A ball screw feed system dynamic characteristic sparse identification method

Abstract

A kind of ball screw feed system dynamic characteristic sparse identification method, it is characterized in that data set is structured by random excitation experiment covering working stroke, ball screw feed system is modeled as linear variable parameter system under nonlinear friction disturbance, construct conventional dictionary function library and hyperbolic tangent dictionary function library respectively to represent position-dependent dynamic characteristics and nonlinear friction and construct regression model, the coefficients of all dictionary functions are determined using sparse regression, and then the final prediction model is obtained.The motor driving torque-workbench position prediction model considering nonlinear friction and position-dependent dynamic characteristics at the same time is identified by the data of one excitation experiment, and accurate and efficient modeling of ball screw feed system dynamic characteristics is realized.

Description

Technical Field

[0001] This invention relates to the field of electromechanical system modeling, and in particular to a method for modeling the dynamic characteristics of a ball screw feed system, specifically a method for sparse identification of the dynamic characteristics of a ball screw feed system. Background Technology

[0002] Ball screw feed systems are widely used in mechanical systems, such as various CNC machine tools, due to their advantages of high transmission efficiency, large working stroke, strong load-bearing capacity, and long service life. The trend of increasing precision and speed in mechanical systems places higher demands on the motion control accuracy of ball screw feed systems, and establishing an accurate model describing the dynamic characteristics of the system is the foundation for ensuring its motion control accuracy.

[0003] Due to the influence of nonlinear time-varying factors such as nonlinear frictional disturbances and position-dependent dynamic characteristics, the dynamic characteristics of ball screw feed systems are difficult to model accurately and efficiently. Current modeling methods are mainly divided into two categories: mechanistic modeling and data-driven modeling. Mechanistic modeling requires identifying various physical parameters in the model, making the modeling process cumbersome, inefficient, and with limited accuracy. Data-driven modeling, which commonly uses neural network models, is limited by its black-box nature, lacking mechanistic interpretability and struggling to achieve stable generalization. Therefore, there is an urgent need for an accurate and efficient modeling method for the dynamic characteristics of ball screw feed systems. Summary of the Invention

[0004] The purpose of this invention is to address the problems of cumbersome and inefficient modeling processes, limited accuracy, poor preparedness, lack of mechanistic interpretability, and difficulty in stable generalization in existing dynamic characteristic modeling of ball screw feed systems. This invention proposes a sparse identification method for the dynamic characteristics of ball screw feed systems. A dataset is constructed by using random excitation experiments covering the working stroke. The ball screw feed system is modeled as a linear variable parameter system under nonlinear frictional disturbance. A conventional dictionary function library and a hyperbolic tangent dictionary function library are constructed to represent position-related dynamic characteristics and nonlinear friction, respectively, and a regression model is constructed. Least square regression and stepwise sparse regression are performed on all coefficients to obtain the final motor drive torque-table displacement prediction model.

[0005] The technical solution of this invention is:

[0006] A method for sparse identification of dynamic characteristics of a ball screw feed system, characterized by comprising the following steps:

[0007] 1) Conduct random excitation experiments covering the working stroke, and simultaneously monitor the motor drive torque and table displacement;

[0008] 2) The ball screw feed system is modeled as a linear variable parameter system under nonlinear friction disturbance;

[0009] 3) Construct a conventional dictionary function library to represent the position-dependent dynamic characteristics of the system;

[0010] 4) Construct a hyperbolic tangent dictionary function library to characterize the nonlinear friction of the system;

[0011] 5) Construct a regression model based on the two types of dictionary function libraries mentioned above;

[0012] 6) Use the least squares method to solve for the coefficients of all dictionary functions in the regression model;

[0013] 7) Divide all coefficients into three parts: displacement, driving torque, and nonlinear friction correlation, and perform stepwise sparse regression;

[0014] 8) Substitute the coefficients from the sparse regression into the regression model and convert them into a prediction form.

[0015] The beneficial effects of this invention are:

[0016] The method disclosed in this invention can identify a motor drive torque-table displacement prediction model that simultaneously considers nonlinear friction and position-related dynamic characteristics using data from a single excitation experiment, thereby enabling accurate and efficient modeling of the dynamic characteristics of the ball screw feed system. Attached Figure Description

[0017] Figure 1 A schematic diagram of the motor driving torque and table trajectory monitored in a random excitation experiment.

[0018] Figure 2 This is a schematic diagram of the regression model structure constructed based on two types of dictionary function libraries.

[0019] Figure 3 This is a schematic diagram of displacement prediction error under random excitation.

[0020] Figure 4 This is a schematic diagram showing the actual displacement and displacement prediction error during the sinusoidal motion of the worktable. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0022] A method for sparse identification of dynamic characteristics of a ball screw feed system includes the following steps:

[0023] Step 1) describes a random excitation experiment covering the working stroke, conducted in open-loop control mode. A random signal in the form of Gaussian white noise is selected as the driving torque. By setting boundary constraints and adjusting the mean of the random signal, the ball screw is subjected to random excitation, enabling the worktable to reciprocate within its working stroke.

[0024] Step 2) describes a linear variable parameter system under nonlinear friction disturbance, where the position-dependent dynamic characteristics of the ball screw feed system are characterized as a discrete-time linear variable parameter system with the table position as the scheduling variable. Nonlinear friction is considered as the disturbance input of the system and is expressed in the following difference equation form:

[0025]

[0026] in, and Let represent the time delay orders related to the system input and output, respectively. . express The workbench displacement at any given moment. express The driving torque at any moment express The speed of time Represents a nonlinear friction function. and These represent the coefficient functions related to the input and output, respectively. express The position of the worktable at any given time (i.e., the sum of the displacement and the initial position). The velocity in the above formula is approximated using the backward difference of the displacement:

[0027]

[0028] in, It is the sampling period of the ball screw feed system, and also the sampling period of the discrete-time model mentioned above.

[0029] Rewriting the above difference equation in standard prediction form, we get:

[0030]

[0031] Since the coefficient function has entered into a fractional form, in order to reduce the complexity of the model and make it easier to identify, the above difference equation is further transformed into an equivalent form:

[0032]

[0033]

[0034] in, For coefficient functions The constant term in and This is the new coefficient function after the above transformation.

[0035] The conventional dictionary function library mentioned in step 3) is represented as follows:

[0036]

[0037] in, The dictionary functions can be represented by constant functions, polynomial functions, exponential functions, and trigonometric functions, etc. Step 3) describes constructing a conventional dictionary function library to represent the position-dependent dynamic characteristics of the system, that is, utilizing... Characteristic coefficient function and :

[0038]

[0039] in, Represents the absence of constant terms , This indicates that it contains a constant term. and , This represents the coefficient vector of the dictionary function corresponding to the coefficient function.

[0040] The hyperbolic tangent dictionary function library mentioned in step 4) is represented as follows:

[0041]

[0042] in, Represents the dictionary function for hyperbolic tangent. Its constant coefficients. Step 4) describes constructing a hyperbolic tangent dictionary function library to characterize the nonlinear friction of the system, that is, using... Characterizing nonlinear friction function . Nonlinear friction at time It can be represented as:

[0043]

[0044] in, express The coefficient vector of the dictionary function corresponding to the nonlinear friction function at time t.

[0045] Step 5) describes constructing a regression model, which involves converting the equivalent form of the system difference equation into the following form based on the coefficient function and the nonlinear friction characterization method:

[0046]

[0047] To decouple and simplify the coupling terms of position-related dynamic characteristics and nonlinear friction in the above equation, the linear variable parameter characteristics in the fourth term of the above equation are ignored, and... Simplifying to constant terms, we obtain the decoupled simplified form of the system difference equation:

[0048]

[0049] To further construct the regression form, let:

[0050]

[0051]

[0052] in, This represents the coefficient vector of all dictionary functions. express At time t, a new state vector is formed by combining all relevant displacements, driving torques, and nonlinear friction with the corresponding dictionary function library. Therefore, the regression model is obtained:

[0053]

[0054] Step 6) describes using the least squares method to solve for the coefficients of all dictionary functions in the regression model. First, the discrete time series is defined. :

[0055]

[0056] in, Indicates the length of the time series, each This represents a discrete time point. A target vector can be constructed from the discrete time series. and state matrix for:

[0057]

[0058]

[0059] Based on the regression model described above, the target vector and state matrix Constructed in regression form:

[0060]

[0061] in, Let be the coefficient vector of all the dictionary functions mentioned above.

[0062] Solving the above equation directly using the least squares method yields the following results: Least square solution :

[0063]

[0064] Step 7) describes a stepwise sparse regression, which first involves... and state matrix It is divided into three parts: displacement correlation, driving torque correlation, and nonlinear friction correlation.

[0065]

[0066]

[0067] Fixed coefficient vector and For the coefficient vector of nonlinear friction Perform sparse regression:

[0068]

[0069] Fixed coefficient vector and The coefficient vector related to the driving torque Perform sparse regression:

[0070]

[0071] Fixed coefficient vector and For the displacement-related coefficient vector Perform sparse regression:

[0072]

[0073] in, , and Representing the coefficient vectors respectively , and Weights of sparse constraints.

[0074] After the above stepwise sparse regression process, the final regression model coefficient vector can be obtained. :

[0075]

[0076] Step 8) involves substituting the coefficients from the sparse regression into the regression model and converting them into a predictive form. First, the coefficient vector of the regression model... Substituting into the regression model, we obtain the decoupled simplified form of the system difference equation. Finally, we convert this model into the standard prediction form:

[0077]

[0078] The following section uses a system consisting of a Panasonic MADLN15BF servo motor and a TOYO GTH8 ball screw as an example to illustrate the specific implementation process and practical application effect of the sparse identification method for dynamic characteristics of the ball screw feed system disclosed in this invention.

[0079] A random excitation experiment covering the working stroke was conducted in open-loop control mode, with simultaneous monitoring of driving torque and table displacement. In the experiment, the motor driving torque was designed as a random signal in the form of Gaussian white noise. The specific strategy was as follows: first, the mean of the random signal was set to a positive value; when the table reached the set boundary, the sign of the mean of the random signal was changed to make it move in the opposite direction, and this process was repeated continuously to achieve the reciprocating motion of the table within the working stroke. The monitored driving torque and table motion trajectory are shown below. Figure 1 As shown.

[0080] The monitored driving torque and table displacement data are used to construct a regression model according to the method disclosed in this invention, the structure of which is as follows: Figure 2 As shown. The state matrix... sum coefficient vector Each consists of three parts: displacement, driving torque, and nonlinear friction correlation, where the state matrix represents the displacement correlation and driving torque correlation. and From the regular dictionary function library Composition, representing the state matrix of nonlinear friction From the hyperbolic tangent dictionary function library Composition. According to the method disclosed in this invention, the final coefficient vector is determined through least squares regression and stepwise sparse regression. This leads to the final prediction model of motor drive torque-table displacement.

[0081] The prediction model was validated using random excitation experimental data. The prediction errors for single-step, 10-step, and 50-step table displacements are shown below. Figure 3 As shown in Table 1, the root mean square error and maximum error are presented. It can be seen that the prediction model has high accuracy, especially in single-step and 10-step predictions.

[0082] Table 1. Displacement prediction error of random excitation experiments

[0083]

[0084] The prediction model was further validated using a sinusoidal trajectory experiment. In position control mode, a sinusoidal position command was set to make the table perform sinusoidal motion. The table trajectory is as follows: Figure 4 As shown in Figure (a), the prediction errors for single-step, 10-step, and 50-step predictions are as follows: Figure 4As shown in (b), (c), and (d), the root mean square error and maximum error are presented in Table 2. Due to the limitations of the PID-based position feedback control system, the system's following error is on the order of millimeters. However, the root mean square errors of the prediction model established by the method of this invention are only 0.5863 for single-step, 10-step, and 50-step predictions, respectively. 3.585 and 40.29 The method described in this invention has great potential to be integrated into model-based control algorithms to improve the motion control accuracy of the system, which fully demonstrates the effectiveness of the method.

[0085] Table 2 Displacement prediction error of sinusoidal trajectory experiment

[0086]

[0087] The parts not covered in this invention are the same as those in the prior art and are implemented using existing technologies.

Claims

1. A method for sparse identification of dynamic characteristics of a ball screw feed system, characterized in that, Includes the following steps: 1) Conduct random excitation experiments covering the working stroke, and simultaneously monitor the motor drive torque and table displacement; 2) The ball screw feed system is modeled as a linear variable parameter system under nonlinear friction disturbance; 3) Construct a conventional dictionary function library to represent the position-dependent dynamic characteristics of the system; 4) Construct a hyperbolic tangent dictionary function library to characterize the nonlinear friction of the system; 5) Construct a regression model based on the two types of dictionary function libraries mentioned above; 6) Use sparse regression to determine the coefficients of all dictionary functions and construct a prediction model; Step 2) describes a linear variable parameter system under nonlinear friction disturbance, where the position-dependent dynamic characteristics of the ball screw feed system are characterized as a discrete-time linear variable parameter system with the table position as the scheduling variable. Nonlinear friction is considered as the disturbance input of the system and is expressed in the following difference equation form: in, and Let represent the time delay orders related to the system input and output, respectively. ; express The workbench displacement at any given moment. express The driving torque at any moment express The speed of time Represents a nonlinear friction function. and These represent the coefficient functions related to the input and output, respectively. express The position of the worktable at any given time is the sum of the displacement and the initial position. The velocity in the above formula is approximated using the backward difference of the displacement: in, It is the sampling period of the ball screw feed system, and also the sampling period of the discrete-time model mentioned above; Rewriting the above difference equation in standard prediction form, we get: Since the coefficient function has entered into a fractional form, in order to reduce the complexity of the model and make it easier to identify, the above difference equation is further transformed into an equivalent form: in, For coefficient functions The constant term in and This is the new coefficient function after the above transformation.

2. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 1, characterized in that: Step 1) describes a random excitation experiment covering the working stroke, conducted in open-loop control mode. A random signal in the form of Gaussian white noise is selected as the driving torque. By setting boundary constraints and adjusting the mean of the random signal, the ball screw is subjected to random excitation, enabling the worktable to reciprocate within its working stroke.

3. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 1, characterized in that: The conventional dictionary function library mentioned in step 3) is represented as follows: in, The dictionary functions are represented by constant, polynomial, exponential, and trigonometric functions; step 3) describes constructing a conventional dictionary function library to characterize the position-dependent dynamic characteristics of the system, i.e., utilizing... The coefficient function described in the characterization and : in, Represents the absence of constant terms , This indicates that it contains a constant term. and , This represents the coefficient vector of the dictionary function corresponding to the coefficient function.

4. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 3, characterized in that: The hyperbolic tangent dictionary function library mentioned in step 4) is represented as follows: in, Represents the dictionary function for hyperbolic tangent. Its constant coefficients; step 4) describes the construction of a hyperbolic tangent dictionary function library to characterize the nonlinear friction of the system, that is, using Characterizing the nonlinear friction function ; Nonlinear friction at time It can be represented as: in, express The coefficient vector of the dictionary function corresponding to the nonlinear friction function at time t.

5. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 4, characterized in that: Step 5) describes constructing a regression model, which involves converting the equivalent form of the system difference equation into the following form based on the coefficient function and the nonlinear friction characterization method: To decouple and simplify the coupling terms of position-related dynamic characteristics and nonlinear friction in the above equation, the linear variable parameter characteristics in the fourth term of the above equation are ignored, and... Simplifying to constant terms, we obtain the decoupled simplified form of the system difference equation: To further construct the regression form, let: in, This represents the coefficient vector of all dictionary functions. express At time t, a new state vector is formed by combining all relevant displacements, driving torques, and nonlinear friction with the corresponding dictionary function library; therefore, the regression model is obtained: 。 6. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 5, characterized in that: Step 6) describes using sparse regression to determine the coefficients of all dictionary functions and construct a prediction model. First, a discrete time series is defined. : in, Indicates the length of the time series, each Represents a discrete time period; a target vector can be constructed from the discrete time series. and state matrix for: Based on the aforementioned regression model, the target vector and state matrix Constructed in regression form: in, Let be the coefficient vector of all the dictionary functions mentioned above; Solving the above equation directly using the least squares method yields the following results: Least square solution : 。 7. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 6, characterized in that: Step 6) involves using sparse regression to determine the coefficients of all dictionary functions and constructing a prediction model. First, the... and state matrix It is divided into three parts: displacement correlation, driving torque correlation, and nonlinear friction correlation. Fixed coefficient vector and For the coefficient vector of nonlinear friction Perform sparse regression: Fixed coefficient vector and The coefficient vector related to the driving torque Perform sparse regression: Fixed coefficient vector and For the displacement-related coefficient vector Perform sparse regression: in, , and Representing the coefficient vectors respectively , and Weights of sparse constraints; After the above stepwise sparse regression process, the final regression model coefficient vector can be obtained. : 。 8. The method for sparse identification of dynamic characteristics of a ball screw feed system according to claim 7, characterized in that: Step 6) describes using sparse regression to determine the coefficients of all dictionary functions and construct a prediction model. First, the regression model coefficient vector... Substituting into the regression model, we obtain the decoupled simplified form of the system difference equation, and finally convert this form of the model into the standard prediction form: 。

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