An online identification method and device for friction model parameters of a servo feeding system

Abstract

The present application belongs to servo feeding system analysis related technical field, it discloses a kind of servo feeding system friction model parameter's on-line identification method and equipment, steps are as follows: (1) increase position related term h (x) on traditional friction model to obtain the friction model of servo feeding system;(2) based on experimental data acquisition servo drive system friction torque under different speed positions Experimental Stribeck curve;(3) the different position x corresponding to experimental data and different speed v are input into friction model, the friction model fitting obtains friction model parameter and fitting Stribeck curve, simultaneously using particle swarm algorithm adjusts friction model parameter, until the friction model parameter that makes the error between experimental Stribeck curve and fitting Stribeck curve minimum is found;(4) using recursive least square method to real-time correction friction model parameter, realize the real-time identification of friction model parameter.The present application improves precision.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of servo feed system analysis, and more particularly, to an online identification method and device for servo feed system friction model parameters. BACKGROUND

[0002] High-precision and high-performance servo feed systems have been one of the main development directions of numerical control machine tools. With the continuous progress of economy and technology, the demand for high-end products has gradually increased, and servo feed systems are playing an increasingly important role in various fields such as aerospace, military, and industry, especially in robots, metallurgy, medical equipment, and other special equipment, which have higher requirements for servo feed systems in terms of precision. Consequently, there is a growing demand for higher precision and higher performance machining equipment. At the same time, high-performance machining equipment cannot be separated from high-performance and high-precision servo feed systems, so the research on high-precision servo feed systems conforms to the trend of the times.

[0003] Numerical control machine tools generally use traditional PID control, which has limited control ability over nonlinear errors in the machine tool, and the servo feed system of the machine tool is easily disturbed by factors such as mechanical clearance, pitch error, friction characteristics, and machine tool vibration in the mechanical transmission link, which has a great impact on the machining precision of the machine tool. Among them, the friction characteristic disturbance, especially the nonlinear friction disturbance, has a great impact on the control precision of the feed system, and may cause crawling and large following error during commutation and startup.

[0004] In view of the influence of friction on the control precision of numerical control machine tools, researchers have used various methods to reduce the influence of friction, such as selecting better lubricants to improve the lubrication level of the two contact surfaces and reduce the difference between dynamic friction and static friction; improving the structure of the machine tool to reduce its transmission link; replacing structures such as air floating guide rails and air floating bearings that have less friction impact to reduce the impact of friction, and various technologies that can improve the surface condition of the contact surface. However, these methods are too costly and complex to operate, and do not take into account the different friction corresponding to different strokes, while existing friction models do not consider the influence of movement stroke on friction, which leads to a low degree of fit between the friction model and the actual situation, and the corresponding precision is not ideal, and the friction problem cannot be fundamentally solved. Therefore, it is necessary to research and establish a servo feed system simulation friction model and corresponding feedforward compensation. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides an online identification method and device for servo feed system friction model parameters, which aims to solve the problem of not considering the influence of movement stroke on friction.

[0006] To achieve the above object, according to one aspect of the present application, there is provided an online identification method of friction model parameters of a servo feeding system, comprising the following steps:

[0007] (1) a position-dependent term h(x) is added to a traditional friction model to obtain a friction model of the servo feeding system;

[0008] (2) an experimental Stribeck curve of friction torque of the servo driving system at different speed positions is obtained based on experimental data;

[0009] (3) different positions x corresponding to the experimental data and different speeds v are input into the friction model, the friction model is fitted to obtain friction model parameters and a fitted Stribeck curve, and a particle swarm algorithm is used to adjust the friction model parameters until the friction model parameters that minimize the error between the experimental Stribeck curve and the fitted Stribeck curve are found;

[0010] (4) a recursive least square method is used to correct the friction model parameters in real time to realize real-time identification of the friction model parameters.

[0011] Further, the expression of the friction model is:

[0012]

[0013] In the formula, F fric represents the total friction force calculated by the model, f C represents the Coulomb friction, sgn(v) represents a sign function of the speed and takes values of +1, -1 or 0, f s represents the sticking friction, v represents the relative speed, v s represents the Stribeck speed, defines the transition speed between the Coulomb friction and the sticking friction, and σ2 represents the viscous friction coefficient, used to represent the linear relationship between the speed and the friction force; h(x) represents the position-dependent term, and x represents the position of the driving shaft.

[0014] Further, experimental data of the servo feeding workbench are collected, a series of stable friction torques of the workbench at the speed positions corresponding to the speed positions are collected from the obtained experimental data, and an experimental Stribeck curve of the friction torque of the servo driving system at different speed positions is obtained.

[0015] Further, the step of correcting the friction model parameters by using the particle swarm algorithm is:

[0016] 5.1 initialize the friction model parameters f C , f s , and v s, σ2, h(x), determine the search space, and initialize the parameter position and velocity;

[0017] 5.2 Set the fitness function, and determine whether the current position of the parameter is optimal;

[0018] 5.3 If the current position of the parameter is better than the best position of the individual, replace the best position of the individual with the current position;

[0019] 5.4 Continuously update the parameter velocity and position;

[0020] 5.5 Repeat steps 5.3 and 5.4, and continuously iterate until the maximum number of iterations or the fitness function reaches the optimal value and no longer decreases, at which time the friction model parameters f C , f s , v s , σ2, h(x) are obtained.

[0021] Further, one of the recursive least squares calculation processes is to obtain the error:

[0022] e(t) = y(t) - φ(t) T θ(t-1),

[0023] In the formula, y(t) is the actual observation value; φ(t) is the input data; θ(t-1) is the model parameter estimation value at the previous moment.

[0024] Further, the gain vector used by the recursive least squares method is updated

[0025]

[0026] Parameter vector update: θ(t) = θ(t-1) + K(t)e(t);

[0027] Where λ is the forgetting factor, which is used to balance the influence of historical data and new data, and ranges from 0 to 1, and P(t-1) is the initial value of the covariance matrix P(t-1) at the previous moment.

[0028] Further, the correction step of the friction model parameters is:

[0029] 6.1. The servo drive system at a certain working speed v and running distance x, the identified friction parameters f C , f s , v s , σ2, h(x) are used as the original parameters of the friction equation;

[0030] 6.2. Real-time acquisition of the speed v and running distance x of the servo drive system using displacement sensors and speed sensors, and substituting v, x into the friction model to obtain the model friction torque prediction value F1;

[0031] 6.3 Directly obtain the friction torque F2 of the current servo drive system by using the torque sensor, calculate the error e(t) by RLS, calculate the gain vector, and update f C , f s , v s , sigma2 and h(x).

[0032] 6.4 Repeat steps 6.2 and 6.3 repeatedly, and continuously update f C , f s , v s , sigma2 and h(x).

[0033] Further, the real-time correction of the friction model parameters by using the recursive least square method further includes a step of reducing the length of the friction torque data used by the recursive least square method, specifically: a servo control system model is established in Simulink; then, friction torque signals of different lengths are set, and the residual sum of squares (Fmodel-Fmeasure) ^2 of the servo control system model output Fmodel and the experimentally measured value Fmeasure under different signal lengths is recorded.

[0034] The application further provides an online identification system for friction model parameters of a servo feeding system, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the online identification method for friction model parameters of the servo feeding system as described above.

[0035] The application further provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions, when called and executed by a processor, cause the processor to implement the online identification method for friction model parameters of the servo feeding system as described above.

[0036] Overall, compared with the prior art, the online identification method for friction model parameters of the servo feeding system and the device provided by the application mainly have the following advantages

[0037] Beneficial effects:

[0038] 1. The application adds a position-dependent term to the traditional model, which considers the feeding position and positive and negative directions of the drive shaft, describes the nonlinear friction behavior of the mechanical shaft in long travel, realizes long-term correction of the friction model, improves accuracy, and is further conducive to better reducing the influence of friction on the control accuracy of the numerical control machine tool, and avoids the influence caused by the position-dependent friction caused by manufacturing errors, misalignment and environment, which is ignored by the traditional friction model.

[0039] 2. Using recursive least square method to update friction model parameters adaptively, using real-time collected data to enhance the adaptability of friction model under different operating and environmental conditions, realizing online identification and update of friction model parameters.

[0040] 3. Limiting the data length used by RLS, realizing updating friction model parameters with less real-time friction torque data, reducing the size of matrix calculation by reducing input data points, improving the running efficiency of RLS algorithm, reducing the time cost of data processing, and being suitable for implementation in real-time system. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is a flow chart of an online identification method of friction model parameters of a servo feeding system provided by the present application;

[0042] Figure 2 is a schematic diagram of a feeding system Simulink simulation model;

[0043] Figure 3 is a schematic diagram of a three-loop control structure of a feeding system;

[0044] Figure 4 is a particle swarm algorithm identification flow chart. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0046] Friction has a great influence on the control accuracy of servo feeding system. Considering the influence of different working conditions and environmental conditions on the physical system during actual operation, it may lead to changes in system performance, resulting in failure of compensation based on friction model, especially in long-stroke and ball screw machines, the position dependence caused by spindle pitch error and assembly tolerance cannot be ignored. In order to make the friction model accurately reflect the physical entity, the present application adds a position related term to the traditional model, which considers the feeding position and positive and negative direction of the driving shaft, and RLS (recursive least square method) can update the friction parameters according to the current small amount of friction torque.

[0047] Please refer to Figure 1 , Figure 2 , Figure 3 and Figure 4The online identification method for friction model parameters of a servo feeding system provided by the application mainly comprises the following steps.

[0048] Step one, a position-related term h(x) is added to the traditional friction model to obtain the friction model of the servo feeding system.

[0049]

[0050] The position-related term h(x) considers the feeding position and positive and negative directions of the driving shaft.

[0051] The expression of the friction model is as follows:

[0052]

[0053] In the formula, F fric represents the total friction force calculated by the model, f C represents the Coulomb friction force, sgn(v) represents the sign function of the speed, and takes the value of +1 (positive direction movement), -1 (negative direction movement) or 0 (static), f s represents the sticking friction force, v represents the relative speed, v s represents the Stribeck speed, defines the transition speed between the Coulomb friction and the sticking friction, and σ2 represents the viscous friction coefficient, which is used to represent the linear relationship between the speed and the friction force. h(x) represents the position-related term, x represents the position of the driving shaft, which is the input variable of the position-related term, and the function h(x) has no fixed expression and is used to describe the nonlinear behavior of the friction force related to the position and direction of the driving shaft.

[0054] Step two, the experimental Stribeck curve of the friction torque of the servo driving system at different speed positions is obtained based on the experimental data.

[0055] The experimental data of the servo feeding workbench are collected, a series of friction torques of the workbench at the speed positions corresponding to the speed positions from low speed to high speed are collected, the stable friction torques corresponding to the uniform speed sections are extracted from the obtained experimental data, and the Stribeck curve of the friction torque of the servo driving system at different speed positions is obtained.

[0056] Step three, the different positions x and different speeds v corresponding to the experimental data are input into the friction model, the friction model fitting is performed to obtain the friction model parameters and the fitting Stribeck curve, and the particle swarm algorithm is used to adjust the friction model parameters until the friction model parameters that make the error between the experimental Stribeck curve and the fitting Stribeck curve minimum are found.

[0057] After the Stribeck curve of the friction torque of the servo driving system at different speed positions is obtained, the friction model Because of the input of different position x, with different speed v, will get different friction torque F fric，ss Data, using heuristic algorithm-particle swarm algorithm, constantly f C , f s , v s , σ2, h(x) and other parameters are adjusted, so that the formula e stat =(F sr(v) -F fric，ss ) 2 Error is minimum, F sr(v) is obtained by experiment Stribeck curve, F fric，ss is the fitting Stribeck curve, when the error e stat is minimum, get f C , f s , v s , σ2, h(x) and other parameters.

[0058] The steps of using particle swarm algorithm to correct the friction model parameters are:

[0059] 5.1 initialization of friction model parameters f C , f s , v s , σ2, h(x), determine the appropriate search space, and initialize the parameter position and speed.

[0060] 5.2 set the appropriate fitness function, and judge whether the current position of the parameters is optimal.

[0061] 5.3 if the current position of the parameters is better than the best position of the individual, replace the best position of the individual with the current position.

[0062] 5.4 constantly update the parameter speed and position.

[0063] 5.5 repeat step 5.3 and 5.4, constantly iterate, until the maximum iteration times or the fitness function reaches the optimal and no longer smaller, at this time get f C , f s , v s , σ2, h(x) and other friction parameters.

[0064] Step four, using recursive least squares method to correct the friction model parameters in real time, realize the real-time identification of friction model parameters.

[0065] RLS(recursive least square) is used to modify the friction parameters constantly, and realize the real-time identification of friction parameters. RLS is an online real-time updating algorithm, which is used to estimate the friction model parameters recursively through the new data input step by step, so as to minimize the sum of squares of errors between the model output and the actual observation value. RLS can efficiently process real-time data, and is suitable for parameter identification and adaptive control of dynamic systems.

[0066] The core calculation process of RLS is to obtain the error:

[0067] e(t)=y(t)-φ(t) T θ(t-1),

[0068] In the formula, y(t) is the actual observation value; φ(t) is the input data (regression vector); θ(t-1) is the model parameter estimation value at the last moment.

[0069]

[0070] Parameter vector update: θ(t)=θ(t-1)+K(t)e(t)

[0071] Where λ is the forgetting factor, which is used to balance the influence of historical data and new data, and the range is 0 to 1. P(t-1) is the initial value of the covariance matrix P(t-1) at the last moment, which is generally set as a diagonal matrix, and all diagonal elements are a large positive number.

[0072] The modification steps of the friction model parameters are as follows:

[0073] 6.1. The identified friction parameters f C , f s , v s , σ2, h(x) are used as the original parameters of the friction equation.

[0074] 6.2. The speed v and running distance x of the servo drive system are collected in real time by the displacement sensor and the speed sensor, and v and x are substituted into the friction model to obtain the model friction torque prediction value F1.

[0075] 6.3. The friction torque F2 of the current servo drive system is directly obtained by the torque sensor, the error e(t) is calculated by RLS, the gain vector is calculated, and the parameters f C , f s , v s , σ2, h(x) are updated.

[0076] 6.4. Repeat steps 6.2 and 6.3 to constantly update the parameters f C , f s , v s, σ2, h(x).

[0077] In this step, the length of the friction torque data used by the RLS is also reduced to improve the efficiency and speed of online identification. The specific operation is as follows:

[0078] 7.1 By analyzing the system composition of the experimental workbench, the control system and the mechanical transmission system are simplified, and a servo control system model is established in Simulink. Because Simulink simulation can run various experiments in a virtual environment, the experimental cost is reduced.

[0079] 7.2 By setting friction torque signals of different lengths, the residual sum of squares (Fmodel-Fmeasure) of the servo control system model output Fmodel and the experimental measurement value Fmeasure under different signal lengths is recorded. ^2 When the residual error tends to be stable, the input signal length at this time is selected.

[0080] The application further provides an online identification system for friction model parameters of a servo feeding system, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the online identification method for friction model parameters of the servo feeding system as described above.

[0081] The application further provides a computer readable storage medium, which stores machine executable instructions, and the machine executable instructions, when called and executed by a processor, cause the processor to implement the online identification method for friction model parameters of the servo feeding system as described above.

[0082] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the application, and is not intended to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. An online identification method for friction model parameters of a servo feed system, characterized in that, The identification method includes the following steps: (1) A position-dependent term h(x) was added to the traditional friction model to obtain the friction model of the servo feed system; (2) Based on experimental data, the experimental Stribeck curves of the friction torque of the servo drive system at different speed positions were obtained; (3) Input the different positions x and different velocities v corresponding to the experimental data into the friction model. The friction model is fitted to obtain the friction model parameters and the fitted Stribeck curve. At the same time, the particle swarm algorithm is used to adjust the friction model parameters until the friction model parameters that minimize the error between the experimental Stribeck curve and the fitted Stribeck curve are found. (4) The recursive least squares method is used to correct the friction model parameters in real time, so as to realize the real-time identification of the friction model parameters; The expression for the friction model is: In the formula, This represents the total friction force calculated by the model. Represents Coulomb friction. The sign function representing velocity, taking values ​​of +1, -1, or 0. This represents adhesive friction. Represents relative velocity. The Stribek velocity is defined as the transition velocity between Coulomb friction and adhesive friction. It represents the coefficient of viscous friction, used to express the linear relationship between velocity and frictional force; Indicates location-related items, Indicates the position of the drive shaft; Experimental data were collected on the servo feed table, and the friction torque of the table at a series of speed positions was collected. The stable friction torque corresponding to the uniform speed segment was extracted from the obtained experimental data, and the experimental Stribeck curves of the friction torque of the servo drive system at different speed positions were obtained.

2. The online identification method for friction model parameters of a servo feed system as described in claim 1, characterized in that: The steps for correcting the friction model parameters using the particle swarm optimization algorithm are as follows: 5.1 Initialize friction model parameters , , , , Define the search space and initialize the parameters position and velocity; 5.2 Set the fitness function and use it to determine whether the parameter is at its optimal position; 5.3 If the current position of the parameter is better than the individual's best position, then replace the individual's best position with the current position; 5.4 Continuously update parameters speed and position; 5.5 Repeat steps 5.3 and 5.4, iterating continuously until the maximum number of iterations or the fitness function reaches its optimum and no longer decreases. At this point, the friction model parameters are obtained. , , , , .

3. The online identification method for friction model parameters of a servo feed system as described in claim 1, characterized in that: One step in the recursive least squares calculation process is to obtain the error: In the formula, These are actual observed values; Input data; These are the estimated values ​​of the model parameters from the previous time step.

4. The online identification method for friction model parameters of a servo feed system as described in claim 3, characterized in that: Gain vector update using recursive least squares method , Parameter vector update: ; in It is the forgetting factor, which is used to weigh the impact of historical data and new data. It ranges from 0 to 1. P(t-1) is the initial value of the covariance matrix P(t-1) of the previous moment.

5. The online identification method for friction model parameters of a servo feed system as described in claim 4, characterized in that: The steps for correcting the friction model parameters are as follows: 6.

1. At a certain operating speed v and running distance x, the servo drive system will identify the friction parameters. , , , , As the original parameters of the friction equation; 6.

2. The speed v and running distance x of the servo transmission system are collected in real time using displacement and velocity sensors. V and x are substituted into the friction model to obtain the predicted friction torque value F1 of the model. 6.3 The frictional torque F2 of the current servo drive system is directly obtained using a torque sensor, and the error is calculated using RLS. Calculate the gain vector, and then... , , , , Update; 6.4 Repeat steps 6.2 and 6.3 repeatedly, continuously updating the parameters. , , , , .

6. The online identification method for friction model parameters of a servo feed system as described in claim 1, characterized in that: The real-time correction of friction model parameters using the recursive least squares method also includes a step of reducing the length of friction torque data used in the recursive least squares method. Specifically, a servo control system model is built in Simulink; then, by setting friction torque signals of different time lengths, the sum of squared residuals (Fmodel - Fmeasure) of the servo control system model output Fmodel and the experimental measurement value Fmeasure under different signal lengths is recorded. ^2 When the residuals tend to stabilize, select the length of the friction torque data at this point.

7. An online identification system for friction model parameters of a servo feed system, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the online identification method for friction model parameters of the servo feed system according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the online identification method for friction model parameters of the servo feed system according to any one of claims 1-6.

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