Method and device for predicting actual position of feeding system
By constructing the main response model and residual response model of the feed system and using convolution operation to make up for the difference, the problems of insufficient prediction accuracy and generalization of the feed system in the existing technology are solved, and high-precision and high-generalization actual position prediction of the feed system is achieved.
Patent Information
- Application Number
- CN202510871874.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-26
- Publication Date
- 2025-09-26
Smart Images
Figure CN120704141A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field related to numerical control, and more specifically, relates to a method and device for predicting the actual position of a feed system. Background Art
[0002] In recent years, digital twin technology for CNC machine tools has gradually become a key technology for intelligent manufacturing. Digital twins of CNC machine tools include functions such as virtual machining, collision warning, and trajectory planning. In practical applications, these functions all rely on accurately predicting the actual position of the feed system. To achieve the prediction of the actual position of the feed system, it is necessary to establish a dynamic model of the feed system. Currently, common dynamic models in engineering are divided into two categories: mathematical models and data-driven models. However, both types of models have obvious shortcomings:
[0003] While mathematical models offer robustness, their ability to describe nonlinearities is weak. When the feed system is operating under conditions with high nonlinear friction, such as during startup and reverse, the model's prediction accuracy is poor. Data-driven models, which utilize algorithms such as neural networks, offer excellent nonlinear description capabilities, but their generalization capabilities are poor. When the model predicts data outside the training set, the prediction error is large.
[0004] Therefore, the existing dynamic model of the feed system has defects in prediction accuracy and generalization, and cannot provide high-precision feed system predicted position data to meet the application of digital twins of CNC machine tools. Summary of the Invention
[0005] To address the aforementioned shortcomings or improvements in the prior art, the present invention provides a method and apparatus for predicting the actual position of a feed system. This method aims to accurately predict the actual position by predicting both linear and nonlinear outputs using convolution operations, thereby addressing the shortcomings of prior art feed system dynamic models in terms of prediction accuracy and generalizability.
[0006] To achieve the above object, according to a first aspect of the present invention, a method for predicting the actual position of a feed system is provided, comprising the following steps:
[0007] Obtaining an input of a feed system and an impulse response of the feed system; geometrically scaling the impulse response of the feed system to obtain a unit impulse response of the feed system; and then substituting the input of the feed system and the unit impulse response of the feed system into a convolution operation to obtain a predicted output of a main response model of the feed system;
[0008] Acquiring operational information of the feed system, and calculating and identifying a nonlinear factor based on the operational information of the feed system; measuring an error between an actual position of the feed system and a predicted output of a main response model of the feed system, and obtaining a unit impulse response of the nonlinear factor based on the error and the nonlinear factor; and then substituting the nonlinear factor and the unit impulse response of the nonlinear factor into a convolution operation to obtain a predicted output of a residual response model of the feed system;
[0009] The predicted output of the main response of the feed system and the predicted output of the residual response of the feed system are added together to obtain the prediction of the actual position of the feed system.
[0010] As a further preference, the nonlinear factor includes at least one of friction, thermal deformation, elastic deformation, thrust fluctuation and cogging effect.
[0011] As a further preference, the input of the feed system and the unit impulse response of the feed system are substituted into a convolution operation to obtain a predicted output of the main response model of the feed system. The calculation formula of the predicted output of the main response model of the feed system is:
[0012]
[0013] Where y1 is the predicted output of the main response of the feed system, h is the unit impulse response, P1 is the length of h, u is the input of the feed system, k is the index of the input and output, and m is the index of the convolution kernel.
[0014] As a further preference, the impulse response of the feed system is geometrically scaled to obtain the unit impulse response of the feed system. The calculation formula for the unit impulse response of the feed system is:
[0015]
[0016] Where h is the unit impulse response, h a is the impulse response of the feed system, u a is the amplitude u a The system input is , i is the vector index.
[0017] As a further preference, the nonlinear factor and the unit impulse response of the nonlinear factor are substituted into the convolution operation to obtain the predicted output of the feed system residual response model. The calculation formula of the predicted output of the feed system residual response model is:
[0018]
[0019] Where, e1 is the predicted output of the residual response of the feed system, h Nis the unit impulse response of the nonlinear factor, P2 is the unit impulse response length of the nonlinear factor, N is the nonlinear factor, k is the input and output index, and m is the index of the convolution kernel.
[0020] As a further preference, in the unit impulse response of the nonlinear factor obtained by identifying the error and the nonlinear factor, the identification method includes polynomial fitting or least squares method.
[0021] As a further preference, when the nonlinear factor is friction, the operation information includes a speed signal and a current signal;
[0022] The Coulomb friction force, the maximum static friction force and the Stribeck speed of the friction force are obtained based on the speed signal and the current signal of the feed system, and the friction force is calculated by adopting the Stribeck friction model;
[0023] The calculation formula of the Stribeck friction force F(v) is:
[0024] F(v)=F c +(F s -F c )exp(-(v / v s ) 2 )
[0025] Where, F c is the Coulomb friction force, F s is the maximum static friction, v s is the Stribeck speed, and v is the speed of the feed system.
[0026] As a further preference, the unit impulse response of the friction force is obtained by identifying the least square method, and the calculation formula of the unit impulse response of the friction force is:
[0027] h F =(F T F) -1 F T e act
[0028] Where h F is the unit impulse response of friction force, F is friction force, T is the inverse sign, e act It is the error between the actual position of the measured feed system and the predicted output of the feed system main response model.
[0029] According to a second aspect of the present invention, a system for predicting the actual position of a feed system is provided, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the method for predicting the actual position of the feed system as described above when executing the computer program.
[0030] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method for predicting the actual position of the feed system as described above.
[0031] In general, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
[0032] 1. The present invention predicts the system response generated by the excitation signal of a single cycle of the feed system through convolution operation to predict the linear output and nonlinear output to obtain the prediction of the actual position, wherein the residual response model is used to compensate for the actual position of the feed system, which simplifies the modeling process and improves the accuracy and generalization of the prediction of the actual position of the feed system.
[0033] 2. The present invention preferably obtains the unit impulse response of the nonlinear factor by means of error and nonlinear factor identification, can successfully apply the convolution operation to the output prediction of the nonlinear system, and effectively apply the generalization advantage of the impulse response model to nonlinear prediction.
[0034] 3. For different types of feed systems, the present invention can identify the nonlinear unit impulse responses of other nonlinear factors other than linear components, including at least one of friction, thermal deformation, elastic deformation, thrust fluctuation and cogging effect, in accordance with the method provided by the present invention, and then apply them to the output prediction of the nonlinear system through convolution operation. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 The flowchart of the actual position prediction method of the feeding system provided by the embodiment of the present invention is exemplified.
[0036] Figure 2 It is an excitation signal used to obtain the unit impulse response in the main response prediction output of the feeding system according to an example of the present invention.
[0037] Figure 3 This is the unit impulse response in the main response prediction output of the feed system obtained by acquisition according to the example of the present invention.
[0038] Figure 4 is the prediction error of the feed system of the present invention; Figure 4(a) is the command speed diagram of the feed system, and (b) is the prediction error of the main response model.
[0039] Figure 5 It is the friction unit impulse response of the residual response model calculated by the least square method according to the example of the present invention.
[0040] Figure 6 is the instruction position of Case 1 of the present invention and the prediction error thereof using this method; wherein, Figure 6 (a) is the command position diagram of the feed system, and (b) is the prediction error.
[0041] Figure 7 is the instruction position of Case 1 of the present invention and the prediction error thereof using this method; wherein, Figure 7 (a) is the command position diagram of the feed system, and (b) is the prediction error.
[0042] Figure 8 is the instruction position of Case 1 of the present invention and the prediction error thereof using this method; wherein, Figure 8 (a) is the command position diagram of the feed system, and (b) is the prediction error. DETAILED DESCRIPTION
[0043] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
[0044] The present invention provides a method for predicting the actual position of a feed system. Existing methods for predicting the actual position of a feed system rely on mathematical models or data-driven models of the feed system, but these methods cannot simultaneously meet both good prediction accuracy and good generalization capabilities under nonlinear working conditions. Therefore, existing methods cannot meet the prediction accuracy requirements of the digital twin technology of CNC machine tools for the actual position of the feed system. In view of this, the present invention converts the modeling object of the feed system into the system response generated by a single-cycle excitation signal, and achieves high-precision prediction of the actual position of the feed system through convolution operations. Referring to the above principles, the present invention separately constructs a main response model and a residual response model of the feed system, and uses the residual response model to compensate for the feed system. The residual response model successfully applies the convolution operation to the calculation of nonlinear systems, ensuring generalization while achieving high-precision prediction of the actual position of the feed system. Experiments have shown that the present method not only has higher prediction accuracy, but also has excellent generalization.
[0045] Specifically, for a linear time-invariant system, its input and output satisfy the linear convolution relationship described by the following equation. Except for friction error and thermal error, the predicted output of the main response of the feed system involved in the present invention is obtained by convolution operation, and the convolution relationship is as follows:
[0046]
[0047] Where y is the predicted output, h is the unit impulse response, u is the input, k is the index of the input and output, and m is the index of the convolution kernel.
[0048] See also Figure 1 , the prediction method mainly includes the following steps:
[0049] (1) The predicted output of the main response of the feed system is:
[0050] The input of the feed system and the impulse response of the feed system are obtained; the impulse response of the feed system is geometrically scaled to obtain the unit impulse response of the feed system; and then, the input of the feed system and the unit impulse response of the feed system are substituted into the convolution operation to obtain the predicted output of the main response model of the feed system.
[0051] The convolution operation here is a linear convolution operation, generally applied to linear systems. Although the feed system is not a fully linear system, its main components, excluding friction and thermal errors, still satisfy linear relationships. Therefore, based on this principle, the feed system is calculated using a convolution operation. In other words, given the feed system input, the position prediction of the feed system output can be achieved simply by knowing its unit impulse response. Therefore, after obtaining the modeling object of the feed system, it is first converted into a unit impulse response h, and then a convolution operation is performed to obtain the predicted output of the feed system's main response.
[0052] The impulse response of the feed system is scaled geometrically to obtain the unit impulse response of the feed system. Specifically, Figure 2 As shown, a magnitude u is input to the feed system. a Pulse signal, collect the pulse response h of the feed system a The actual output of the feed system is measured by a linear scale and acquired using dedicated sampling software. The unit impulse response h of the feed system is calculated using the following formula. Figure 3 The obtained unit impulse response h is shown.
[0053]
[0054] Where h a is the impulse response of the feed system, h is the unit impulse response, u ais the amplitude u a The system input is , i is the vector index.
[0055] Depend on Figure 3 It can be seen that the impulse response of the feed system does not continue forever. When the impulse response decays to a negligible level, it is considered that the impulse response has stopped. If the impulse response lasts for P1 cycles at this time, then the impulse response is a finite impulse response with a length of P1. Under the premise of knowing the input u of the feed system, combined with the unit impulse response h, the predicted output of the main response of the feed system can be realized according to the convolution operation. In the predicted output of the main response of the feed system obtained by the convolution operation, the calculation formula in the convolution operation is:
[0056]
[0057] Where y1 is the predicted output of the main response model of the feed system, h is the unit impulse response, P1 is the length of h, u is the input of the feed system, k is the index of the input and output, and m is the index of the convolution kernel.
[0058] (2) Prediction output of the residual response of the feed system, specifically: obtaining the operating information of the feed system, and calculating and identifying the parameters of the nonlinear factor based on the operating information of the feed system; measuring the error between the actual position of the feed system and the predicted output of the main response model of the feed system, and obtaining the unit impulse response of the nonlinear factor based on the error and the parameter identification of the nonlinear factor; then, substituting the parameters of the nonlinear factor and the unit impulse response of the nonlinear factor into the convolution operation to obtain the predicted output of the residual response model of the feed system;
[0059] In the above steps, the output of the feed system is predicted by convolution operation based on the impulse response h of the feed system. However, since the feed system is not a completely linear system, the position of the feed system obtained by the above prediction must have errors. These errors are expressed as e act , which is calculated by the following formula, where y act is the actual position of the feed system.
[0060] e act [i]=y act [i]-y1[i],i>0
[0061] Where, e act is the error between the actual position of the feed system measured and the predicted output of the feed system main response model, y act is the measured actual position of the feed system, and y1 is the predicted output of the main response of the feed system.
[0062] For example, Figure 4The position prediction effect of the feed system mentioned above was demonstrated, and it was found that there was still a prediction error of about 6 microns. Therefore, a residual response output was constructed in the prediction of the actual position of the feed system as a supplement to the main response prediction output of the feed system. Considering that these residual response outputs are mainly system responses caused by nonlinear factors, and these nonlinear factors are difficult to directly apply convolution operations, after obtaining the operating information of the feed system, different nonlinear factors (i.e., residual response models) were identified. At the same time, the unit impulse response of the nonlinear factor was obtained by calculating the unit impulse response of the nonlinear factor based on the error and nonlinear factor identification, and then the nonlinear factor and the unit impulse response of the nonlinear factor were predicted through convolution operations. Among them, the nonlinear factors include at least one of friction, thermal deformation, elastic deformation, thrust fluctuation, cogging effect, etc.
[0063] Therefore, the convolution relationship in the predicted output of the feed system residual response model is as follows
[0064]
[0065] Where, e1 is the predicted output of the residual response of the feed system, h N is the unit impulse response of the nonlinear factor, P2 is the unit impulse response length of the nonlinear factor, N is the nonlinear factor, k is the input and output index, and m is the index of the convolution kernel.
[0066] (3) Prediction of the actual position of the feed system, including adding the predicted output of the feed system main response and the predicted output of the feed system residual response obtained above, which is the prediction of the actual position of the feed system.
[0067] At this point, given the known system input and system operation information, the residual of the main response model can be predicted through convolution operation. Finally, the prediction of the actual position of the feed system can be obtained as follows:
[0068] y=y1+e1
[0069] In some embodiments, it is considered that these residual response outputs are mainly system responses caused by nonlinear factors, and nonlinear factors include, for example, friction, thermal deformation, elastic deformation, thrust fluctuation, cogging effect, etc., and the nonlinear factors in different feed systems have different emphases. For example, the nonlinear factors in the ball screw feed system are mainly caused by friction, and the nonlinear factors in the linear motor feed system are mainly caused by thrust fluctuation. Therefore, in the prediction method of the actual position of the feed system of the present invention, the predicted output of the residual response of the feed system is different.
[0070] For example, in a ball screw feed system, when the machine tool is in thermal steady-state conditions, considering that these residuals are mainly caused by friction, and drawing on the convolution law of linear systems, these residuals are considered to be the system response caused by friction. Therefore, referring to the aforementioned convolution relationship, the output e1 of the residual response model caused by friction can be predicted by the following formula:
[0071]
[0072] Where h F is the unit impulse response of friction, P2 is the length of the unit impulse response of friction, and F is the friction force.
[0073] In the prediction output of the feed system residual response model, the friction force is calculated using the Stribeck friction model. The calculation formula of the Stribeck friction force F(v) is as follows:
[0074] F(v)=F c +(F s -F c )exp(-(v / v s ) 2 )
[0075] Where, F c is the Coulomb friction force, F s is the maximum static friction, v s is the Stribeck velocity and v is the velocity.
[0076] F in the formula c 、F s and v s The parameters calculated by the three Stribeck friction models are obtained by identifying the operating information of the feed system. Specifically, after obtaining the operating information of the feed system, the speed signal and current signal in the operating information are identified to obtain F c 、F s and v s These three parameters are calculated using the Stribeck friction model. Since Stribeck friction is widely used in engineering, the specific identification methods for friction parameters will not be detailed here. Similarly, other nonlinear parameters, such as thermal deformation, have well-established identification methods in industry.
[0077] Here we only introduce the friction pulse response h F The identification methods include polynomial fitting or least squares method. The following introduces a method for identifying the three key parameters of friction force using the least squares method. The specific method is as follows:
[0078] First, the formula It can be converted into matrix form and then simplified to: e1=Ph F ;
[0079] Among them, the dimension of vector e1 is (R,1), the dimension of matrix F is (R,P2), and the dimension of vector h F The dimension is (P2,1). If R is greater than P2, and e1 and F are both known, use the least squares method to calculate h F The optimal solution of the least squares method is shown in the following formula.
[0080] h F =(F T F) -1 FTe act
[0081] Where h F is the unit impulse response of friction force, F is the friction force, T is the inverse, e act It is the error between the actual position of the feed system measured and the predicted output of the feed system main response model.
[0082] Synchronous, this method was experimentally verified on an actual machine tool. Figure 5 is the friction pulse response of the machine tool X-axis. Figure 6-8 Three test cases and prediction results are shown. The prediction results demonstrate that the proposed method for predicting the actual position of the feed system has good prediction accuracy, achieving accuracy within 5 microns. The consistent level of prediction error across multiple test cases also demonstrates the method's good generalizability.
[0083] For example, when the feed system is a servo motor, since the servo motor has a relatively significant cogging effect, these residuals in the system are mainly caused by the combination of friction and cogging torque. Drawing on the convolution law of linear systems, these residuals are considered to be the system response caused by friction and cogging torque. Therefore, referring to the aforementioned convolution relationship, the output e1 of the residual response model caused by friction and cogging torque can be predicted by the following formula: The error e1 can be predicted by the following formula:
[0084]
[0085] Where h N is the unit impulse response generated by the friction force and the cogging torque, P2 is the length of the friction unit impulse response, and N is the nonlinear force composed of the friction force and the cogging torque.
[0086] Among them, N is the nonlinear force composed of friction and cogging torque, which is obtained by identification based on current, speed, position and other data. The specific method is relatively mature in this field and will not be repeated here.
[0087] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, to the extent such modifications and variations fall within the scope of the present invention and its equivalents, the present invention is intended to encompass such modifications and variations. The above-described embodiments are merely preferred embodiments for the purpose of fully illustrating the present invention and are not intended to limit the scope of protection. Any equivalent substitutions or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention.
Claims
1. A method for predicting the actual position of a feed system, characterized in that: The steps include: Obtaining an input of a feed system and an impulse response of the feed system; and obtaining a unit impulse response of the feed system by geometrically scaling the impulse response of the feed system; Then, the input of the feed system and the unit impulse response of the feed system are substituted into a convolution operation to obtain a predicted output of a main response model of the feed system; Acquiring operational information of the feed system, and calculating and identifying a nonlinear factor based on the operational information of the feed system; measuring an error between an actual position of the feed system and a predicted output of a main response model of the feed system, and obtaining a unit impulse response of the nonlinear factor based on the error and the nonlinear factor; Then, the nonlinear factor and the unit impulse response of the nonlinear factor are substituted into a convolution operation to obtain a predicted output of a residual response model of the feed system; The predicted output of the main response of the feed system and the predicted output of the residual response of the feed system are added together to obtain the prediction of the actual position of the feed system.
2. The method for predicting the actual position of a feed system according to claim 1, characterized in that: The nonlinear factor includes at least one of friction, thermal deformation, elastic deformation, thrust fluctuation and cogging effect.
3. The method for predicting the actual position of a feeding system according to claim 1, characterized in that: Substituting the input of the feed system and the unit impulse response of the feed system into the convolution operation, the predicted output of the main response model of the feed system is obtained. The calculation formula of the predicted output of the main response model of the feed system is: Where y1 is the predicted output of the main response of the feed system, h is the unit impulse response, P1 is the length of h, u is the input of the feed system, k is the index of the input and output, and m is the index of the convolution kernel.
4. The method for predicting the actual position of a feeding system according to claim 1, characterized in that: The impulse response of the feed system is geometrically scaled to obtain the unit impulse response of the feed system. The calculation formula for the unit impulse response of the feed system is: Where h is the unit impulse response, h a is the impulse response of the feed system, u a is the amplitude u a The system input is , i is the vector index.
5. The method for predicting the actual position of a feeding system according to claim 1, characterized in that: Substituting the nonlinear factor and the unit impulse response of the nonlinear factor into the convolution operation to obtain the predicted output of the feed system residual response model, the calculation formula of the predicted output of the feed system residual response model is: Where, e1 is the predicted output of the residual response of the feed system, h N is the unit impulse response of the nonlinear factor, P2 is the unit impulse response length of the nonlinear factor, N is the nonlinear factor, k is the input and output index, and m is the index of the convolution kernel.
6. The method for predicting the actual position of a feeding system according to claim 1, characterized in that: In the unit impulse response of the nonlinear factor obtained by identifying the error and the nonlinear factor, the identification method includes polynomial fitting or least square method.
7. The method for predicting the actual position of a feeding system according to claim 2, characterized in that: When the nonlinear factor is friction, the operation information includes a speed signal and a current signal; The Coulomb friction force, the maximum static friction force and the Stribeck speed of the friction force are obtained based on the speed signal and the current signal of the feed system, and the friction force is calculated by adopting the Stribeck friction model; The calculation formula of the Stribeck friction force F(v) is: F(v)=F c +(F s -F c )exp(-(v / ν s ) 2 ) Where, F c is the Coulomb friction force, F s is the maximum static friction, v s is the Stribeck speed, and v is the speed of the feed system.
8. The method for predicting the actual position of a feeding system according to claim 7, characterized in that: The unit impulse response of the friction force is obtained by the least squares method, and the calculation formula of the unit impulse response of the friction force is: h F =(F T F) -1 F T e act Where h F is the unit impulse response of friction force, F is friction force, T is inverse, e act It is the error between the measured actual position of the feed system and the predicted output of the feed system main response model.
9. A system for predicting the actual position of a feed system, characterized in that: The system includes a memory and a processor, the memory stores a computer program, and the processor executes the method for predicting the actual position of the feeding system according to any one of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the method for predicting the actual position of the feeding system according to any one of claims 1 to 8.