not be repeated here.

[0226] The memory and the processor are electrically connected directly or indirectly to achieve data transmission or interaction. For example, these elements can be electrically connected to each other through one or more communication buses or signal lines. The memory stores a computer program that can be run on the processor, and the processor implements the method of the present invention by running the computer program stored in the memory.

[0227] The memory may be, but is not limited to, a random access memory (RAM), a read only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), etc. The memory is used to store a program, and the processor executes the program after receiving an execution instruction.

[0228] The processor may be an integrated circuit chip with data processing capabilities. The above-mentioned processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc. The methods, steps and logic block diagrams disclosed in the embodiments of the present invention may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0229] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0230] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A multi-axis collaborative control method based on digital-analog linkage, characterized in that: The multi-axis collaborative control method based on digital-analog linkage includes: A data-driven offline single-axis tracking error prediction model is constructed, and the tracking error prediction value corresponding to the reference trajectory is outputted using the offline single-axis tracking error prediction model. The tracking error prediction value is then compensated to the reference trajectory to obtain a new reference trajectory for each axis. A disturbance suppression tracking controller based on a mechanism model is constructed, wherein the disturbance suppression tracking controller includes a feedback controller and a disturbance observer, wherein the feedback controller generates a control signal according to a new reference trajectory of a single axis and an actual trajectory output by the mechanism model, and the disturbance observer estimates the external disturbance in real time based on the control signal and the actual trajectory, and outputs a disturbance estimation result; An online real-time contour error estimation and compensation controller is constructed. The online real-time contour error estimation and compensation controller estimates the contour error by using the Newton iteration method according to the reference trajectory and the actual trajectory of each axis, and inputs the contour error into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis; The control signal of a single axis, the disturbance estimation result and the contour error compensation are combined as the control input of the mechanism model to obtain the actual trajectory of the mechanism model output.

2. The multi-axis collaborative control method based on digital-analog linkage according to claim 1 is characterized in that: The construction of a data-driven offline single-axis tracking error prediction model includes: The tracking error is defined as ,in for The reference trajectory of the axis, for The actual trajectory of the axis, is the axis index; An acquisition data set is divided into a training set and a validation set, wherein the data set is historical operation data of a multi-axis device; The training set is input into the machine learning algorithm to establish the mapping relationship between the reference trajectory and the tracking error, and the machine learning model with the best prediction effect on the validation set is selected and saved as the offline single-axis tracking error prediction model.

3. The multi-axis collaborative control method based on digital-analog linkage according to claim 2 is characterized in that: The feedback controller adopts a PID controller, which is expressed as: ； In the formula, for The control signal output by the axis PID controller, for The tracking error of the axis with respect to the new reference trajectory, for The first-order differential of for The scale factor of the axis, for The differential coefficient of the axis, for The integration coefficient of the axis; ； In the formula, The output of the offline single-axis tracking error prediction model is The tracking error prediction of the axis.

4. The multi-axis collaborative control method based on digital-analog linkage according to claim 1 is characterized in that: The method of estimating the contour error by Newton iteration method comprises: Denote the reference trajectory as time The function is as follows: ； In the formula, express The reference position at the moment, express The X-axis coordinate of the reference position at the moment, express The Y-axis coordinate of the reference position at the moment; Will The actual position at a moment is expressed as: ； In the formula, express The actual location at the moment, express The X-axis coordinate of the actual position at the moment, express The Y-axis coordinate of the actual position at the moment; The error vector is defined as: ； In the formula, Indicates from the actual location arrive Reference position at time vector of; The contour error Defined as: ； Indicated in Moment profile error Get the minimum value, where express The reference position at the moment, i.e. the contour error point, represents the L2 norm; The cost function is constructed as follows: ； In the formula, is the cost function, represents the Euclidean norm; The Newton iteration method is used to calculate the minimum value of the cost function, and we get The contour error corresponding to the moment and contour error points , as the estimated contour error and contour error point.

5. The multi-axis collaborative control method based on digital-analog linkage according to claim 1 is characterized in that: The contour error is input into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis, including: Output contour error points through Newton iteration method And contour error ,Pick Reference position at time , Actual location at the moment , according to the reference position and actual location Determine the axial tracking error corresponding to the X-axis Axial tracking error corresponding to the Y axis ; Connect contour error points and reference position ,straight line Axial tracking error Where the straight lines intersect the point , axial tracking error Linear and axial tracking errors The straight line is compared to the point , then the triangle is constructed ,Pick The actual location point To the straight line The distance between the two ends is obtained, and the calculation expression of the profile error of the straight line profile by the cross-coupling control is obtained as follows: ； In the formula, Indicates angle , and the contour error is obtained and distance The relationship between them is: ； In the formula, is the contour error and distance The angle between Described as an analytical expression for the axial tracking error, namely: ； The contour error compensation output by the generalized cross-coupling controller is obtained , expressed as: ； ； ； ； ； In the formula, is the proportional gain, is the differential gain, is the contour error The first-order differential of is the cross-coupling gain of the X-axis, is the cross-coupling gain on the Y axis, is the contour error compensation of the X-axis, is the contour error compensation amount of the Y axis.

6. The multi-axis collaborative control method based on digital-analog linkage according to claim 1 is characterized in that: The method of combining the control signal of the single axis, the disturbance estimation result and the contour error compensation amount as the control input of the mechanism model includes: ； In the formula, for The control input of the axis mechanism model, for The control signal output by the axis feedback controller, for The contour error compensation of the axis, for The perturbation estimation results of the axis.

7. A multi-axis collaborative control system based on digital-analog linkage, characterized in that: The multi-axis collaborative control system based on digital-analog linkage includes a data-driven prediction module, a disturbance suppression tracking control module, a contour error estimation and compensation module and an output module, wherein: The data-driven prediction module is configured to: output a tracking error prediction value corresponding to a reference trajectory using an offline single-axis tracking error prediction model, and compensate the tracking error prediction value to the reference trajectory to obtain a new reference trajectory for each axis; The disturbance suppression tracking control module is configured to: generate a control signal according to a new reference trajectory of a single axis and an actual trajectory output by a mechanism model using a feedback controller, estimate an external disturbance in real time based on the control signal and the actual trajectory using a disturbance observer, and output a disturbance estimation result; The contour error estimation and compensation module is configured to: estimate the contour error using the Newton iteration method according to the reference trajectory and the actual trajectory of each axis, and input the contour error into the generalized cross-coupling controller to calculate the contour error compensation amount for each single axis; The output module is configured to: combine the control signal of the single axis, the disturbance estimation result and the contour error compensation amount as the control input of the mechanism model to obtain the actual trajectory of the mechanism model output.

8. A multi-axis collaborative control device based on digital-analog linkage, comprising a processor and a memory storing a plurality of computer instructions, characterized in that: When the computer instructions are executed by the processor, the steps of the multi-axis collaborative control method based on digital-analog linkage described in any one of claims 1 to 6 are implemented.

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